{"chunkIndex": 0, "stories": [{"id": "f400ad2ec3bd", "title": "self-attention: Attention(Q,K,V) = softmax(QK^T/\u221ad_k)V", "slug": "self-attention-attention-q-k-v-softmax-qk-t-d-k-v", "headline": "Ever wondered how computers understand what's important in a sentence?", "summary": "Write the equation for self-attention: Attention(Q,K,V) = softmax(QK^T/\u221ad_k)V", "source": "Write the equation for self-attention: Attention(Q,K,V) = softmax(QK^T/\u221ad_k)V", "sourceUrl": "https://en.wikipedia.org/wiki/Attention_(machine_learning)", "articleUrl": "https://en.wikipedia.org/wiki/Attention_(machine_learning)", "publishedAt": "2026-07-03", "category": "learn", "cohortScore": 0.5, "embedding": [-9, -1, 3, -8, 1, -2, 10, 0, 7, -5, 6, -4, 6, 2, 10, 5, -1, -2, -6, -3, 12, -7, -3, -2, 0, -2, 3, 0, 1, -21, -4, 3, 10, 0, -4, 0, -3, -6, -5, 1, 2, 3, 1, 4, -2, -8, -5, -10, -3, -4, -4, 2, -3, 2, 8, 1, 2, 3, 3, -8, 9, 5, -14, 3, 3, 5, -7, -5, -6, 14, -2, 0, 0, 4, 3, 2, -1, 0, 7, -2, 2, 2, -6, -2, -1, 1, 1, 2, 8, -3, -7, -3, -2, -9, 1, -3, -5, -1, -4, 43, 5, -5, -3, -6, 5, -11, 3, -6, -4, 0, -6, -7, 2, -3, 2, -1, 10, 6, 5, -8, -3, 3, 0, -8, 6, -2, -3, 14, -1, 2, 8, -4, -3, 1, -4, -4, 3, 0, 1, -1, 0, 1, 4, -2, -8, 16, -4, -6, 0, -2, 4, -3, 2, -9, 0, 2, 3, -6, -7, -5, -5, -2, -9, 14, 1, 1, 5, 0, 0, -5, 5, -1, -6, 7, 6, -1, -3, 7, -2, 3, 0, -4, -5, 4, 3, -2, 3, -2, 3, 3, 4, 2, 0, 1, -11, 2, 2, -1, -7, -1, -6, -2, -4, -3, 5, 2, 4, 4, 10, 2, -6, -3, 1, -2, -7, -4, -3, 6, 3, 1, -3, -9, -11, -39, -7, 4, -4, 6, -2, 9, 1, 4, 7, 14, -1, -1, -12, 2, -1, -3, 7, -6, 0, 3, 2, 6, -3, -7, 0, 18, 1, 7, 7, 1, -1, -6, -7, 0, -3, 0, 6, -8, 1, -5, -4, -5, -1, -6, -1, 3, 2, -4, 9, 4, -4, 1, 0, 1, -5, -7, -5, -10, 1, -2, -4, -2, -2, -3, -1, 6, 5, 5, 3, -7, 10, 2, -1, 10, -1, 7, 6, 1, -3, 6, 1, 3, -3, 7, 2, 8, -1, -1, 5, -11, -2, 6, -3, 2, -1, -38, 5, 0, 1, 2, 3, 8, -6, -6, 3, -8, 8, -4, 0, -4, -2, 4, -1, 6, -2, 6, 3, 22, -2, 9, -6, -3, -2, 7, -2, 0, 0, 12, 3, 4, 3, -7, 4, 10, 10, 4, 0, -2, -3, 13, 7, 3, -12, -5, 1, -2, 4, 0, 3, 3, 9, 0, 3, 5, -4, -6, -1, 10, 3, 1], "imageUrl": "https://upload.wikimedia.org/wikipedia/commons/e/e3/Projection-on-diagonal.gif", "imageLicense": "CC BY-SA 4.0", "imageArtist": "GruenerBogen", "explanation": ["Imagine you're reading a long email and trying to find the key points quickly. You want to skip the less important details and focus on what's truly important.", "Think of the email as a sequence of words. The attention mechanism helps the computer figure out which words are more important, like picking out the key points in your email."], "example": "If the sentence is \"The meeting was postponed due to unforeseen circumstances,\" the attention mechanism might highlight \"postponed\" as the key word.", "whyItMatters": "The key insight is that attention helps computers focus on the most important parts of data, like picking out key points in an email."}, {"id": "5624f4b207c5", "title": "Cosine similarity", "slug": "cosine-similarity", "headline": "Cosine similarity formula: cos(\u03b8) = (A \u00b7 B) / (||A|| ||B||)", "summary": "Write the formula for cosine similarity between two vectors", "source": "Write the formula for cosine similarity between two vectors", "sourceUrl": "https://en.wikipedia.org/wiki/Cosine_similarity", "articleUrl": "https://en.wikipedia.org/wiki/Cosine_similarity", "publishedAt": "2026-06-12", "category": "learn", "cohortScore": 0.5, "embedding": [-13, -1, -4, -2, -8, -4, 4, -4, 8, -6, -3, -11, 4, 2, 3, -13, -1, 9, -8, -4, 3, -2, -4, -5, 3, 13, -1, 1, 1, -22, 1, -1, 7, -5, 4, -1, -4, -1, -3, -1, 0, -1, 7, 2, -8, 6, -10, 3, -4, 0, 5, -5, -4, 4, 4, 7, 0, 6, 4, 7, 6, 2, -20, 10, 1, 5, -2, -7, 2, 7, -3, 1, 1, 2, -2, 7, -9, 1, -6, -4, -5, 3, 0, 4, -3, 1, -2, 1, 6, -6, -2, 0, -1, 3, -5, -6, -1, -2, 3, 37, 1, 4, 2, -4, 4, -4, -5, -6, 2, -1, -1, -3, -2, -12, -3, -4, 14, 1, 7, -4, 1, 1, -1, 0, -1, 1, 1, 1, 3, 6, 6, 6, -1, -2, -6, 1, -6, -2, -6, 0, 6, -5, 7, -1, 4, 16, -16, 0, -3, -4, 4, -1, 1, 1, -4, 4, 2, -1, 0, -4, -2, -2, -4, 11, 2, -10, 7, 5, 11, 1, 1, -1, 0, 4, 6, -2, -12, -2, 9, 2, 8, -4, -3, 7, -1, 2, -4, -7, -2, -1, 1, -2, -6, 1, -11, 1, -2, -4, -5, 6, 10, 2, 1, 1, 3, -3, 7, -8, -3, 3, 2, -9, -9, 1, -4, 2, 5, 10, 1, 8, -1, -12, -4, -38, -4, 3, -4, 3, -5, 0, -4, 2, 7, -1, 10, -2, -3, -6, 1, 6, 5, 7, -2, -2, -5, 3, -1, 8, -3, 22, -1, 10, -5, -2, -4, -3, 8, -1, -1, 2, 15, 1, -10, -4, 6, 6, -2, -3, -1, -4, -2, 0, 13, 2, 7, 0, -3, 2, 1, -4, 3, -2, 0, -1, -9, 6, 2, 1, 2, 2, -13, 3, 10, -1, 9, -5, -3, 2, -4, 7, 2, -1, 4, -1, 1, 3, 2, 8, -1, 9, 5, 8, 1, -2, -4, 2, 1, -7, -2, -34, 2, 1, 8, -5, -6, 1, -15, -7, -2, -4, 8, 4, 2, -1, 3, 9, -9, 0, 0, 5, -5, 19, -5, -1, -6, 4, 4, 3, 0, -4, -3, 6, 1, 0, 9, -6, 5, 10, -5, 3, -5, -5, 4, 10, 11, 0, -7, -3, -6, -1, 5, -5, 3, 0, 7, -13, -9, 0, 1, -2, -1, 9, -2, 2], "explanation": ["Cosine similarity measures the cosine of the angle between two vectors, which is calculated as the dot product of the vectors divided by the product of their lengths. This metric is useful for determining the similarity between vectors without being affected by their magnitudes.", "For instance, if vector A = [1, 2] and vector B = [2, 4], the dot product A \u00b7 B = 1*2 + 2*4 = 10. The lengths ||A|| = \u221a(1\u00b2 + 2\u00b2) = \u221a5 and ||B|| = \u221a(2\u00b2 + 4\u00b2) = \u221a20. Thus, cosine similarity = 10 / (\u221a5 * \u221a20) = 10 / \u221a100 = 1.", "Understanding cosine similarity is crucial in fields like information retrieval and text mining, where it helps compare documents represented as vectors of word occurrences."], "whyItMatters": "Cosine similarity is a fundamental concept in vector space models used in various applications, including search engines and recommendation systems.", "imageUrl": "https://upload.wikimedia.org/wikipedia/commons/thumb/2/26/Plastic_vormenstoof_of_puzzelbal_van_%E2%80%9CTupperware_Toy%E2%80%9D%2C_objectnr_83212.JPG/1280px-Plastic_vormenstoof_of_puzzelbal_van_%E2%80%9CTupperware_Toy%E2%80%9D%2C_objectnr_83212.JPG", "imageLicense": "CC BY-SA 3.0", "imageArtist": "Tupperware Ltd."}, {"id": "9884e884de30", "title": "Matrix norm", "slug": "matrix-norm", "headline": "L1 norm of a vector is the sum of absolute values of its components", "summary": "Write the equation for L1 norm of a vector", "source": "Write the equation for L1 norm of a vector", "sourceUrl": "https://en.wikipedia.org/wiki/Matrix_norm", "articleUrl": "https://en.wikipedia.org/wiki/Matrix_norm", "publishedAt": "2026-06-12", "category": "learn", "cohortScore": 0.5, "embedding": [-9, -5, 0, -3, -3, -1, 4, 9, 11, 2, 7, -2, 8, -1, 4, -6, 3, 9, -7, -1, 5, -11, 0, -4, 14, 9, -5, -1, 1, -29, -1, 3, 8, -2, -4, 6, 1, -2, -5, -3, 4, -5, 0, -11, -2, -1, -9, 2, 2, 3, 5, 2, -2, 0, 0, 1, -1, 0, -3, 5, 6, -7, -22, 12, 6, 3, -2, -5, -1, 10, -5, -3, 5, 0, 4, -2, -9, -7, 1, 1, -1, -2, -3, 7, 0, 1, 12, -2, 4, -6, -3, -7, -4, 6, -2, -11, -2, 3, 5, 43, -5, 6, -1, -2, -3, 1, 0, -6, -4, -7, -4, -1, -3, -13, 7, -8, 6, 0, 1, -3, 2, 1, 3, -2, 7, -1, 4, 14, 3, 17, 3, 1, -3, -6, 0, 6, 0, 6, -3, 5, -2, -4, -2, 2, -1, 13, -4, -12, 5, -5, -3, -2, 1, 5, 2, 5, 1, -3, -5, -7, -10, -4, -6, 6, -2, -2, 11, 6, 5, -2, 6, -7, -1, 0, 8, 3, -4, 1, 5, 5, 1, -5, -2, 5, 6, 1, -3, 3, -1, -5, -3, 0, -1, -1, -10, -5, -1, -5, 3, -5, 7, 6, 6, -1, 3, 1, 2, -5, -4, 7, -2, -3, -2, -1, -8, 5, 0, -1, -1, 2, -2, -5, -11, -34, 2, 0, -4, 5, -4, 6, -1, -3, 3, 9, 5, -5, -7, -6, -4, -1, 4, 0, 3, -9, -2, 1, 2, 3, -1, 20, -1, 9, 1, -1, 2, -2, 7, -5, -2, -6, 7, -3, -7, 3, 2, -9, 1, -6, 0, 0, -2, -4, 2, 2, -3, 5, 1, 7, 2, -13, 2, -4, 4, 3, 1, 11, -4, 3, 0, 6, -5, 1, 2, 4, 7, 0, -5, 6, -2, -1, 11, 1, 1, 0, -3, 8, -2, 4, 5, 2, 3, -1, 9, -7, -2, 0, 3, -11, -2, -34, -7, -1, -5, -4, -1, 4, -11, -13, 8, -5, 6, 2, -1, -2, -9, 3, -5, 3, -9, 9, 2, 20, -9, -1, -1, 0, -8, 2, 1, 1, 2, 12, 6, 2, 6, -5, 2, 5, 2, 6, 4, 0, 5, 5, 6, 3, -4, 0, -4, 2, 5, 6, 0, -6, 2, -9, -1, -1, 3, 3, 2, 8, -5, 4], "explanation": ["The L1 norm, also known as the Manhattan norm, represents the sum of the absolute values of the components of a vector. It measures the distance from the origin to the point in a grid-like path, akin to navigating city blocks."], "example": "For a vector v = [3, -4, 2], the L1 norm is calculated as |3| + |-4| + |2| = 3 + 4 + 2 = 9.", "whyItMatters": "Understanding the L1 norm is crucial for applications in optimization and machine learning, where it helps measure distances and errors.", "imageUrl": "https://upload.wikimedia.org/wikipedia/commons/7/71/Serpiente_alquimica.jpg", "imageLicense": "Public domain", "imageArtist": "anonymous medieval illuminator; uploader Carlos adanero"}, {"id": "93aef0dc395a", "title": "Normalization (machine learning)", "slug": "normalization-machine-learning", "headline": "L2 normalization equation: x_i' = x_i / ||x||_2", "summary": "Write the equation for L2 normalization of a vector", "source": "Write the equation for L2 normalization of a vector", "sourceUrl": "https://en.wikipedia.org/wiki/Normalization_(machine_learning)", "articleUrl": "https://en.wikipedia.org/wiki/Normalization_(machine_learning)", "publishedAt": "2026-06-12", "category": "learn", "cohortScore": 0.5, "embedding": [-11, -4, -3, -1, 1, -6, 0, 3, 7, -2, 3, -2, 5, -1, 8, -8, -3, 10, -10, -1, 1, -5, 1, -6, 11, 10, -5, -1, 0, -27, 2, -3, 11, -4, 2, 0, -7, 1, -3, -5, 4, -4, -2, -8, 2, -2, -12, -2, 1, 0, 2, 1, 0, -1, 4, 2, 2, -1, 4, 13, 4, 0, -19, 10, -1, 0, -5, -4, -1, 13, -1, -4, 1, 6, 8, 1, -6, -7, 2, 0, -2, -2, -2, 4, 6, 1, 9, -7, 2, -8, -2, 1, -4, -1, -4, -10, 2, 4, 3, 42, 2, 5, 4, 5, -1, -6, -6, -4, -7, -9, -9, 1, 4, -9, 3, -1, 5, 4, 1, 2, 1, -1, -5, -1, 12, -3, 5, 5, -3, 11, 3, 6, -9, 0, -3, 1, -2, 2, -3, 0, 0, -2, -1, -1, 1, 17, -8, -13, -5, -4, 2, -1, 1, 0, 11, 4, 6, -8, -8, -4, -4, -6, -6, 7, -4, 0, 6, 5, 4, 3, 8, 2, 0, 0, 7, 1, -8, -1, 7, 7, 5, 1, 2, 4, 7, -5, -6, 5, -3, 1, 1, 1, -5, 1, -9, 1, -3, 2, -1, -6, 8, 7, 2, -4, -3, -1, 11, -7, -8, 8, 1, -10, 3, -3, -6, 10, -3, 3, -2, 3, -1, -6, -10, -39, -2, 4, -1, 2, -5, 0, -1, -5, 5, 4, 5, -4, -6, -1, -4, 3, 4, -1, 1, -3, -3, -1, -3, 6, 4, 17, 3, 8, 0, 1, -1, 2, 4, 2, -4, 0, 9, -1, -7, 6, 2, -3, 2, -5, -1, 3, -1, -2, -4, 0, 7, 6, -5, 3, -1, -13, 6, -8, 0, -4, -6, 6, -7, -5, -5, 8, -7, 4, 3, 1, 5, 2, -1, 6, 0, -3, 4, 0, -7, 2, 1, 5, 1, 5, 2, 4, 0, -3, 6, -10, -6, 4, 8, -7, -1, -35, -7, 7, 1, -1, 3, 1, -8, -12, 3, -9, 9, 8, 3, -1, -9, 8, -5, 2, -7, 3, -2, 19, -7, 0, -3, -2, -6, 5, -3, 1, 3, 12, 6, 4, 8, -4, 0, 6, -3, 4, 2, -3, 3, 3, 2, 4, -1, -2, 0, 3, 7, -2, 1, 0, 8, -4, -6, 2, 3, 1, 0, 11, -4, 7], "explanation": ["L2 normalization is a technique used to scale vectors in machine learning. The equation x_i' = x_i / ||x||_2 represents this process, where x_i' is the normalized vector, x_i is the original vector, and ||x||_2 is the L2 norm of the vector x."], "example": "Consider a vector x = [3, 4]. The L2 norm ||x||_2 is calculated as \u221a(3\u00b2 + 4\u00b2) = 5. Thus, the L2 normalized vector x' = [3/5, 4/5] = [0.6, 0.8].", "whyItMatters": "L2 normalization ensures that vectors have a unit norm, which can improve the performance of machine learning algorithms and facilitate better convergence during training.", "imageUrl": "https://upload.wikimedia.org/wikipedia/commons/thumb/8/89/Einstein_blackboard.jpg/1280px-Einstein_blackboard.jpg", "imageLicense": "CC BY-SA 3.0", "imageArtist": "decltype"}, {"id": "0bc376b72dad", "title": "Softmax function", "slug": "softmax-function", "headline": "Softmax converts real numbers into a probability distribution", "summary": "Write the formula for softmax of a vector", "source": "Write the formula for softmax of a vector", "sourceUrl": "https://en.wikipedia.org/wiki/Softmax_function", "articleUrl": "https://en.wikipedia.org/wiki/Softmax_function", "publishedAt": "2026-06-12", "category": "learn", "cohortScore": 0.5, "embedding": [-9, -3, 4, -2, 1, 6, 2, 2, 9, 1, 12, -2, 4, -3, 7, 1, 2, 5, -7, 3, 10, -11, -3, -7, 7, 2, -5, -1, -7, -27, 0, 3, 4, -7, 3, 1, -10, 0, 1, 6, -2, 2, -3, 1, 2, -4, -4, -10, -3, 2, -6, 3, -2, 2, 11, 2, 2, 1, 2, 6, 0, 7, -12, 5, 4, 1, -10, -7, 4, 7, -1, 1, -1, 12, 3, 4, -2, -4, 1, 2, -1, -2, 0, 5, 4, -2, 10, -6, 8, -4, -2, 11, 0, 2, 0, 1, 4, 0, 7, 38, 4, -5, -3, -6, 3, -11, -5, -3, -8, -4, -8, -5, -4, -2, 1, -6, 4, 4, -3, -8, -7, 3, 6, 2, 6, 4, -10, 12, -2, 8, 5, 2, -11, 2, 0, -3, -4, 5, 2, 6, 2, 6, 7, -1, -1, 15, -10, -4, -3, -6, 9, 0, 7, -8, 12, -7, -1, -2, -9, -4, -3, -5, 0, 14, -3, -3, 8, 3, 0, 4, 2, -7, -2, 7, 3, 0, -11, -4, 4, 3, -3, 0, -6, -3, 0, 0, 0, -1, 1, 0, 1, -2, 0, 1, -6, -3, 3, 3, 1, 2, -5, 1, -7, -6, 3, 0, 0, -3, 7, 9, 5, -5, 4, -1, -6, 8, -2, 8, 5, 0, 3, -6, -11, -39, 0, -1, -6, -1, -3, 7, -2, 4, 1, 11, -3, -9, -8, 4, -4, -1, 7, -3, 6, -1, 1, 0, 5, 8, 1, 17, -5, 7, 3, -2, -1, 2, 4, -4, -1, 4, 4, -1, -4, 0, -2, -2, -7, -4, -6, 1, 6, -2, 6, 0, 0, 6, -2, 6, -13, -5, 4, -9, 0, 0, -10, 8, -10, -4, -4, 9, -6, -1, 3, -1, 6, 2, 2, 13, -3, 3, 0, -5, -8, -4, 0, 2, -2, 4, 1, 5, 3, -8, 10, -2, -4, 0, 4, -3, -1, -36, -3, 0, 2, -3, -1, 4, -7, -11, 1, -3, 9, 7, 3, 3, -3, -6, -5, 6, -7, 2, -2, 23, -11, -2, 4, 0, -1, 4, -7, 2, 7, 12, 3, -2, 12, -6, 1, 6, 0, 6, -3, 3, 1, 16, 5, -1, -5, -4, 1, -7, 1, -3, -1, -3, 3, 2, 0, -1, -3, -1, -3, 6, 0, -3], "explanation": ["The softmax function takes a vector of real numbers and applies the exponential function to each element, then normalizes these values by dividing by the sum of all exponentials. This transformation ensures that the output values are non-negative and sum up to one, making them a valid probability distribution. The softmax function is particularly useful in neural networks for tasks like classification, where it helps to convert the raw output scores into probabilities for each class."], "example": "Given a vector [2, 1, 0.1], the softmax function will first compute the exponentials: exp(2) = 7.389, exp(1) = 2.718, exp(0.1) = 1.105. Then, it normalizes these values by dividing each by the sum of all exponentials: 7.389 + 2.718 + 1.105 = 11.212. The resulting softmax probabilities are approximately [0.655, 0.245, 0.010].", "whyItMatters": "Understanding the softmax function is crucial for interpreting neural network outputs in classification tasks, as it provides a clear probability distribution over possible outcomes.", "imageUrl": "https://upload.wikimedia.org/wikipedia/commons/thumb/6/6b/Dice%2C_game_%28AM_2015.20.16-2%29_%28cropped%29.jpg/1280px-Dice%2C_game_%28AM_2015.20.16-2%29_%28cropped%29.jpg", "imageLicense": "CC BY 4.0", "imageArtist": "Unknown authorUnknown author"}, {"id": "da338bafd68b", "title": "Cross-entropy", "slug": "cross-entropy", "headline": "Cross-entropy loss equation: H(p, q) = -\u03a3(p(x) * log(q(x)))", "summary": "Write the equation for cross-entropy loss", "source": "Write the equation for cross-entropy loss", "sourceUrl": "https://en.wikipedia.org/wiki/Cross-entropy", "articleUrl": "https://en.wikipedia.org/wiki/Cross-entropy", "publishedAt": "2026-06-12", "category": "learn", "cohortScore": 0.5, "embedding": [-11, 4, 4, -6, -5, 5, 5, -3, 4, 2, 4, -8, 8, -5, -1, -1, -9, 4, -8, 0, 7, -5, -1, -7, 4, 5, 0, 0, -8, -24, 3, -7, 2, -5, 0, 5, -1, 5, -4, 5, 4, 1, 5, 3, 1, -4, -8, -3, -1, -3, -1, 13, -5, -1, 2, 3, 6, 5, 1, 2, 4, 4, -18, 3, 4, 5, -5, -4, -4, 10, -8, -4, 2, 6, -1, -1, -4, -6, -3, -6, 0, 1, -5, -1, 3, -1, 11, -1, 1, -3, -1, -1, -3, 2, -4, -4, 2, 6, 4, 42, 3, 4, -2, -1, -3, -9, 2, -1, 2, -5, -1, 1, 7, -10, 1, -1, 4, 11, -2, 0, 0, -1, 4, 2, 8, 4, -9, 12, -3, 3, 2, -6, 5, -3, 2, -1, -5, 1, 5, 3, 7, -6, 2, -8, 0, 12, -3, -2, -8, -2, 0, 0, -1, -9, 2, 6, 4, 0, -3, 1, -4, -7, 4, 7, 0, 4, 14, 2, 6, -8, 0, 2, 1, -11, 9, 3, -2, -4, 6, 3, -1, -5, -10, -1, 6, -1, -5, 0, -2, 5, 5, -8, 0, 10, -5, 5, -3, 1, -5, 2, 5, 3, -3, -3, -8, 2, 3, -3, -2, 3, 0, -2, 1, 1, -2, 1, 6, 3, 6, 4, -6, -17, -3, -40, -9, 1, -2, 13, -7, 3, -7, -5, 6, 13, 6, -8, -5, 1, 4, 7, -4, -8, 1, 1, 1, 4, -6, 4, -1, 14, -1, 12, 5, 0, 2, -5, 5, 5, 3, 0, 2, -6, -16, -4, 4, -5, 5, -3, -3, -4, -3, -6, 6, 8, 4, 2, -3, 1, 0, -5, -3, -9, -1, 0, -3, 3, -1, -5, -7, 5, -3, 3, 3, -2, 8, -1, -4, 6, 1, 1, 6, -5, -3, 12, -2, 6, 6, 8, 6, 4, -3, -3, -2, -8, -7, 4, 1, -2, -5, -35, 0, -1, 6, -2, -4, 4, -6, -8, 2, -3, 5, 2, 3, 5, -11, -2, -9, 5, 5, 4, -2, 20, 7, 5, -6, 2, 3, 9, -2, -1, 0, 13, -3, 9, 5, -1, 3, 10, -6, 9, -5, 2, 0, 14, 4, 2, -6, -7, -2, -1, 4, -1, 2, -2, 8, -9, -10, 1, -5, 3, 1, 3, -5, 1], "explanation": ["Cross-entropy loss is a measure used in machine learning to quantify the difference between two probability distributions. It is particularly useful for comparing the predicted probabilities (q) with the actual probabilities (p) of events.", "Cross-entropy loss helps in optimizing machine learning models by providing a clear metric for how well the model's predictions align with the true data distribution. By minimizing this loss, models can improve their accuracy and performance over time.", "The equation for cross-entropy loss is H(p, q) = -\u03a3(p(x) * log(q(x))), where p(x) represents the actual probability distribution, q(x) represents the predicted probability distribution, and the summation \u03a3 extends over all possible events x."], "example": "Suppose we have a binary classification problem with two classes: A and B. Let p(A) = 0.7 and p(B) = 0.3 be the true probabilities. If our model predicts q(A) = 0.6 and q(B) = 0.4, the cross-entropy loss would be calculated as follows:\n\nH(p, q) = -[ (0.7 * log(0.6)) + (0.3 * log(0.4)) ]", "whyItMatters": "Understanding and applying the cross-entropy loss equation is crucial for improving the performance of machine learning models, as it directly influences how well the model's predictions match the actual data.", "imageUrl": "https://upload.wikimedia.org/wikipedia/commons/e/e9/GoldenSpiralLogarithmic_color_in.gif", "imageLicense": "CC0", "imageArtist": "Jahobr"}, {"id": "5ecb89f76b94", "title": "Bayes' theorem", "slug": "bayes-theorem", "headline": "Bayes' theorem formula: P(A|B) = [P(B|A) * P(A)] / P(B)", "summary": "Write the formula for Bayes' theorem", "source": "Write the formula for Bayes' theorem", "sourceUrl": "https://en.wikipedia.org/wiki/Bayes%27_theorem", "articleUrl": "https://en.wikipedia.org/wiki/Bayes%27_theorem", "publishedAt": "2026-06-12", "category": "learn", "cohortScore": 0.5, "embedding": [-14, -1, -5, -6, -8, 1, 7, -1, 10, 2, 5, -11, 2, 0, -4, 2, -5, 4, -1, -2, 11, -4, -9, -7, 11, 15, 2, 6, -5, -22, -2, 1, 6, -5, 1, 2, -5, 1, 2, 3, 2, 5, 6, 5, -1, 1, 0, -4, -3, -5, 2, 4, 0, -1, -2, 0, 0, 10, 2, 10, 5, 2, -13, 3, 2, 2, -10, 0, -6, 9, -2, 4, 1, 8, 6, 0, -3, 0, -1, -1, -10, -3, 7, 7, -3, -7, 0, -5, 5, 1, -1, 4, -2, -4, -2, -3, 1, 2, 6, 42, -2, 0, -7, -2, 1, -6, 0, -8, -5, -2, -1, 0, 5, -10, -5, -4, 6, 3, -1, -8, -1, 0, 10, 0, 5, 0, -6, 13, 0, 9, 13, 2, 5, 0, 3, -5, -5, -1, 4, 3, -1, -7, 7, 1, 10, 16, -3, 2, -6, 0, 6, 2, 3, -7, 7, -2, 4, 2, -9, -3, -8, 0, 0, 13, 1, 2, 7, 0, 5, 6, -2, 5, -2, 2, 3, -2, -4, -6, 8, 3, 8, -4, -4, -3, -5, 5, -11, -5, 1, -1, 8, -4, -2, -4, -7, -9, -7, -3, -7, 1, 6, -5, -6, 0, 0, 1, 8, 5, -2, 4, 0, -3, -9, 5, -1, 5, 3, 8, 0, 4, -1, -4, -3, -35, -7, 5, -7, -5, -3, -3, 4, -9, 8, 3, -7, -7, -1, -7, -7, 4, -4, -2, -1, -6, -6, -5, -3, 6, 7, 14, 5, 6, 5, 2, 3, -6, 6, 2, -1, -9, 6, -5, -6, 0, 4, -5, 1, -9, -2, 1, 1, -4, 8, 0, 4, 7, -10, 1, -6, 2, 5, -7, 4, 6, -1, 5, 5, -3, -8, 1, -6, 2, 3, -8, 11, 2, -7, 5, -1, 7, 0, 1, -3, 3, -4, 4, 5, 2, 1, 5, 4, 4, 3, -9, -1, -6, 6, -8, -1, -35, 1, -1, 2, -4, -2, 2, -7, -9, -8, -3, 5, 5, 2, -5, -6, 3, -7, 6, 0, 7, -3, 24, -2, 4, 1, 7, 0, 5, -4, 1, -5, 7, 0, 4, 8, -1, 7, 5, -9, 5, -10, -5, -2, 15, 3, -2, -5, -5, 0, -4, 5, -1, 2, 3, 0, -5, -3, -4, -2, 1, 5, 16, 0, 6], "explanation": ["Bayes' theorem provides a way to update the probability of a hypothesis as more evidence becomes available. It is expressed as P(A|B) = [P(B|A) * P(A)] / P(B), where P(A|B) is the probability of event A given that B is true, P(B|A) is the probability of event B given that A is true, P(A) is the prior probability of A, and P(B) is the prior probability of B."], "example": "Suppose we want to find the probability that a patient has a disease (A) given that they tested positive (B). If the probability of testing positive given the disease is present (P(B|A)) is 0.98, the prior probability of having the disease (P(A)) is 0.01, and the probability of testing positive (P(B)) is 0.05, then using Bayes' theorem, P(A|B) = [0.98 * 0.01] / 0.05 = 0.196.", "whyItMatters": "Bayes' theorem is crucial for making informed decisions based on new evidence, as it allows for the calculation of conditional probabilities in various fields such as medicine, finance, and machine learning.", "imageUrl": "https://upload.wikimedia.org/wikipedia/commons/thumb/8/8d/P._Oxy._I_29.jpg/1280px-P._Oxy._I_29.jpg", "imageLicense": "Public domain", "imageArtist": "Euclid"}, {"id": "a3bdf3f87424", "title": "Gradient descent", "slug": "gradient-descent", "headline": "Gradient descent weight update equation: w := w - \u03b1 * \u2207J(w)", "summary": "Write the equation for gradient descent weight update", "source": "Write the equation for gradient descent weight update", "sourceUrl": "https://en.wikipedia.org/wiki/Gradient_descent", "articleUrl": "https://en.wikipedia.org/wiki/Gradient_descent", "publishedAt": "2026-06-12", "category": "learn", "cohortScore": 0.5, "embedding": [-16, -1, 1, 1, -7, 2, -9, 2, 11, 6, 5, -6, 3, 0, 3, -3, -1, 2, -8, 1, 5, -2, 1, -5, 6, 6, -3, 4, -5, -24, 1, -7, 10, -1, 5, 2, -2, 2, -6, 3, -3, 1, -7, 0, -1, -2, -4, -9, -6, 3, 4, 1, 0, -1, 3, -3, 5, 4, 4, 5, 8, -2, -20, 11, 3, -3, -7, -10, -1, 17, -2, 4, 10, 5, 0, 5, -3, -1, 8, 1, 4, 2, -3, -3, -1, -7, 4, -1, 9, -1, -7, -10, -5, 1, -7, -4, 1, 1, -12, 41, -2, 3, 2, 9, 2, -8, -1, -2, 2, -7, -9, 5, 7, -6, -5, 0, 2, 10, -5, 2, 1, -7, 6, 1, 4, -1, -2, 9, 1, 8, 3, 1, -4, -1, -2, 1, -1, -2, -2, -1, -4, -2, -2, -5, -5, 23, -6, -2, -3, -5, -3, 3, 1, 0, -3, 1, 1, -2, -7, 3, -9, 1, -5, 6, 4, -3, 1, 1, 0, 0, 9, 6, 2, -9, 7, -6, -6, -2, 8, 4, 5, -3, -8, 1, 5, 2, -2, -7, 2, 7, -2, -3, 1, 0, -3, -4, -5, 2, -2, 1, -2, 7, 6, -1, 1, -1, 6, -7, 1, 3, -9, -10, -2, 0, -3, 0, -1, -4, 1, 4, -3, -9, -3, -37, -8, 10, -3, 6, -7, 9, -2, -4, 5, 12, 4, 1, -3, 6, 1, 5, -6, 3, 0, -3, -6, 5, -5, 7, 1, 17, -1, 8, -2, -3, -2, 9, 4, 7, 0, 0, 3, -6, -2, -2, 8, 2, -7, -4, 0, -4, -6, -5, 3, 4, 6, 6, -3, 0, 0, -4, 7, -3, 3, -1, -8, 3, -1, -1, -5, 4, -3, 1, 2, -4, 3, 3, 1, 4, 5, -6, 4, -4, -5, -3, 2, 12, 8, 0, 7, 5, -2, -3, 4, -15, -3, 1, 3, 0, 1, -36, -3, 2, 0, 2, -3, 12, -5, -12, -2, -11, 4, -3, 0, 6, -7, 6, -3, 4, -3, 1, 6, 20, -2, 5, 3, 2, 0, 8, 3, -4, 0, 15, 0, 5, 7, -9, -2, 7, -2, 9, 3, -3, 4, 4, 10, 3, -2, -6, -2, 2, 5, 0, -6, 8, 0, -9, -3, -7, 3, -1, -2, -2, -5, -1], "explanation": ["Gradient descent is an optimization algorithm used to minimize functions by iteratively moving towards the steepest descent direction.", "The weight update equation w := w - \u03b1 * \u2207J(w) represents the core of gradient descent, where w is the current weight vector, \u03b1 (alpha) is the learning rate, and \u2207J(w) is the gradient of the cost function J with respect to the weights w.", "This equation ensures that the weights are adjusted in the direction that reduces the cost function, leading to convergence towards the minimum value of J."], "example": "Suppose we have a cost function J(w) = (w - 3)\u00b2, the gradient \u2207J(w) = 2(w - 3). If our current weight w = 5 and learning rate \u03b1 = 0.1, the weight update would be w := 5 - 0.1 * 2(5 - 3) = 5 - 0.1 * 4 = 4.6.", "whyItMatters": "Understanding the weight update equation is crucial for implementing gradient descent in machine learning models, enabling them to learn and minimize error effectively.", "imageUrl": "https://upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Gradient_Descent_in_2D.webm/500px--Gradient_Descent_in_2D.webm.jpg"}, {"id": "39dadabb602d", "title": "Mean squared error", "slug": "mean-squared-error", "headline": "Mean squared error (MSE) formula: MSE = (1/n) * \u03a3(y_i - \u0177_i)\u00b2", "summary": "Write the formula for mean squared error", "source": "Write the formula for mean squared error", "sourceUrl": "https://en.wikipedia.org/wiki/Mean_squared_error", "articleUrl": "https://en.wikipedia.org/wiki/Mean_squared_error", "publishedAt": "2026-06-12", "category": "learn", "cohortScore": 0.5, "embedding": [-10, -2, 9, -7, 0, -3, -2, 3, 10, 1, 4, -12, 8, -3, -7, -1, -3, -4, -6, 4, 5, 1, -3, -5, 4, 8, -4, -8, -3, -25, 1, 0, 8, -5, -4, -5, -4, -2, 2, -1, 3, 2, 9, -2, 0, -2, -5, 1, 1, -3, 6, 0, -9, 1, 8, 1, -2, 3, -1, 6, 8, 6, -16, 4, 1, -2, -2, -3, -7, 9, -3, -8, -4, 6, 5, 6, 0, 3, -5, 6, -6, -2, 3, 0, -3, 1, 4, 5, 16, -2, 2, 4, 0, -1, -4, 1, 0, 1, 0, 36, 3, 2, -5, 0, -1, -9, -1, -5, 3, -7, 2, 2, -2, -11, -1, -3, 3, -3, -2, -6, 3, -1, 4, -2, 9, 2, 6, 10, -3, 7, 3, -1, -1, 1, 1, 1, -6, 1, 1, -1, 7, -8, 0, 8, 4, 19, -5, -3, -2, -1, 9, 5, -1, 1, 7, 0, 2, -4, -10, -9, -7, -5, 0, 8, 4, -1, 3, 7, 3, -5, 9, 1, -2, 0, 6, 1, 1, 10, 5, -3, 5, 2, -1, -4, 4, 5, -5, -8, 1, 5, -1, -3, -8, -1, -7, -2, -5, -5, -4, -5, 15, 0, 1, -7, 5, 3, 6, -1, -10, 7, 1, -9, 6, 0, -6, 7, 2, 9, 3, 2, 5, -7, -11, -33, -4, 9, -7, -1, 3, 0, -2, -3, 10, 4, 0, -6, -9, 0, -9, -3, -9, -2, 2, -3, -3, -4, 1, 5, 2, 14, -10, 9, -3, 0, -2, 4, 7, 6, -2, -1, 11, -4, -12, -2, 2, 5, -1, -5, -2, 1, -10, -4, 0, -2, 1, 9, 2, 1, 1, -8, 4, 1, -5, 4, -5, 7, -4, -5, -2, 9, -12, 9, -1, 5, 13, -4, -3, 5, -2, -1, -1, 0, 5, 0, -5, 3, -2, 7, 6, 7, 0, 3, -1, -9, -3, 0, 7, -13, -4, -33, 6, 2, 5, -5, -11, 3, -8, -12, 3, -9, 9, 5, 2, 4, -2, 5, -6, 8, -1, 11, 0, 20, 0, -3, 5, -2, -1, 16, -4, 2, -4, 11, 4, 6, 3, -10, 0, 11, -4, 7, -1, -1, 3, 11, -2, 5, -7, -3, -5, -6, 8, -1, 5, -4, -2, -5, -6, 0, 0, -5, -6, 10, -2, 2], "explanation": ["The mean squared error (MSE) is a measure of the average squared difference between estimated values (\u0177_i) and true values (y_i). It quantifies the accuracy of an estimator by calculating the squared errors, summing them up, and then averaging them over the number of observations (n).", "MSE incorporates both the variance and bias of an estimator. Variance refers to the spread of the estimates across different data samples, while bias refers to the systematic error that occurs when the estimator consistently deviates from the true value. By squaring the errors, MSE ensures that all deviations are positive and emphasizes larger errors more significantly.", "The MSE formula is crucial in fields like machine learning and statistics, where it serves as a risk function. It helps in evaluating and comparing different estimators by providing a single metric that reflects both variance and bias. A lower MSE indicates a better estimator that produces estimates closer to the true values."], "example": "Suppose we have an estimator \u0177_i for the true values y_i of a dataset with 5 observations. The squared errors are as follows: (y_1 - \u0177_1)\u00b2 = 4, (y_2 - \u0177_2)\u00b2 = 9, (y_3 - \u0177_3)\u00b2 = 1, (y_4 - \u0177_4)\u00b2 = 16, (y_5 - \u0177_5)\u00b2 = 0. The MSE is calculated as (1/5) * (4 + 9 + 1 + 16 + 0) = 6.", "whyItMatters": "Understanding the MSE formula is essential for evaluating the performance of estimators in statistical models and machine learning algorithms. It provides a clear metric for assessing accuracy and helps in selecting the best estimator for a given problem.", "imageUrl": "https://upload.wikimedia.org/wikipedia/commons/b/be/Normdist_regression.png", "imageLicense": "Public domain", "imageArtist": "Amatulic at English Wikipedia (same as Anachronist on Wikimedia)"}, {"id": "d009fe4d5038", "title": "Activation function", "slug": "activation-function", "headline": "Tanh activation function equation: tanh(x) = (e^x - e^(-x)) / (e^x + e^(-x))", "summary": "Write the equation for tanh activation", "source": "Write the equation for tanh activation", "sourceUrl": "https://en.wikipedia.org/wiki/Activation_function", "articleUrl": "https://en.wikipedia.org/wiki/Activation_function", "publishedAt": "2026-06-12", "category": "learn", "cohortScore": 0.5, "embedding": [-7, 6, 4, 0, -8, 5, 5, 0, 1, 1, -2, -6, 2, -2, 4, -4, -6, 2, -12, 4, 7, -1, 4, -2, 12, 11, 0, 3, -4, -18, -5, 0, 11, -5, 1, -6, 4, -2, -4, -5, 1, -2, 0, 3, 1, 2, -8, 3, 4, -4, 3, 3, 4, 3, -1, -5, 6, 5, 2, -3, 10, 7, -13, 8, 3, -3, 4, -9, -2, 14, -3, 2, 1, 5, 2, -1, 1, -4, -3, -7, -4, 0, -4, 2, 2, -1, 3, -5, 2, 2, 5, -1, 2, -2, -5, -7, 2, 4, 0, 40, -7, 2, -10, 1, 0, -10, -7, 6, -2, -5, -13, -6, 2, -13, -1, 0, 0, 3, 2, -2, 5, 1, 0, -1, 2, -2, 2, 11, 3, 9, 4, -5, 1, 6, 6, 13, -3, -9, -7, 0, 4, -1, -1, -5, -2, 8, 0, -7, -3, -4, -3, 3, 3, 2, 1, 8, 1, 1, -4, -2, -12, -4, -3, 12, 1, 3, -1, 8, 1, -8, -2, 5, -6, -2, 17, 1, 5, -4, 3, 8, 5, -5, -5, 3, 2, -1, -3, 4, -1, 2, 2, 0, -7, 2, -8, -11, 3, -5, -2, 5, 3, 1, -7, -2, -2, -1, 3, 5, -5, 6, -6, 7, 4, -1, 0, -4, 1, -1, 2, 2, -1, -13, -2, -38, -9, 7, -1, 10, -5, 8, -7, 0, 1, 9, 10, -2, -7, 2, -3, 0, -15, 3, -1, -3, 2, 4, -8, 7, 7, 12, 4, 11, -5, -3, -9, -5, 4, 6, -4, 2, 1, 0, -13, -4, -3, -7, 5, -1, 3, -6, -1, -5, -1, 7, 5, 6, -1, 2, -2, -2, 14, -7, -1, -8, 3, -3, 0, -4, -3, 1, -1, 9, 2, -2, 7, -4, 5, 6, -3, -3, 6, 0, -4, 4, -7, 7, -6, -1, 4, 5, 4, 4, -5, -7, 5, 12, 5, -3, -2, -37, -5, 3, 0, 2, 1, 7, -5, -16, -2, -4, 5, 0, 7, -1, -11, 1, -8, 0, 0, 4, 1, 22, 0, 6, 3, 3, -2, 10, -10, 4, -1, 3, -3, 1, 2, 2, 6, 6, 0, 0, -1, -4, -5, 6, -2, 6, -5, -3, 1, 3, 7, 0, 8, 4, 13, -4, -6, -9, 6, -6, -2, 5, 5, 5], "explanation": ["The tanh activation function is a hyperbolic tangent function that maps input values to a range between -1 and 1. It is used in neural networks to introduce nonlinearity, allowing the model to learn complex patterns.", "The tanh function is defined mathematically as tanh(x) = (e^x - e^(-x)) / (e^x + e^(-x)). This formula uses the exponential function e^x and its reciprocal e^(-x) to calculate the output for any given input x.", "The tanh function is particularly useful in neural networks because it helps the model to converge faster during training. It also helps to mitigate the vanishing gradient problem, which can occur with other activation functions like the sigmoid function."], "example": "If the input x is 1, then tanh(1) = (e^1 - e^(-1)) / (e^1 + e^(-1)) \u2248 0.7615941559557649", "whyItMatters": "Understanding the equation for the tanh activation function is important for implementing it correctly in neural networks and for analyzing its behavior during the training process.", "imageUrl": "https://upload.wikimedia.org/wikipedia/commons/thumb/8/88/Logistic-curve.svg/1280px-Logistic-curve.svg.png"}, {"id": "6bdcc0263834", "title": "ReLU and Leaky ReLU", "slug": "relu-and-leaky-relu", "headline": "Why do computers sometimes struggle with simple decisions?", "summary": "Write the equation for ReLU and Leaky ReLU", "source": "Write the equation for ReLU and Leaky ReLU", "sourceUrl": "https://en.wikipedia.org/wiki/Rectified_linear_unit", "articleUrl": "https://en.wikipedia.org/wiki/Rectified_linear_unit", "publishedAt": "2026-07-03", "category": "learn", "cohortScore": 0.5, "embedding": [-11, -1, 1, -4, -8, -4, 4, 3, 9, -6, 0, 3, 7, -2, 6, 4, -10, -4, -2, 0, 8, -5, -1, -4, -4, -2, 2, -3, -4, -28, -3, -4, 6, -4, 2, 3, -3, -1, -5, -1, -6, 0, 3, -2, 0, -1, 3, -1, 2, -1, -1, 1, -1, 3, 2, 4, 11, 9, 6, -5, 5, 0, -10, 7, 10, -1, 0, -6, 2, 6, -7, 1, -4, 5, -1, -1, 0, -1, 3, 3, 8, -2, -3, 3, -1, -6, -6, 6, 10, -10, -2, 0, 5, 1, -3, 2, 7, 2, -13, 44, 1, 5, 5, 1, 1, -9, -1, -5, -4, -4, 2, -1, 10, 1, 3, 9, -2, -3, 1, -1, -7, -3, 0, 0, 3, -5, -9, 16, -7, 3, 7, -4, 1, 4, 6, 2, -5, 0, 1, -3, -3, 10, 2, 0, -7, 18, 0, -1, -4, -1, -2, 3, -1, -10, -1, 5, 0, -2, -2, -4, -3, -4, -8, 11, 1, 1, 2, -5, 0, 3, -2, 2, 0, -2, -5, -3, -9, -5, -2, 4, 2, 3, -3, 3, 6, -5, 1, 2, -2, 9, -3, -6, -2, 0, -5, -7, 6, -3, -6, 0, -6, 4, -4, 1, 8, 2, 1, -7, 7, 5, -2, 0, -4, -4, -2, -3, 1, 1, 9, 2, 3, -4, -1, -40, -5, -4, -10, 8, -4, 6, -1, -6, 10, 5, -5, -2, -10, -1, -4, -3, 4, -8, 2, -2, 3, 4, -11, -5, 8, 23, -10, 11, 4, 2, 5, -3, -2, 6, 9, 1, 2, 2, -4, -2, -5, -3, -1, -2, -1, -6, -4, -7, 6, -2, 3, 3, 1, 1, 0, -2, 0, 4, 0, 3, -3, -5, -7, 4, -1, 3, -6, 6, 4, -1, 16, -5, -1, 3, 0, 3, -5, -1, -6, 8, -2, 6, 6, 6, -3, 9, -3, -1, -5, -4, -3, 2, -4, 2, -1, -35, 2, 1, 3, 3, 4, 0, 2, -8, 2, -1, 6, -7, -1, -1, -3, 10, -10, 5, -3, 2, 6, 26, -7, 5, 4, 5, -2, 8, 1, -3, -4, 3, -4, 3, 4, -5, -1, 6, -2, 4, 2, -4, -4, 15, 6, 5, -3, 6, 1, -7, -4, 2, -2, 7, 6, -3, -2, -2, 0, 2, 1, 13, 3, -4], "imageUrl": "https://upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Gradient_Descent_in_2D.webm/500px--Gradient_Descent_in_2D.webm.jpg", "imageLicense": "CC BY-SA 4.0", "imageArtist": "Gpeyre", "explanation": ["Imagine you're trying to decide if you should walk or drive to work. If it's sunny and warm, you might choose to walk. If it's raining or cold, you'd probably drive. But what if you can't decide? That's what happens in computers when they can't make a simple decision.", "Computers need rules to help them make decisions. The ReLU function helps by saying, \"If the input is positive, keep it; if not, ignore it.\" This way, computers can make decisions without getting stuck."], "example": "If the input is 5 (sunny and warm), ReLU keeps it as 5 (walk). If the input is -3 (raining and cold), ReLU ignores it, and the output is 0 (drive).", "whyItMatters": "ReLU helps computers make decisions by ignoring negative inputs, simplifying the choice."}, {"id": "93ed0584af08", "title": "Mutual information", "slug": "mutual-information", "headline": "Mutual information formula: I(X;Y) = \u2211_x\u2208X \u2211_y\u2208Y p(x,y) log(p(x,y)/(p(x)p(y)))", "summary": "Write the formula for mutual information I(X;Y)", "source": "Write the formula for mutual information I(X;Y)", "sourceUrl": "https://en.wikipedia.org/wiki/Mutual_information", "articleUrl": "https://en.wikipedia.org/wiki/Mutual_information", "publishedAt": "2026-06-12", "category": "learn", "cohortScore": 0.5, "embedding": [-6, -3, 6, -5, -1, 2, 6, 1, 10, -3, 0, -9, 6, 1, -1, -1, -10, -2, -4, -3, 12, -7, -8, -6, 8, 6, -1, 0, 0, -18, 0, 5, 2, -4, 3, 0, -3, 1, -2, 7, -4, 5, 7, 8, 4, -9, -7, -1, -2, -5, -1, 10, -4, -1, 3, 6, -3, 7, -1, 5, 7, 10, -11, 6, 7, -2, -8, 4, 5, 14, -2, 3, -1, 5, -1, 7, -5, -2, -8, -1, -14, 5, -2, 3, 0, -4, 6, -3, 7, -3, -3, 6, -2, 4, -2, -5, -1, 3, 6, 39, -5, 0, 3, -6, 0, -9, -4, -8, -5, 0, -4, -4, -2, -5, -4, -4, 8, 2, 6, -5, 5, -2, 4, 7, 8, 2, -2, 7, -4, 5, 3, 3, 5, -4, -3, -3, -6, -3, 4, 4, 4, -3, 8, -2, -5, 21, -6, -3, -5, 1, -6, 6, 4, -7, 8, -5, 5, -5, -5, 2, -7, -4, 5, 16, 2, -6, 4, 10, 3, -7, 2, 5, -1, -8, 2, -2, -1, 4, 2, -2, -2, -9, -4, -2, 1, 7, -6, 1, -2, 9, 0, 2, 2, 3, -11, -6, 1, -1, -13, -3, -2, -1, -3, -2, 2, -1, 5, -2, -2, -1, 0, 0, 2, -2, 0, 0, 3, 5, 3, 4, -4, -12, -5, -40, -9, 0, -3, 3, -8, 1, 0, -6, 13, 6, 4, -5, -6, 0, -1, 9, 1, 1, 4, 0, -2, -1, -4, 0, 2, 10, -4, 3, -1, 1, 3, -4, 2, 0, 3, -4, 7, -5, -10, -8, 6, 0, 3, -5, -1, 3, -7, -7, 0, 8, 9, -1, 1, 2, -3, 0, 1, -7, 2, -7, -6, -2, -4, -4, -6, -1, -8, 3, 3, -4, 12, 3, -6, 7, 0, 5, 2, -4, 1, 1, -10, 8, 8, 6, -3, 8, 5, -2, 1, -3, -4, 9, 2, 1, -7, -38, 2, -5, 5, 0, -2, 6, -2, -14, -1, 5, 4, -2, 1, 3, -3, 2, -3, 0, 3, 7, 2, 23, 4, 7, -1, -3, 4, 6, 4, 2, -6, 11, 1, 9, -1, -2, -2, 9, -4, 4, -2, -2, -5, 13, 11, -1, -4, -13, 6, -5, 3, -7, 5, 6, 10, -3, -2, 0, -4, -3, -1, 3, -5, 2], "explanation": ["Mutual information quantifies the amount of information obtained about one random variable by observing another. It is calculated using the joint probability distribution p(x,y) and the marginal distributions p(x) and p(y). The formula I(X;Y) = \u2211_x\u2208X \u2211_y\u2208Y p(x,y) log(p(x,y)/(p(x)p(y))) captures this relationship by summing over all possible values of X and Y.", "The formula I(X;Y) = \u2211_x\u2208X \u2211_y\u2208Y p(x,y) log(p(x,y)/(p(x)p(y))) uses the joint probability distribution p(x,y) and the marginal distributions p(x) and p(y) to measure the mutual dependence between X and Y. This formula is more general than the correlation coefficient and determines how different the joint distribution of (X,Y) is from the product of the marginal distributions of X and Y.", "The concept of mutual information is linked to entropy, which quantifies the expected amount of information held in a random variable. Mutual information measures the expected value of the pointwise mutual information (PMI), which is the amount of information obtained about one random variable by observing another. This concept was defined and analyzed by Claude Shannon in his landmark paper \"A Mathematical Theory of Communication.\""], "example": "Consider two random variables X and Y with joint distribution p(x,y) and marginal distributions p(x) and p(y). If X and Y are independent, then p(x,y) = p(x)p(y). In this case, the mutual information I(X;Y) = \u2211_x\u2208X \u2211_y\u2208Y p(x,y) log(p(x,y)/(p(x)p(y))) will be zero, indicating no mutual dependence between X and Y.", "whyItMatters": "Understanding the formula for mutual information is crucial for analyzing the dependence between random variables and quantifying the amount of information shared between them. This knowledge is fundamental in fields such as information theory, communication systems, and machine learning.", "imageUrl": "https://upload.wikimedia.org/wikipedia/commons/thumb/d/d4/Entropy-mutual-information-relative-entropy-relation-diagram.svg/1280px-Entropy-mutual-information-relative-entropy-relation-diagram.svg.png"}, {"id": "099ddc32c833", "title": "Jensen\u2013Shannon divergence", "slug": "jensen-shannon-divergence", "headline": "Jensen-Shannon divergence formula: D_JS(P||Q) = 1/2 * D_KL(P||(M)) + 1/2 * D_KL(Q||(M))", "summary": "Write the formula for Jensen-Shannon divergence", "source": "Write the formula for Jensen-Shannon divergence", "sourceUrl": "https://en.wikipedia.org/wiki/Jensen%E2%80%93Shannon_divergence", "articleUrl": "https://en.wikipedia.org/wiki/Jensen%E2%80%93Shannon_divergence", "publishedAt": "2026-06-12", "category": "learn", "cohortScore": 0.5, "embedding": [-19, 4, 0, -6, -5, 1, 2, -1, 9, -3, 8, -12, 3, -7, 3, 0, -8, 1, -9, -1, 9, -5, 0, -9, -2, 3, 3, 4, 6, -23, -2, -2, -5, -7, -4, -1, -1, -2, 1, 5, -4, 1, -2, -2, 2, -3, -15, 4, 0, 0, 1, 6, -2, 0, 10, 2, 5, 6, 6, 5, 4, 7, -14, 6, 0, 3, -5, -10, 1, 3, 1, 0, -6, 5, 7, 0, -3, -5, -1, -4, -1, 2, -3, -3, -2, 3, 3, -3, 0, -1, -4, 6, -3, 0, -10, 1, 3, 0, 8, 43, 3, 3, -2, -4, 0, -7, -1, -1, 4, -6, -2, 0, -1, -10, -2, -4, 7, -1, 4, 1, -1, 2, 6, 4, 9, 5, -5, 7, -4, 11, 4, -5, 3, -4, 0, -3, -8, -2, 5, 4, 1, 0, 2, 7, 3, 15, -11, -2, -5, -3, 7, 6, -2, -4, 11, 0, -1, 4, -4, -3, -4, -6, 5, 17, 0, 2, 4, 2, 3, -8, 1, 0, -5, 1, 3, 1, -5, 0, 6, -7, -3, -7, -7, -1, -1, 5, -4, -3, 1, 3, 6, -5, -2, 1, -7, 0, -9, 1, 0, -4, 7, 1, -3, 5, 0, 7, 1, -1, -6, 4, -4, -5, -5, -5, 2, 6, 8, 5, -4, 4, -3, -7, -7, -37, -1, 0, -4, 1, 0, 5, -6, 2, 4, 2, 3, -5, -2, -2, -3, 3, -1, -1, 4, 1, -1, -2, -2, 4, 2, 14, -2, 15, -4, 0, -1, -4, 4, 2, -2, -5, 1, -7, -11, -4, 1, -3, 0, -3, -3, -11, 0, 5, 2, 0, 6, 13, -1, 3, 3, -3, -2, -8, -3, -3, -2, 6, -4, -2, -1, 1, -8, 3, 0, -8, 10, 3, -2, 5, 0, -6, 4, -1, 2, 5, -3, 9, -3, 6, 2, 3, 3, -1, -2, -3, 0, 1, 5, -4, -1, -38, 1, -2, 1, 1, 3, 9, -13, -15, 0, -3, 9, -1, 2, 7, -2, 7, -4, 11, 6, 9, 3, 23, 3, -6, 2, 8, 2, 6, -3, 0, 4, 8, 2, 6, 7, -4, 5, 5, -1, 16, -4, 2, -4, 18, 0, 1, -7, -3, -3, -6, 7, 3, 1, 7, 7, -5, -3, -7, -11, -2, -5, 1, 0, 6], "explanation": ["The Jensen-Shannon divergence formula is a symmetric measure of similarity between two probability distributions P and Q. It is derived from the Kullback-Leibler divergence by averaging the two distributions (M = 1/2 * (P + Q)) and then calculating the divergence from each distribution to the average.", "The formula D_JS(P||Q) = 1/2 * D_KL(P||(M)) + 1/2 * D_KL(Q||(M)) ensures that the divergence is always finite and symmetric, unlike the Kullback-Leibler divergence. This makes it a more robust measure for comparing probability distributions.", "The Jensen-Shannon distance, which is the square root of the Jensen-Shannon divergence, provides a metric for quantifying the similarity between distributions. A smaller Jensen-Shannon distance indicates greater similarity between the distributions."], "example": "Consider two probability distributions P and Q, where P = [0.1, 0.9] and Q = [0.8, 0.2]. The average distribution M = [0.45, 0.65]. The Jensen-Shannon divergence D_JS(P||Q) = 1/2 * D_KL(P||(M)) + 1/2 * D_KL(Q||(M)) can be calculated using the Kullback-Leibler divergence formula.", "whyItMatters": "Understanding the Jensen-Shannon divergence formula is crucial for accurately measuring the similarity between probability distributions in various fields such as machine learning, information theory, and statistics.", "imageUrl": "https://upload.wikimedia.org/wikipedia/commons/4/4d/Edward_Larsson_1885_I.jpg", "imageLicense": "Public domain", "imageArtist": "Edward Larsson"}, {"id": "05bf60c50a8b", "title": "Dot product", "slug": "dot-product", "headline": "Dot product = sum of products of corresponding entries", "summary": "Write the equation for dot product of two vectors", "source": "Write the equation for dot product of two vectors", "sourceUrl": "https://en.wikipedia.org/wiki/Dot_product", "articleUrl": "https://en.wikipedia.org/wiki/Dot_product", "publishedAt": "2026-06-12", "category": "learn", "cohortScore": 0.5, "embedding": [-11, -7, 0, -6, -6, -6, 3, 4, 1, -1, -1, -13, 7, -8, 1, -4, 2, 6, -4, 0, 1, -8, -10, -4, 12, 14, 1, -2, -5, -23, 6, 0, 3, 0, -1, 4, 1, 0, -6, -11, 1, -6, -1, -4, 1, 5, -10, -4, 3, -2, -2, -4, -1, -1, -1, 1, 0, 0, 0, 11, 8, -1, -18, 8, 4, 5, -2, -5, 2, 13, 0, 6, -5, 3, -2, 3, -8, -4, -4, 2, 1, 1, -5, 10, -1, 4, 8, -6, 10, -4, -1, -1, -1, 1, -1, 1, 6, -4, 10, 40, 3, 0, -2, -5, -6, -4, -6, -5, -3, -3, 2, 1, 2, -11, 9, 0, 2, 4, -1, -2, 1, -3, 3, 0, -2, -4, 5, 11, 0, 8, 7, 2, -7, 4, 2, 3, -9, 1, -5, 3, 5, -4, 4, 1, 4, 22, -3, -7, 2, -7, 1, 2, 2, 8, 2, 2, -2, -5, -2, -4, -4, 2, -3, 4, 2, -3, 6, 5, 3, -5, 1, -3, -2, -3, 3, 2, -6, -1, 6, 0, 3, 3, -4, 5, 1, -4, -4, 0, -2, 4, -1, 1, -3, 4, -11, -4, 1, -4, -5, -1, 8, -2, -2, 3, 4, 2, 4, -7, 2, -2, 0, -5, 0, -4, -4, 6, 3, 2, 2, 5, -3, -13, -8, -35, -7, 6, -6, 3, -5, 2, 2, -6, 6, 11, 8, -1, -9, -4, -4, -4, 9, 7, 2, -2, -4, 13, 1, 4, -3, 23, 2, -1, -2, 3, -2, -7, 5, 5, 2, -3, 11, -2, -11, 0, 3, -4, 0, 1, -2, -5, 1, -2, 7, 2, 4, 12, -1, 1, -3, -4, 7, -9, 4, -2, -9, 3, 5, 0, 0, 11, -10, 4, 4, -1, 5, -2, -2, 4, -4, -1, 12, -3, -3, 2, -2, 3, 8, 8, -2, 2, 4, -5, 4, -5, -1, 3, 11, -8, 1, -36, 0, 1, 1, -2, -3, 7, -6, -11, -1, -2, 2, 1, 2, 4, -4, 6, -7, 4, -5, 10, 1, 22, -7, 0, -8, 7, -6, 8, 5, -2, -5, 17, -1, -2, 3, -10, 1, 6, 5, 2, 1, -8, 4, 7, 7, -1, -6, -3, 1, 0, 3, 0, -1, -3, 2, -8, -8, -1, 11, -6, -3, 2, 1, -1], "explanation": ["The dot product of two vectors is calculated by multiplying their corresponding entries and summing the results. This operation results in a scalar value, not a vector. The dot product is essential for determining the angle between vectors and for projecting one vector onto another."], "example": "For vectors A = [a1, a2] and B = [b1, b2], the dot product A \u00b7 B = a1*b1 + a2*b2. If A = [2, 3] and B = [4, 5], then A \u00b7 B = 2*4 + 3*5 = 8 + 15 = 23.", "whyItMatters": "Understanding the dot product is crucial for applications in physics, engineering, and computer science, where vector operations are fundamental.", "imageUrl": "https://upload.wikimedia.org/wikipedia/commons/8/83/Piet_Mondriaan.jpg", "imageLicense": "Public domain", "imageArtist": "AnonymousUnknown author"}, {"id": "13b3c0cdd74d", "title": "Euclidean distance", "slug": "euclidean-distance", "headline": "Euclidean distance formula: \u221a((x2 - x1)\u00b2 + (y2 - y1)\u00b2)", "summary": "Write the formula for Euclidean distance", "source": "Write the formula for Euclidean distance", "sourceUrl": "https://en.wikipedia.org/wiki/Euclidean_distance", "articleUrl": "https://en.wikipedia.org/wiki/Euclidean_distance", "publishedAt": "2026-06-12", "category": "learn", "cohortScore": 0.5, "embedding": [-8, -3, 9, -3, -11, -1, -3, 8, 4, -1, 1, -11, 2, -3, 0, -10, -7, 6, -10, 1, 17, -5, -1, -3, 3, 17, -2, -1, 3, -20, 4, 1, 4, 1, -3, -1, -6, 5, -4, -2, 6, 0, 7, -1, -4, -4, -14, 4, 1, -1, 6, -5, -5, 1, 8, -3, 2, 7, 2, 4, 6, 6, -14, 7, -3, 3, -4, -6, -1, 15, -2, 4, 0, 6, 1, 2, -7, -11, -1, 1, -1, 0, -7, 9, 1, 0, 3, -2, 8, 3, -3, 2, -2, -1, -7, -19, -3, 0, 5, 35, 4, 3, -1, 0, -3, -2, 1, -13, 2, -2, -3, 2, -4, -6, 4, -9, 7, 2, 0, 0, -3, 2, -3, -2, 0, -1, 3, 6, 0, 14, 10, -1, -1, 2, 0, 0, 3, 0, -3, 7, 4, -4, 6, 8, 14, 16, -4, -4, -4, -3, 4, 0, 0, -7, 7, 2, 7, 1, -6, 0, -2, -4, -2, 10, 3, -5, 9, 3, 3, 2, 9, -4, 0, 0, 7, 2, -8, 7, 7, 0, 5, -3, -1, -4, 3, -1, -5, 0, -2, 2, 3, -7, -10, -2, -4, -3, -3, 0, -5, 3, 13, -5, 3, -6, 9, -2, 15, -11, -7, 5, 1, -7, -2, -6, -3, 3, 6, 5, 1, 1, -1, -5, -6, -33, -3, 2, 1, 2, -3, -1, 0, -5, 7, 8, -1, -3, 2, -3, -7, -1, 3, 3, 0, 1, -3, -1, -2, -5, -3, 19, -7, 3, -7, 0, -6, -8, 3, -1, -6, -3, 4, -7, -9, -7, 7, -3, 1, -3, 4, 1, -6, 5, 7, 1, 5, 9, 2, -1, -1, -3, 4, -6, 0, -7, -6, 5, 4, 0, -1, 0, -11, 4, 4, -1, 4, 0, -3, 8, -7, 6, 12, 4, 2, 3, 0, 2, -7, 1, 1, 4, 7, -1, -2, -5, -1, -1, 2, -3, -7, -35, 6, 5, 5, -4, -5, 10, -2, -14, -5, -2, 6, -2, -3, 2, -4, 7, -4, -2, 5, 15, -4, 18, -4, 3, -1, 0, 5, 14, -3, -4, -5, 6, -1, 1, 5, -1, 6, 12, -2, 8, -9, -5, 2, 10, 7, -5, -6, -4, -5, -7, 5, -3, 7, -2, 6, -5, -8, -1, -4, -5, -3, 4, -12, 6], "explanation": ["The Euclidean distance formula is derived from the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. This theorem is applied to calculate the distance between two points in a Euclidean space by treating the difference in their coordinates as the legs of a right triangle, and the distance as the hypotenuse.", "The formula for Euclidean distance between two points (x1, y1) and (x2, y2) in a Cartesian plane is \u221a((x2 - x1)\u00b2 + (y2 - y1)\u00b2). This equation calculates the straight-line distance between the points, reflecting the shortest path connecting them. The square root function ensures that the distance is non-negative, as distances cannot be negative.", "Understanding the Euclidean distance formula is crucial for various applications in mathematics, physics, and computer science. It is used in fields such as geometry, navigation, and machine learning for tasks like clustering, classification, and optimization. The formula provides a fundamental tool for measuring and comparing distances in a Euclidean space."], "example": "Calculate the Euclidean distance between points A(3, 4) and B(7, 1).\nUsing the formula: \u221a((7 - 3)\u00b2 + (1 - 4)\u00b2) = \u221a(4\u00b2 + (-3)\u00b2) = \u221a(16 + 9) = \u221a25 = 5", "whyItMatters": "The Euclidean distance formula is essential for accurately determining the straight-line distance between two points in a Euclidean space, which is fundamental in various scientific and mathematical applications.", "imageUrl": "https://upload.wikimedia.org/wikipedia/commons/thumb/5/55/Euclidean_distance_2d.svg/1280px-Euclidean_distance_2d.svg.png"}, {"id": "cded188ebfb5", "title": "Distance transform", "slug": "distance-transform", "headline": "Manhattan distance formula: |x1 - x2| + |y1 - y2|", "summary": "Write the formula for Manhattan distance", "source": "Write the formula for Manhattan distance", "sourceUrl": "https://en.wikipedia.org/wiki/Distance_transform", "articleUrl": "https://en.wikipedia.org/wiki/Distance_transform", "publishedAt": "2026-06-12", "category": "learn", "cohortScore": 0.5, "embedding": [-5, -7, 11, -5, -8, 1, -5, 2, 7, -3, -1, -8, -2, 1, 4, -11, -6, 3, -4, 1, 13, -4, -8, -4, 5, 14, 0, 2, -1, -22, 2, 1, 8, 1, 1, 0, -6, 3, -5, 3, 3, 5, 6, 4, -4, -2, -11, -3, 3, -3, 6, -1, -9, 5, 9, -2, 0, 1, 0, 9, 0, 2, -15, 6, 4, -3, 2, -4, -3, 17, -2, 1, 1, 8, 1, -1, -4, -9, 1, 3, -2, -3, -6, 4, 3, 3, -3, 0, 6, 4, -4, 2, -5, -3, -11, -12, 6, 2, 8, 37, 7, 2, 1, 0, 0, -2, -1, -16, 1, -4, 2, -3, -1, -5, 3, -6, 11, 2, -1, -4, -4, 1, -1, 3, -3, -2, 5, 8, -1, 12, 4, 4, -7, 0, 1, 0, 0, -3, -5, -1, 3, -1, 3, 1, 10, 16, -8, -4, 0, -4, 2, -7, 1, -11, 2, 5, 6, -2, -6, 5, -3, -1, 1, 5, 5, -9, 9, 7, 3, -2, 4, -1, 2, -1, 10, 0, -7, 5, 6, 5, -2, -1, -1, -5, 7, 2, -5, -1, -3, 10, 3, -6, -7, -1, -5, -4, -3, 4, 1, -3, 13, -1, -3, -8, 4, -3, 16, -7, 0, 8, 1, -6, 4, 0, 4, -1, 2, 3, 3, 8, 2, -4, -7, -36, -3, 6, -4, -3, -8, -3, -2, -2, 5, 14, -3, 3, -2, -5, -3, -2, 2, 5, 0, 3, 3, -7, -1, 0, -4, 15, -1, 2, -2, 1, -5, -7, 6, -4, -3, 2, 6, -6, -8, -11, 5, 3, 2, -5, 2, -2, -2, 3, 4, 4, 3, 2, -4, -2, -5, -4, 6, -10, -1, -5, -4, 1, 1, 2, 4, 1, -12, 3, 8, 3, 4, 4, 1, 7, -5, 5, 6, 1, -1, 1, 3, 10, -2, 1, 2, 8, 6, -1, 0, -7, 2, 3, -4, -4, -10, -34, 2, 0, 4, -9, -11, 6, -6, -8, -1, -2, 9, 2, -8, 3, -8, 3, 8, 0, 1, 16, -4, 22, -6, 3, 3, -2, 4, 8, -5, 0, -5, 7, -1, -2, 3, -5, 6, 9, -4, -1, -6, -5, -5, 16, 7, -6, 0, -8, -3, -5, 3, -2, 6, 4, 9, -5, -4, -6, -1, -2, 0, 7, -11, 5], "explanation": ["Manhattan distance, also known as City block distance, measures the distance between two points in a grid-based path. It is calculated as the sum of the absolute differences of their Cartesian coordinates."], "example": "If point A is at (3, 4) and point B is at (1, 1), the Manhattan distance is |3 - 1| + |4 - 1| = 2 + 3 = 5.", "whyItMatters": "Understanding Manhattan distance is crucial in grid-based pathfinding algorithms, such as those used in urban planning and video game navigation.", "imageUrl": "https://upload.wikimedia.org/wikipedia/commons/f/f7/Distance_Transformation.gif"}, {"id": "872fb7297053", "title": "Minkowski spacetime", "slug": "minkowski-spacetime", "headline": "Minkowski distance formula: D = (\u03a3 |x_i - y_i|^p)^(1/p)", "summary": "Write the formula for Minkowski distance and how p changes its behavior", "source": "Write the formula for Minkowski distance and how p changes its behavior", "sourceUrl": "https://en.wikipedia.org/wiki/Minkowski_spacetime", "articleUrl": "https://en.wikipedia.org/wiki/Minkowski_spacetime", "publishedAt": "2026-06-12", "category": "learn", "cohortScore": 0.5, "embedding": [-10, 2, 9, -6, -10, 2, 0, 3, 5, -8, 6, -9, -3, -1, -4, -5, -7, 5, -12, 5, 10, -6, -4, -2, 11, 14, 6, 2, -1, -26, -1, -5, 6, -7, -3, 0, -7, 0, 3, 9, 2, 2, 4, 3, -2, -6, -9, -5, -8, -1, -4, 1, -9, 2, 5, -1, 3, 3, 7, 2, 3, 2, -13, 4, 7, 0, -9, -7, -4, 9, -6, 4, 0, 5, 5, -3, -6, -4, 0, -1, -6, 3, -11, 5, 2, 3, -1, -3, 5, 0, -2, 1, -2, 2, -10, -10, 2, -1, 8, 39, -2, 5, -5, 6, 0, -1, 4, -5, -3, 3, -3, -2, -5, -4, -2, -11, 6, 4, 1, 0, -1, 8, -4, 1, 2, 5, 1, 8, -3, 10, 9, 0, 4, 1, 5, -1, -5, 0, 6, -1, 0, 1, 7, -2, 10, 21, -10, -2, 2, 3, 3, 0, -7, -2, 3, 0, 3, 0, -3, 0, -10, 0, 8, 8, 4, 3, 5, 5, 2, -7, 1, 2, -1, -7, 6, 1, -5, 1, 3, 5, 3, -1, 1, -7, 0, 5, -5, -1, 3, 7, 6, -10, -5, -4, -6, -3, -5, -1, -7, 3, 12, 1, -2, -2, 3, 1, 11, -4, -1, 8, -4, -12, -4, -1, 3, 3, -1, 2, -1, 5, -7, -5, -5, -34, 0, -2, -1, 3, -7, 2, 1, -2, 4, 11, -4, -5, -4, -4, -4, 1, -4, -1, -4, -1, -1, -7, -2, -1, -4, 11, -1, 8, -6, -3, -6, -10, 7, -1, 0, -2, -1, -6, -5, -5, 4, -1, 7, -10, -1, 3, 2, 5, 12, 0, 5, 4, -1, -1, -6, 1, 3, -7, 3, 0, -1, 8, -2, 2, 3, 2, -9, 8, 7, 3, 11, -4, -3, 10, -4, 7, 16, -1, -3, 10, 5, 3, -3, 3, 0, 7, 1, -6, -1, -8, 2, 3, 8, -4, -3, -35, 3, 1, 3, -4, -2, 1, -1, -10, -6, -1, 5, -1, 5, 1, 0, 2, -4, 0, 0, 12, -1, 26, -4, 0, -8, 4, 6, 10, 4, -4, -1, 8, 0, -1, 3, -1, 0, 7, -3, 5, -11, 1, -5, 14, 1, -4, -1, -6, 0, -7, 1, 0, -1, -1, 10, 1, -3, 0, -2, 2, -2, 8, -12, 6], "explanation": ["The Minkowski distance formula is a generalization of various distance measures, including Euclidean distance (when p=2) and Manhattan distance (when p=1).", "Minkowski distance combines the differences between corresponding coordinates raised to the power of p, summed together, and then takes the p-th root of the total sum. This formula is versatile and can represent different types of distances depending on the value of p.", "When p=2, Minkowski distance simplifies to the Euclidean distance, which is commonly used in geometry and physics. As p approaches 1, it becomes the Manhattan distance, often used in urban planning and computer science for grid-like structures."], "example": "Consider two points in a 2D space: A(1, 2) and B(4, 6). For Euclidean distance (p=2), D = ((1-4)^2 + (2-6)^2)^(1/2) = (9 + 16)^(1/2) = 5. For Manhattan distance (p=1), D = |1-4| + |2-6| = 3 + 4 = 7.", "whyItMatters": "Understanding Minkowski distance helps in choosing the appropriate distance measure for various applications, such as clustering, classification, and spatial analysis.", "imageUrl": "https://upload.wikimedia.org/wikipedia/commons/thumb/c/c5/De_Raum_zeit_Minkowski_Bild.jpg/1280px-De_Raum_zeit_Minkowski_Bild.jpg"}, {"id": "3aa8d2985ba7", "title": "Mahalanobis distance", "slug": "mahalanobis-distance", "headline": "Mahalanobis distance formula: D^2 = (x - \u03bc)'\u03a3^(-1)(x - \u03bc)", "summary": "Write the formula for Mahalanobis distance", "source": "Write the formula for Mahalanobis distance", "sourceUrl": "https://en.wikipedia.org/wiki/Mahalanobis_distance", "articleUrl": "https://en.wikipedia.org/wiki/Mahalanobis_distance", "publishedAt": "2026-06-12", "category": "learn", "cohortScore": 0.5, "embedding": [-11, -1, 4, 0, -10, 3, 3, -2, 6, -2, 10, -12, 7, -2, 1, -10, 1, 4, -12, 2, 16, 7, -2, -3, 10, 18, -1, 3, -6, -22, -3, -2, 7, -1, -3, -3, -3, 2, -1, -1, 5, -2, 7, -2, -6, -5, -8, 4, -2, -3, 2, -3, -10, 5, 3, 3, 3, 0, 4, 4, 4, 4, -13, 3, 2, -3, 2, -7, -2, 9, -1, -1, 7, 6, 1, -1, -4, -8, -2, 0, -3, 1, -3, 1, -4, 5, 5, -5, 8, 4, 3, 2, -2, -2, -16, -15, -3, -4, 8, 38, 3, -1, -3, 2, -2, 2, 1, -6, -2, -3, 2, -2, -6, 0, -3, -2, 6, -2, -3, 4, -4, 0, -1, -2, 9, 1, 4, 6, -1, 13, 7, 2, -6, 4, 4, -2, -1, -2, 2, 2, 3, -1, 8, 9, 9, 13, -8, -7, 4, 1, 4, -2, 0, 3, 6, 4, 3, 2, -5, 0, -3, -5, 2, 10, 2, -6, 7, 5, -4, 1, 11, -3, -4, -6, 11, 4, -1, 6, 10, 6, 5, 1, -2, -8, 5, -1, -6, 1, 0, 4, -2, -5, -4, 0, -7, -4, -4, 0, -5, 6, 10, -4, 0, -4, 9, -2, 11, -6, -4, 5, -2, -8, -5, -3, -5, 2, 6, 4, 0, 3, 0, -8, -8, -34, 0, -1, -4, 1, -6, -1, 0, 0, 2, 14, -2, 0, -6, -11, -2, -3, -2, 4, -1, 2, 2, -4, 3, 3, 3, 17, -7, 13, -6, 0, -1, -9, 3, -3, -10, -6, 3, -3, -10, -3, 6, -3, 4, 0, 5, -3, 1, -1, 2, 1, 6, 7, 1, 1, 0, -6, 2, -7, 1, -5, -6, 4, -1, -4, -2, 3, -11, 4, 6, 2, 6, -6, -5, 7, -3, 5, 2, 2, 0, 6, 2, 3, -1, 3, 2, 7, 5, -1, -1, -8, -9, 4, 11, -3, -5, -33, 2, -1, 3, -11, -6, 5, -6, -13, 0, -6, 6, 2, 2, 0, -6, 4, 0, -2, -1, 9, -2, 21, 2, -2, 0, 4, 0, 15, 0, -2, -4, 10, -5, 1, 5, -6, 8, 7, -1, 4, -8, -5, -4, 17, 5, -2, -4, -5, -3, -7, 1, -2, 9, 2, 9, -5, -6, -5, -3, -7, -6, 7, -12, 5], "explanation": ["The Mahalanobis distance formula is a multivariate measure that quantifies the distance between a point and a probability distribution. It generalizes the concept of standard score distance, taking into account the covariance among variables. This distance is zero for points within the distribution and increases with the distance from the mean."], "example": "Given a point P with coordinates (x1, x2) and a distribution D with mean \u03bc = (\u03bc1, \u03bc2) and covariance matrix \u03a3, the Mahalanobis distance D^2 is calculated as D^2 = [(x1 - \u03bc1), (x2 - \u03bc2)]'\u03a3^(-1)[(x1 - \u03bc1), (x2 - \u03bc2)].", "whyItMatters": "Understanding the Mahalanobis distance formula is crucial for applications in multivariate statistics, such as clustering and classification, where it helps measure similarity and differentiate between groups.", "imageUrl": "https://upload.wikimedia.org/wikipedia/commons/2/25/Kepler-solar-system-2.png", "imageLicense": "Public domain"}, {"id": "3878b8839b8a", "title": "Rotation matrix", "slug": "rotation-matrix", "headline": "Determinant of a 2x2 matrix: ad - bc", "summary": "Write the equation for matrix determinant of a 2x2 matrix", "source": "Write the equation for matrix determinant of a 2x2 matrix", "sourceUrl": "https://en.wikipedia.org/wiki/Rotation_matrix", "articleUrl": "https://en.wikipedia.org/wiki/Rotation_matrix", "publishedAt": "2026-06-12", "category": "learn", "cohortScore": 0.5, "embedding": [-12, 7, -5, -7, -3, -7, 5, 6, 1, -1, 4, -10, 8, -3, 3, 3, -3, 8, -2, 0, -2, -2, -3, -9, 15, 13, -3, 5, -2, -26, -3, 4, 9, -4, 2, -4, -2, 3, -2, -4, -2, 2, 4, 7, -4, 6, -3, -1, 5, -1, -3, 4, -2, 2, 11, -1, -5, -2, -8, 7, 6, 0, -19, 11, 9, 8, -1, -6, 2, 13, -2, 1, -2, -3, 3, -1, -2, -2, 0, -4, -5, 0, 2, 5, -2, -1, 3, -4, 5, -3, 3, 0, -3, 1, -4, -6, 1, 1, 3, 38, -2, 0, -2, 4, -3, -9, -3, -5, -7, -6, 1, 3, 4, -5, 5, -2, 0, 9, -2, -4, -3, -4, 6, -2, 5, -3, -6, 9, 1, 8, -1, 4, 8, -1, 2, -6, 2, 2, -3, 0, 9, -4, 6, 7, -2, 14, -3, -5, 0, 3, 2, 5, -3, 3, 5, 1, 8, -3, -12, 2, -4, -1, -2, 6, 6, 1, 3, 3, 4, -3, 5, -3, -7, -6, 5, -1, -5, -1, 9, -1, 0, -3, 7, 7, 7, -5, -7, -3, 2, 1, -2, 0, -12, 6, -9, -5, 2, 0, 0, 3, 9, -1, -5, 2, 2, -2, 12, -4, -9, 6, -2, -2, 1, 0, -7, 3, -5, 1, 1, 3, 2, 0, -12, -38, 2, 0, -1, 7, -10, 9, -7, -5, 8, 4, 4, 7, 0, -3, -9, -2, -2, 1, 3, -5, -7, 6, 15, 1, 4, 19, 2, 7, 3, -1, 0, 0, -1, -3, -4, -5, 7, -4, -8, 7, 1, -6, -3, 1, -2, 3, -2, -2, 2, 5, 3, 3, -4, 0, 1, -7, 3, -7, -2, -2, -9, -1, -3, -7, 6, 1, -14, -6, 1, 1, 7, 5, -8, 5, -11, 4, 8, 0, -8, -1, -4, 1, 2, 7, 0, 6, -2, -1, 1, -7, -1, 3, 9, -5, 2, -34, -6, 3, 0, 1, -4, 9, -9, -9, -6, -8, 7, 6, 3, 3, -3, 8, -7, -2, -1, 4, -2, 22, -4, 5, -5, -3, 2, 11, -2, 6, -3, 10, -6, 3, 4, -8, 9, 8, 1, 0, 0, -8, -9, 8, 2, 0, 1, -3, 0, 0, -1, 4, 4, -3, -1, -9, -9, 0, 3, -6, 3, 7, -4, 9], "explanation": ["The determinant of a 2x2 matrix is calculated using the formula ad - bc, where a, b, c, and d are the elements of the matrix. This formula is essential for understanding various properties of matrices, such as invertibility and the area scaling factor of linear transformations. Determinants also play a crucial role in solving systems of linear equations and in understanding eigenvalues and eigenvectors."], "example": "Consider the matrix A = [ [2, 3], [1, 4] ]. The determinant of A is calculated as follows: det(A) = (2 * 4) - (3 * 1) = 8 - 3 = 5.", "whyItMatters": "Knowing the determinant helps in determining if a matrix is invertible and understanding the scaling effect of linear transformations.", "imageUrl": "https://upload.wikimedia.org/wikipedia/en/thumb/2/2f/Franti%C5%A1ek_Kupka%2C_1912%2C_Amorpha%2C_fugue_en_deux_couleurs_%28Fugue_in_Two_Colors%29%2C_210_x_200_cm%2C_Narodni_Galerie%2C_Prague.jpg/1280px-Franti%C5%A1ek_Kupka%2C_1912%2C_Amorpha%2C_fugue_en_deux_couleurs_%28Fugue_in_Two_Colors%29%2C_210_x_200_cm%2C_Narodni_Galerie%2C_Prague.jpg", "imageLicense": "PD-US", "imageArtist": "Franti\u0161ek Kupka"}, {"id": "6c975edec0d0", "title": "Standard deviation", "slug": "standard-deviation", "headline": "Standard deviation (\u03c3) is the square root of variance", "summary": "Write the formula for standard deviation", "source": "Write the formula for standard deviation", "sourceUrl": "https://en.wikipedia.org/wiki/Standard_deviation", "articleUrl": "https://en.wikipedia.org/wiki/Standard_deviation", "publishedAt": "2026-06-12", "category": "learn", "cohortScore": 0.5, "embedding": [-5, -6, 6, -4, 3, -3, 2, 4, 4, 0, 7, -4, 11, -3, -5, -2, -6, 1, -3, 4, 15, 0, -1, -5, 5, 4, 0, -10, -4, -23, 2, 1, 6, -2, -6, -3, -10, 0, 5, -4, 4, -4, 5, 1, 1, -7, -5, 6, 0, -1, -2, -6, -5, 4, 5, 6, 4, 0, 6, 6, 9, 4, -21, 0, 2, 4, -4, -5, -6, -2, -1, -4, -1, 6, 2, 3, -6, -5, -6, 5, -5, 3, -3, 7, -4, 1, 8, 0, 13, -2, 4, 0, -2, -2, -5, -4, -4, -4, 8, 36, 2, 5, -6, 1, -2, -13, 4, -3, 7, -4, 0, -1, -4, -16, -6, -11, 1, -3, -1, 2, 2, 1, -1, -6, 14, 0, 0, 8, -5, 7, 4, 2, 2, 0, 2, 8, -5, 6, 4, 0, 4, -8, 3, 2, 0, 14, -8, -2, 4, -1, 4, 4, 0, -1, 10, -4, 2, 4, -8, -8, -11, -8, 0, 9, 0, 0, 6, 8, 2, -7, 16, -2, -1, -2, 9, 3, 0, 0, 8, -2, 4, -1, 5, -1, 1, 2, -11, -5, -2, 2, 3, -5, -10, 5, -3, 2, -3, 4, -4, 0, 3, 1, -5, -4, 8, 3, 1, -9, -5, 8, -2, -3, 2, -1, -7, 3, 2, 6, 4, 8, 1, -3, -11, -36, -4, 5, 1, 8, 0, 6, -3, -6, 1, 8, 6, -4, -8, -4, -7, -1, -3, -4, 6, 1, -2, -1, -1, -4, 7, 17, -6, 5, -6, 1, 2, 3, 8, 2, -5, -1, 6, -8, -6, 3, 6, -4, -4, -3, -3, 1, -1, -6, 0, -5, 4, 4, 0, 6, 1, -9, 4, -2, -5, 3, 0, 12, -4, -5, -3, 3, -6, 1, -1, -1, 8, -5, -4, 5, 1, 1, 1, -2, 5, 3, -4, 1, 2, 7, 3, 4, 3, 3, 6, -7, -2, 7, -1, -10, -2, -36, -1, -2, 2, 6, -11, 1, -6, -14, 7, -6, 5, 2, 4, 1, -3, 2, -4, 4, -1, 13, 1, 24, 4, -2, 4, 7, 2, 12, -3, 0, -4, 15, 4, 4, 3, -5, 4, 3, -6, 2, -5, -3, 1, 16, -7, 1, -7, 0, -2, -9, 8, -5, 2, -1, 1, -4, -4, -3, 0, -1, -8, 2, 7, 2], "explanation": ["Standard deviation measures the variation of values around their mean. It is denoted by the Greek letter \u03c3 (sigma) and is expressed in the same units as the data. Standard deviation is a crucial concept in statistics as it quantifies the amount of dispersion or spread in a dataset."], "example": "If the mean of a dataset is 10 and the variance is 4, the standard deviation (\u03c3) would be \u221a4 = 2.", "whyItMatters": "Understanding standard deviation is essential for interpreting data variability and making informed decisions based on statistical analysis.", "imageUrl": "https://upload.wikimedia.org/wikipedia/commons/thumb/8/8c/Standard_deviation_diagram.svg/1280px-Standard_deviation_diagram.svg.png"}, {"id": "5c6a43925339", "title": "Covariance matrix", "slug": "covariance-matrix", "headline": "Covariance formula: Cov(X, Y) = E[(X - E[X])(Y - E[Y])]", "summary": "Write the formula for covariance between X and Y", "source": "Write the formula for covariance between X and Y", "sourceUrl": "https://en.wikipedia.org/wiki/Covariance_matrix", "articleUrl": "https://en.wikipedia.org/wiki/Covariance_matrix", "publishedAt": "2026-06-12", "category": "learn", "cohortScore": 0.5, "embedding": [-6, -1, 9, -2, -1, -1, 3, -2, 8, -2, -2, -8, 1, -1, -3, -8, -6, 9, -10, 4, 4, -3, -4, -1, 9, 10, -4, -1, -1, -21, -4, -4, 3, -3, -3, 0, -3, 2, 0, 1, -3, 2, 4, 1, -6, -3, -10, 1, -7, -3, 0, 1, -3, 2, 1, 13, -4, 5, 4, 5, -2, 7, -19, 9, 3, 3, 0, -2, 1, 10, -3, 1, -4, 5, 2, 1, -7, -1, -4, -4, -1, 12, -1, 4, -1, -2, 3, -3, 2, 1, -5, 3, -1, 1, -4, -7, 6, 3, 5, 39, 0, 0, 1, 2, 5, -10, -9, -8, 5, 0, 0, 4, -4, -15, -12, -11, 5, 0, 3, -10, 5, 3, 4, 6, 8, 2, 4, 10, 0, 7, 4, 3, 2, 3, -2, 5, -5, 1, 0, 3, 2, -1, 6, -6, 4, 14, -6, 3, 0, -2, 0, 6, -1, -1, -1, 10, 0, -3, -8, -3, -9, -1, 1, 9, -2, -1, 7, 10, 5, 1, 3, 3, -3, -4, 11, 3, -3, 6, 6, 2, 0, -5, -3, 10, 2, 11, -7, -11, -4, 1, 7, -7, -3, 1, -10, 2, 0, 3, -1, 5, 7, 1, 5, 0, -4, -5, 7, -3, -1, 7, -5, -5, -2, 1, -6, 9, 2, 6, 1, 5, -5, -12, -5, -39, -2, -2, 2, 1, -5, 1, -2, -4, 3, 7, 9, -6, -8, -2, -2, 0, -1, -3, 4, -5, -9, -4, -2, 6, -2, 12, 2, 6, -4, -4, -6, 0, 12, 2, 0, 0, 13, -6, -10, 2, 5, 6, 8, -7, -2, -3, 5, 2, 5, 6, 3, 4, -3, -1, 0, -6, 8, -2, -3, -1, -1, 2, 2, -4, -7, 7, -11, 3, 4, -8, 10, -3, -2, 6, -3, 4, 5, -5, 6, -1, -3, 2, 2, 13, -3, 1, 5, 8, 4, -9, -5, -1, 1, -7, 4, -33, -1, -2, 7, 2, -10, 4, -14, -14, -3, -2, 3, 1, 8, 5, 5, 3, -10, 1, 0, 6, -2, 20, -10, 3, -2, -3, 3, 7, 0, -6, -3, 10, 5, 4, 0, -7, -2, 15, -4, 3, 6, 4, -4, 13, 2, 1, -7, -5, 0, -3, 5, -4, 3, 3, -1, -7, -6, -1, -6, -4, -5, 6, -7, -2], "explanation": ["Covariance measures the joint variability of two random variables. It quantifies how much the variables X and Y change together. Covariance is calculated as the expected value of the product of their deviations from their respective means."], "example": "Suppose X represents the number of hours studied and Y represents the test scores. Cov(X, Y) = E[(X - E[X])(Y - E[Y])] measures how changes in study hours are associated with changes in test scores.", "whyItMatters": "Understanding covariance helps in analyzing relationships between variables, which is crucial for statistical modeling and prediction.", "imageUrl": "https://upload.wikimedia.org/wikipedia/commons/c/c0/Gaussian-2d.png"}, {"id": "adf189056c58", "title": "Pearson correlation coefficient", "slug": "pearson-correlation-coefficient", "headline": "Pearson correlation coefficient formula: r = \u03a3[(xi - x\u0304)(yi - \u0233)] / [\u221a(\u03a3(xi - x\u0304)\u00b2) * \u221a(\u03a3(yi - \u0233)\u00b2)]", "summary": "Write the formula for Pearson correlation coefficient", "source": "Write the formula for Pearson correlation coefficient", "sourceUrl": "https://en.wikipedia.org/wiki/Pearson_correlation_coefficient", "articleUrl": "https://en.wikipedia.org/wiki/Pearson_correlation_coefficient", "publishedAt": "2026-06-12", "category": "learn", "cohortScore": 0.5, "embedding": [-7, 3, 8, 3, 0, -1, 3, 5, 11, -1, 8, -12, 8, -8, 2, -7, -7, 2, -10, -2, 9, -4, 0, 0, 3, 9, -3, -6, -5, -21, 2, 0, 8, 2, 1, 1, -5, 1, 0, 2, -7, 5, 0, 8, -2, -2, -7, 7, -2, -3, 3, -5, -3, 0, -1, 5, 7, 3, 4, 10, 1, 11, -16, 5, 11, -1, -3, -2, 6, 5, -5, 0, -3, 2, 1, 2, -8, -2, -5, 3, -3, 11, 0, 1, 2, -6, 2, -7, 4, 5, -1, -1, -1, 0, -9, -5, 4, -5, 5, 34, 1, -2, -3, 5, -5, -13, 3, -4, 1, -4, -2, 2, -4, -12, 2, -6, -3, 2, 2, -2, 1, 3, -2, -1, 6, 1, -2, 7, -4, 6, 4, 4, -1, 2, -4, 11, -3, 1, 4, 2, 12, -5, -2, 3, 3, 20, -14, 3, -2, 2, 2, 10, -1, -4, 1, -2, 0, 4, -4, -2, -11, -8, 0, 8, 0, -5, 6, 9, -2, -4, 5, 2, -3, -3, 11, 3, 0, 3, 12, -2, 7, 1, 0, 4, -2, 10, -8, -10, -8, 8, 0, -7, -11, 3, -10, 1, 0, -1, -5, 2, 10, -3, -1, 3, -1, -1, 9, -2, -4, 6, 3, -4, 7, -3, -4, 5, 3, 5, -1, 2, 2, -12, -4, -34, -3, 4, -2, 3, 0, 3, -1, -4, 11, 8, 11, -5, -10, -5, -3, 1, -4, 2, 4, -2, -11, 3, 7, 0, 2, 9, -6, 4, -8, -4, -1, -3, 6, 3, -5, -2, 0, -5, -13, -1, 8, 1, -1, -8, 2, -4, -8, 1, 6, 8, 4, 10, 0, 1, 0, -4, 8, -7, -4, -6, -8, 3, -5, -5, -6, 1, -4, 5, 5, -3, 10, -1, -3, 6, -4, 0, 2, 2, 3, 10, 0, 8, 6, 2, -2, 3, 0, 2, 0, -5, -3, 2, 1, -7, 0, -34, -2, 0, 1, 3, -10, 11, -10, -16, 8, -2, 5, 3, -3, 6, -7, 3, -8, 6, 1, 7, -2, 16, 0, 7, -1, -2, -4, 8, 4, -1, -3, 6, -3, 0, -1, -8, 0, 9, -2, 9, -1, -11, -8, 12, 9, 0, -16, -7, -1, -11, 3, -8, 5, 5, 8, -2, -2, -6, 0, -8, 4, 3, 6, 3], "explanation": ["The Pearson correlation coefficient formula is a mathematical representation used to quantify the linear relationship between two variables. It is calculated by taking the sum of the product of the deviations of each variable from their respective means, and then dividing by the product of the standard deviations of the variables.", "The numerator of the formula, \u03a3[(xi - x\u0304)(yi - \u0233)], represents the covariance between the two variables, which measures how much the variables change together. The denominator, \u221a(\u03a3(xi - x\u0304)\u00b2) * \u221a(\u03a3(yi - \u0233)\u00b2), normalizes this measure by accounting for the variability of each variable, ensuring the result falls between -1 and 1.", "Understanding the Pearson correlation coefficient formula is crucial for analyzing and interpreting the strength and direction of linear relationships between variables in statistical studies."], "example": "Consider two variables, X and Y, with the following values: X = [1, 2, 3, 4, 5] and Y = [2, 4, 6, 8, 10]. The mean of X (x\u0304) is 3, and the mean of Y (\u0233) is 6. The Pearson correlation coefficient (r) can be calculated as follows: r = [(1-3)(2-6) + (2-3)(4-6) + (3-3)(6-6) + (4-3)(8-6) + (5-3)(10-6)] / [\u221a((1-3)\u00b2 + (2-3)\u00b2 + (3-3)\u00b2 + (4-3)\u00b2 + (5-3)\u00b2) * \u221a((2-6)\u00b2 + (4-6)\u00b2 + (6-6)\u00b2 + (8-6)\u00b2 + (10-6)\u00b2)] = 1.", "whyItMatters": "The Pearson correlation coefficient formula is essential for determining the strength and direction of linear relationships between variables, which is fundamental in statistical analysis and research.", "imageUrl": "https://upload.wikimedia.org/wikipedia/commons/thumb/d/d4/Correlation_examples2.svg/1280px-Correlation_examples2.svg.png"}, {"id": "b931f0d74131", "title": "Regression analysis", "slug": "regression-analysis", "headline": "Linear regression equation: \u0177 = \u03b20 + \u03b21X", "summary": "Write the equation for linear regression prediction", "source": "Write the equation for linear regression prediction", "sourceUrl": "https://en.wikipedia.org/wiki/Regression_analysis", "articleUrl": "https://en.wikipedia.org/wiki/Regression_analysis", "publishedAt": "2026-06-12", "category": "learn", "cohortScore": 0.5, "embedding": [-3, -3, 3, -2, -1, 0, -2, 8, 8, 0, 3, 0, -2, -4, 4, -4, 3, 3, -5, 4, 12, 1, -5, -3, 8, 4, 1, 0, -1, -22, -1, -1, 11, 0, 2, 2, 3, 6, -8, 3, -1, -4, 3, 1, 2, -4, -2, -3, 0, -4, 1, 1, -5, 1, 4, -2, 2, 4, 0, 5, 10, -1, -22, 3, 1, 7, -6, -5, -3, 16, -1, -3, 2, 3, 0, 5, -1, 2, -3, 3, 6, 2, 1, -1, 0, -9, 11, -3, 6, -4, -4, -5, -4, 0, -8, -5, 5, 5, 1, 39, -3, 2, -3, -1, 4, -5, -1, -2, 3, -10, -4, -5, 3, -3, -2, -10, 2, 3, -2, 1, 3, -7, 3, -5, 8, -5, 4, 17, -3, 10, 2, 3, -7, -2, -1, -3, 1, 3, -3, -1, 3, 1, 6, 3, -8, 15, -2, -10, -4, -4, -3, 7, 0, 2, -2, 6, 2, -8, -7, 5, -9, -6, -3, -4, 2, -3, 9, 7, 4, -3, 5, -8, 0, -12, 2, 4, 2, 4, 6, 0, -3, -4, -2, 5, 11, 3, -2, -5, -1, 5, 2, -3, -5, 4, -3, 1, 6, -2, 0, -3, 7, 4, 2, 4, 4, 4, 14, -2, -4, 7, -2, -4, 9, 0, -13, 6, -2, 2, -1, 3, 3, -6, -3, -39, -3, 7, -5, 4, -7, 6, -3, -4, 11, 8, 2, 0, -5, 1, -5, 1, -5, 0, -1, -12, -10, 3, -3, -1, 2, 12, -2, 8, 4, -2, -5, -3, 3, 5, -2, 5, 3, -7, -11, 0, 3, 0, 0, -9, -2, -4, 1, -6, 9, 6, -1, 12, 2, 4, 0, -9, 4, 0, -1, 0, -9, 1, -1, -4, -3, 3, -9, -1, 0, -2, 8, 0, -3, 7, 1, -5, -1, -11, 4, 3, -5, 8, 7, 4, 4, 8, 0, 4, 2, -15, -9, 0, 5, -5, 4, -37, 0, 0, 3, -1, -4, 16, -7, -12, 5, -7, 7, 3, -3, 8, -9, 8, -8, 0, -6, 3, 3, 20, -3, 4, 0, -3, -7, 11, 1, -1, -2, 13, -2, 4, 4, -7, -4, 3, 0, 3, 1, -9, 3, 10, 5, 4, -5, -2, -6, -5, 6, 3, 2, 0, 1, -6, -4, -6, 0, -2, -3, 3, -4, 2], "explanation": ["Linear regression aims to predict the dependent variable (\u0177) using the independent variable (X) and its relationship with the dependent variable. The equation includes a y-intercept (\u03b20) and a slope (\u03b21), which represent the starting point and the rate of change, respectively."], "example": "If we want to predict a person's weight (\u0177) based on their height (X), the linear regression equation could be \u0177 = 50 + 2X, where 50 is the y-intercept and 2 is the slope.", "whyItMatters": "Understanding the linear regression equation is crucial for making accurate predictions and interpreting the relationship between variables in statistical modeling.", "imageUrl": "https://upload.wikimedia.org/wikipedia/commons/b/be/Normdist_regression.png"}, {"id": "5dfec6fd678a", "title": "Logistic regression", "slug": "logistic-regression", "headline": "Logistic regression probability formula: P(Y=1) = 1 / (1 + exp(-z))", "summary": "Write the formula for logistic regression probability", "source": "Write the formula for logistic regression probability", "sourceUrl": "https://en.wikipedia.org/wiki/Logistic_regression", "articleUrl": "https://en.wikipedia.org/wiki/Logistic_regression", "publishedAt": "2026-06-12", "category": "learn", "cohortScore": 0.5, "embedding": [-5, 6, 6, -8, -5, 8, 0, 6, 9, 1, 2, -7, -1, -1, -1, 2, -10, -4, -5, 4, 9, -9, -4, -8, 7, 3, -4, 3, -3, -25, -1, -2, 2, -10, -2, 5, 2, 7, 1, 11, -7, 1, -1, 4, 0, -11, -4, -4, -6, 0, 1, 5, -7, -1, 0, -5, 5, 5, -2, 4, -2, 6, -15, 4, 7, 0, -8, -5, -4, 11, -6, 4, -5, 11, 1, 7, 0, -6, -7, 2, -5, 6, -1, -1, 2, -2, 10, -5, 6, 0, 5, 10, -5, 1, -5, -1, 8, 7, 8, 37, -4, 1, -4, -1, -1, -12, -6, -3, -2, 0, 3, -2, 2, -6, -10, -8, 4, 4, 3, -5, 3, -2, 5, -2, 3, 2, -4, 15, -1, 4, 4, -2, -6, 3, -2, -3, 3, 9, -9, 2, 3, -1, 1, 1, -4, 17, -9, -1, -5, -8, 0, 8, 5, -6, 7, 5, 2, -5, -5, 2, -5, -13, 3, 5, 6, -3, 8, -1, 3, -7, 6, 3, 4, -7, -1, 1, -2, 2, 6, 1, 2, 1, -4, -4, 4, 2, -12, -7, 5, 9, 7, -6, -5, -4, -4, 1, -1, 2, 0, 0, 8, 2, -7, -2, -2, 4, 9, 4, -1, 1, -5, -3, 1, 0, 3, 9, 0, 11, 8, 4, -3, -5, 0, -33, 0, 7, -4, -1, -2, -2, -3, -6, 10, 7, -4, -6, -2, -4, -6, -2, -5, -4, 6, -4, -8, -3, 4, 7, 1, 6, -2, 5, 1, -4, -6, -4, 7, 5, 5, -1, -2, -7, -7, -1, 10, -4, -8, -15, -3, 1, 5, -1, 11, 8, 6, 10, -1, 5, -6, -2, 11, -3, -2, -2, -2, 6, -2, -7, -1, 1, -10, 7, -1, 2, 14, 2, -3, 10, 2, 8, -4, -4, -2, 1, -2, 4, 2, 1, 2, 3, -4, 2, 8, -6, -8, 2, 6, -5, 6, -36, 0, -5, 6, 3, -1, 7, -1, -10, -2, -1, 3, 6, 1, 0, -11, -3, -5, 5, 0, 8, -7, 19, 0, 2, 2, -1, -2, 16, -4, 2, 1, 10, -5, 3, 3, 2, -5, 0, -8, 6, -6, 2, -2, 18, 2, 0, -10, -6, 8, -4, 0, -3, 3, 0, 0, 5, -3, -1, -7, 1, 2, 5, -4, -5], "explanation": ["Logistic regression is a statistical model used to predict the probability of a binary outcome. The formula P(Y=1) = 1 / (1 + exp(-z)) represents the probability of the event occurring, where z is the linear combination of independent variables and their coefficients.", "The logistic function, exp(-z), transforms the linear combination z into a value between 0 and 1, which can be interpreted as the log-odds of the event. This transformation is crucial for converting the linear combination into a probability.", "Understanding this formula is essential for interpreting logistic regression results and making predictions about binary outcomes based on input variables."], "example": "Suppose we have a logistic regression model predicting whether a patient has a disease (Y=1) based on age (X1) and blood pressure (X2). The model's equation might be: z = -2 + 0.03*X1 + 0.05*X2. For a patient aged 50 with a blood pressure of 120, the calculation would be: z = -2 + 0.03*50 + 0.05*120 = 3.5. The probability of the patient having the disease is P(Y=1) = 1 / (1 + exp(-3.5)) \u2248 0.97.", "whyItMatters": "Knowing the logistic regression probability formula allows researchers and analysts to make informed predictions about binary outcomes, which is crucial in fields like medicine, marketing, and social sciences.", "imageUrl": "https://upload.wikimedia.org/wikipedia/commons/thumb/c/cb/Exam_pass_logistic_curve.svg/1280px-Exam_pass_logistic_curve.svg.png"}, {"id": "18eff377bce2", "title": "Batch normalization", "slug": "batch-normalization", "headline": "Batch normalization formula: Y = (X - \u03bc) / \u03c3 * \u03b3 + \u03b2", "summary": "Write the formula for batch normalization", "source": "Write the formula for batch normalization", "sourceUrl": "https://en.wikipedia.org/wiki/Batch_normalization", "articleUrl": "https://en.wikipedia.org/wiki/Batch_normalization", "publishedAt": "2026-06-12", "category": "learn", "cohortScore": 0.5, "embedding": [-14, 1, 6, -1, -3, 1, -6, -3, 7, 2, 4, -6, -2, 1, -1, -8, -5, 6, -9, 0, 11, -5, -7, -4, 11, 1, -11, -2, -5, -27, 4, -3, 14, -6, 6, 1, -7, 1, -1, 3, 10, 1, -3, -5, -2, -9, -7, 0, -4, 3, -1, -2, -4, 3, 2, 0, 4, 2, 8, 8, 0, 7, -15, 2, 5, -5, -5, -6, 2, 13, -9, -2, 2, 13, 1, -1, 0, -5, -10, 2, -6, 1, 3, -2, 3, 0, 5, -1, 4, 0, -4, 3, -1, -3, -6, -6, 3, 2, 0, 38, 0, 3, 1, 1, -2, -2, -4, -1, 2, -6, -1, -2, 8, -6, 0, -8, 7, -1, 3, -2, 7, -2, -2, -3, 8, 3, 0, 10, -11, 8, 4, 2, -3, 1, 2, 4, -2, 0, -1, 0, -2, 3, 2, 0, 5, 15, -11, -14, -2, -3, 5, 1, 4, 1, 6, 1, 6, -6, -5, 0, -8, -10, 0, 10, 2, -3, 1, -2, 1, 4, 11, -1, 0, 0, 2, -4, 3, 6, 4, -2, 7, 0, 5, -2, 8, -1, -2, 0, -5, 3, -1, -4, -8, 1, -3, -2, 4, -2, -4, -5, 12, 9, -1, -6, 1, 1, 6, -3, -1, 9, -1, -12, 5, -5, -8, 3, 3, 5, 2, -2, 0, -1, -10, -39, 0, 6, -2, 3, -6, 5, -1, -4, 4, 7, -4, 1, -5, -4, 4, 4, -1, 4, 2, -1, 2, -2, -7, 7, 1, 13, 0, 11, -5, -1, -4, -1, 6, 4, -3, -2, 6, -1, -1, -1, 3, 1, -9, 0, 0, -2, -2, -1, -3, -6, 1, 3, -5, 3, -6, -8, 8, -9, 1, -1, -14, 4, -1, -5, -7, 9, -6, 7, 2, -4, 8, 5, -2, 11, -1, 1, 0, -8, -2, 3, 1, 8, 1, 8, 3, 11, 4, 1, 1, -9, -4, 0, 5, 0, 1, -34, -1, -2, 4, 4, -7, 3, -6, -7, 0, -8, 12, 5, 5, 5, -5, 7, -1, 2, -7, 4, -1, 22, -5, -4, 1, 4, -2, 11, 1, 0, 2, 20, 5, 6, 8, -3, -5, 5, -3, 0, 0, 1, -8, 10, -3, -2, -4, -4, 1, -8, 9, -7, 2, 7, 3, -1, -1, -5, 3, -4, -3, 6, -3, -5], "explanation": ["Batch normalization adjusts the inputs to each layer in a neural network. It re-centers them around zero and re-scaales them to a standard size, making training faster and more stable."], "example": "If X = [1, 2, 3], \u03bc = 2, and \u03c3 = 1, then Y = [(1-2)/1, (2-2)/1, (3-2)/1] * \u03b3 + \u03b2 = [-1, 0, 1] * \u03b3 + \u03b2 = [-1*\u03b3 + \u03b2, 0*\u03b3 + \u03b2, 1*\u03b3 + \u03b2].", "whyItMatters": "Understanding the formula for batch normalization is crucial for implementing this technique correctly in neural networks.", "imageUrl": "https://upload.wikimedia.org/wikipedia/commons/8/8b/Typhoon_Mawar_2005_computer_simulation_thumbnail.gif", "imageLicense": "CC BY-SA 3.0", "imageArtist": "Typhoon_Mawar_2005_computer_simulation.gif: Atmoz\nderivative work: Atmoz (talk)"}, {"id": "fe62ce921d92", "title": "Adam optimizer weight update with m and v terms", "slug": "adam-optimizer-weight-update-with-m-and-v-terms", "headline": "Ever wondered how we can predict complex financial markets with high accuracy?", "summary": "Write the equation for Adam optimizer weight update with m and v terms", "source": "Write the equation for Adam optimizer weight update with m and v terms", "sourceUrl": "https://en.wikipedia.org/wiki/Deep_backward_stochastic_differential_equation_method", "articleUrl": "https://en.wikipedia.org/wiki/Deep_backward_stochastic_differential_equation_method", "publishedAt": "2026-07-03", "category": "learn", "cohortScore": 0.5, "embedding": [-9, -4, -4, 2, 0, 1, -7, -2, 8, 2, 4, -5, -1, 1, 5, -3, 0, -5, -3, 4, 7, -1, -3, -8, 2, -1, 1, 1, -5, -27, 6, -6, 8, -2, 3, 1, 1, 1, -5, 2, -3, 1, 0, -6, 7, 1, 1, -1, -7, 6, 0, -5, -4, 4, 3, 8, 3, -2, 2, 6, 8, 3, -20, 10, 3, -5, -4, -6, -5, 14, 4, 1, 5, 0, 0, 8, 5, -1, -1, 3, 4, -1, -6, -1, -1, 1, 3, 4, 9, -4, -3, -3, -1, -5, -5, 1, -1, 4, -6, 46, 6, -4, -4, -3, -2, -2, -4, -1, 3, -3, -9, 0, 3, -6, -1, 0, 4, -1, 2, 0, 0, -3, 2, 3, -3, -5, -4, 13, -4, -1, 4, 3, -8, 2, 4, 1, -5, 1, -3, 4, -11, 4, -6, -3, -6, 18, 3, -2, -4, -11, -2, 1, 2, -7, -3, -2, 9, -6, -9, -2, -10, -5, -5, 10, -4, -11, -1, 3, -1, -1, 2, 6, -3, 2, 9, 0, -8, -2, 1, 3, -3, -10, -1, 3, 5, 0, 0, -4, -1, 0, 2, -4, -3, 8, -9, 0, -2, 6, -1, -8, -4, 2, 3, -4, 7, -1, 3, 1, 7, 6, 0, -7, 0, 0, -6, -5, 1, 2, -1, 4, 5, -1, -1, -40, -4, 7, -4, 6, -8, 14, -6, 3, 9, 1, 0, 1, -8, 8, -4, -5, -3, -3, -1, -8, 2, 1, -11, 10, 3, 12, 1, 3, 4, -1, 2, 1, 1, 8, 0, 10, 5, -5, -3, -5, 0, -1, -3, -8, 3, 2, 2, -9, 9, 3, 5, 7, -4, -3, -3, -7, 8, -1, -3, 2, -6, -1, 3, -1, -5, 12, -8, -3, 0, -4, 5, -1, 2, 10, 0, -2, 1, -6, 6, 2, 4, 12, 9, 6, 7, 6, -1, -1, 8, 0, 0, -1, 2, 0, 0, -32, -1, -2, 4, 0, -3, 7, -7, -8, -4, -7, -1, 7, -2, 1, -6, 8, -11, 2, 0, 4, 8, 26, -6, 3, 5, 0, 0, 13, -1, 2, 0, 3, 0, 3, 6, -7, 0, 10, 0, 11, 5, 1, 4, 5, 4, 2, -2, -5, 2, -3, -2, 3, 0, 8, 2, -7, -8, -2, 1, -3, 2, 0, -11, -3], "imageUrl": "https://upload.wikimedia.org/wikipedia/commons/7/73/AtmosphericModelSchematic.png", "imageLicense": "Public domain", "imageArtist": "NOAA", "explanation": ["Imagine trying to forecast the price of a stock that fluctuates wildly due to countless unpredictable factors.", "Picture a stock price as a ball rolling down a hill. The Adam optimizer helps us predict where the ball will land next by adjusting its path based on past movements (m and v terms)."], "example": "If the ball's current position is 10 units down the hill and it has moved 2 units to the left (m term) and 1 unit to the right (v term) in the past, the optimizer adjusts the ball's path accordingly.", "whyItMatters": "The Adam optimizer's m and v terms help us fine-tune predictions by learning from previous adjustments."}, {"id": "64e8cca5545e", "title": "Learning to rank", "slug": "learning-to-rank", "headline": "Learning rate cosine annealing formula: learning_rate = learning_rate_initial * 0.5 * (1 + cos(pi * epoch / total_epochs))", "summary": "Write the formula for learning rate cosine annealing", "source": "Write the formula for learning rate cosine annealing", "sourceUrl": "https://en.wikipedia.org/wiki/Learning_to_rank", "articleUrl": "https://en.wikipedia.org/wiki/Learning_to_rank", "publishedAt": "2026-06-12", "category": "learn", "cohortScore": 0.5, "embedding": [-13, -1, 3, -4, -8, -2, -3, -6, 12, 1, 3, -11, 3, 5, -5, 0, -5, 0, 3, -8, 7, -8, -2, -1, -3, 4, 0, -6, -2, -25, -4, -1, 4, -6, 3, -2, 2, 5, -3, 13, -3, 2, 0, 0, 0, 2, -4, 0, -4, 1, 2, 3, -3, 5, 0, 1, 6, 10, 5, 1, 5, 6, -21, 7, -1, 7, -3, -4, 3, 10, -6, 0, 1, -3, 10, 10, -5, -2, 2, -4, -11, 5, -3, -3, 4, -8, 3, 1, 7, 5, 3, 0, -3, 5, -1, 7, 2, 8, -6, 37, -5, 4, -2, -1, 3, -9, -1, -4, -2, -4, -8, 2, 2, -13, 1, -3, 5, 3, 7, 2, 6, -5, 3, 0, 2, -1, -6, 3, -7, 4, 6, -6, -1, 1, -3, 3, -6, 2, -3, -2, -1, -4, 5, -2, -3, 15, -10, 1, -8, -1, -2, 6, -2, -8, -4, 4, -1, -1, -4, -4, -11, -7, -2, 11, 3, -5, 2, 4, 4, 0, 5, -2, -8, 2, 9, -1, -8, 1, 1, -1, 10, -5, 0, 3, -4, 1, -2, -12, -5, -4, 0, 0, -7, 8, -13, 0, -1, 1, -4, -3, 5, -3, 2, 1, 9, 1, 8, -5, 6, 0, -3, -8, 3, -2, 4, -3, 3, 5, -3, 3, -3, -2, -6, -39, 1, 6, -5, 8, -6, 10, -3, 3, 4, 2, 5, 2, -4, -3, -3, 12, -2, 8, 3, 6, -5, 3, -8, 4, 5, 17, -5, 3, -6, 2, -3, -2, 8, 1, -4, 9, 9, -3, -8, -1, 6, 4, -6, -7, 3, -3, 4, -3, 5, 1, 4, 4, -7, 1, -7, -5, 1, -6, -2, 2, -10, 3, -6, -5, -6, 2, -5, 2, 1, 6, 15, 2, -8, 5, -8, 1, 0, -2, 1, -6, -6, 2, 3, 4, 1, 9, -1, -1, 8, -3, -4, 0, 8, -2, -1, -36, 8, 3, 6, 4, -6, 4, -5, -4, 1, -11, 4, 0, 4, 0, 6, 4, -7, 5, -3, 6, -1, 20, 0, 3, 7, -1, 7, 12, 2, -1, 1, 4, 3, 7, 7, -6, -2, 7, 5, 6, -1, 1, 7, 6, 6, 4, -16, -10, -4, -1, 1, 3, 0, 4, 7, -6, -11, -3, -1, 4, -6, 12, 1, -1], "explanation": ["Learning rate cosine annealing is a technique used to adjust the learning rate during training. It starts with an initial learning rate and gradually decreases it following a cosine curve. This approach helps in achieving a balance between fast convergence and fine-tuning of the model parameters.", "The formula for learning rate cosine annealing is: learning_rate = learning_rate_initial * 0.5 * (1 + cos(pi * epoch / total_epochs)). In this formula, learning_rate_initial is the starting learning rate, epoch represents the current training iteration, and total_epochs is the total number of training iterations. The cosine function ensures a smooth transition of the learning rate from its initial value to a final value of 0.5 * learning_rate_initial.", "Cosine annealing helps in preventing the learning rate from becoming too small too quickly, which can lead to slow convergence or getting stuck in local minima. By gradually decreasing the learning rate, the model can fine-tune its parameters more effectively, leading to better performance and generalization on unseen data."], "example": "Suppose the initial learning rate is 0.1, and we have a total of 100 epochs. At epoch 50, the learning rate would be calculated as follows: learning_rate = 0.1 * 0.5 * (1 + cos(pi * 50 / 100)) = 0.1 * 0.5 * (1 + cos(pi * 0.5)) = 0.1 * 0.5 * (1 + 0) = 0.05.", "whyItMatters": "Learning rate cosine annealing is crucial for optimizing the training process of machine learning models, ensuring efficient convergence and improved model performance.", "imageUrl": "https://upload.wikimedia.org/wikipedia/commons/d/da/Magent-graph-2.gif", "imageLicense": "CC BY-SA 4.0", "imageArtist": "Jordan K. Terry"}, {"id": "b65b7e4ba8cc", "title": "Dropout (neural networks)", "slug": "dropout-neural-networks", "headline": "Dropout randomly sets neuron inputs/outputs to zero during training", "summary": "Write the equation for dropout during training", "source": "Write the equation for dropout during training", "sourceUrl": "https://en.wikipedia.org/wiki/Dropout_(neural_networks)", "articleUrl": "https://en.wikipedia.org/wiki/Dropout_(neural_networks)", "publishedAt": "2026-06-12", "category": "learn", "cohortScore": 0.5, "embedding": [-7, -2, 4, -1, -5, 5, 2, 1, 14, -5, 6, -1, 1, 9, 1, -3, -5, -1, -5, 3, 2, -8, 5, -2, 2, -1, -4, -2, -7, -25, 2, 3, 6, 0, 0, 2, -2, 4, -1, 4, 1, -1, 2, -9, 7, -1, 0, -14, 3, -4, -3, -10, 1, 3, 2, -2, 3, 5, 3, 7, 0, 6, -17, 4, 10, -5, -5, -6, -2, 6, -3, 1, 1, 1, 4, -1, 1, -2, 5, 2, 4, -1, -5, 2, 0, -1, 2, -7, -2, 0, -1, 6, -7, 0, -3, 3, 4, -5, -9, 46, 3, 1, 2, 2, -3, -6, 0, -5, -4, -4, -4, -3, 3, -5, 2, 1, 5, 4, 0, 0, -2, -5, 4, 1, 9, -3, -6, 19, -3, -2, 7, -4, -3, -2, -2, -2, 3, 2, -9, 0, 8, 4, 7, 1, -5, 17, -6, -1, 2, -5, -2, 5, 4, 0, 3, 7, 0, -5, -8, 1, -11, -8, 1, 6, 1, 8, -4, 1, 2, -9, -3, -8, 7, -5, 7, -1, -6, -3, 0, 4, 7, -7, -2, 8, 0, -3, 1, -3, -3, 7, -10, -7, -3, -10, -5, -6, -1, -2, -5, -2, 1, 2, 4, -3, 4, 4, 1, -1, 8, 6, -4, -6, 6, 3, 0, 2, -7, 1, 0, -5, 6, -2, -2, -40, 3, 4, -6, 4, -4, 5, -2, 4, 10, 10, -1, 2, -1, 1, 4, 4, -3, -8, 6, 0, 1, 7, -10, -2, 6, 13, 0, 12, -3, -3, 12, 0, 1, 8, 2, -2, 2, -1, -4, -5, 4, 6, -5, -8, -1, -8, -2, -10, -1, 4, -1, 1, -6, 9, -5, -7, 6, -5, 0, 4, -5, -2, -11, -1, 2, 4, -5, 13, 1, 1, 13, 8, 3, 9, -4, -8, -8, -10, 0, 1, -1, 7, 13, 4, 4, 9, -6, 7, 2, -4, 3, -1, 2, 11, -2, -31, 3, 4, 1, 8, 6, 1, -5, -7, 1, -9, -3, -2, -1, -1, 3, 4, -12, 9, -9, 8, 2, 14, -2, 0, 0, -3, -4, 8, -3, 1, 6, 10, 4, 0, 3, -9, 0, 6, -7, 5, -3, 0, -5, 12, 2, 2, -1, 0, 1, -5, -3, 8, -4, 1, 13, -1, -5, 1, -2, -4, -4, 7, -6, -4], "explanation": ["Dropout is a regularization technique used to prevent overfitting in neural networks by randomly disabling neurons during training. This randomness helps the network learn more robust features that are not reliant on specific neurons."], "example": "During training, if a neuron has a 50% chance of being dropped out, the input to that neuron will be set to zero for that training instance.", "whyItMatters": "Dropout reduces the risk of overfitting by ensuring that the neural network does not become overly reliant on any single neuron, promoting better generalization.", "imageUrl": "https://upload.wikimedia.org/wikipedia/commons/thumb/e/ed/Dropout_mechanism.png/1280px-Dropout_mechanism.png"}, {"id": "f9423c2d19e3", "title": "Precision and recall", "slug": "precision-and-recall", "headline": "Precision = Relevant retrieved instances / All retrieved instances", "summary": "Write the formula for F1 score from precision and recall", "source": "Write the formula for F1 score from precision and recall", "sourceUrl": "https://en.wikipedia.org/wiki/Precision_and_recall", "articleUrl": "https://en.wikipedia.org/wiki/Precision_and_recall", "publishedAt": "2026-06-12", "category": "learn", "cohortScore": 0.5, "embedding": [-9, 1, 3, -2, -3, 5, -3, 7, 9, 3, -2, -10, 8, 4, -8, -2, -4, 5, 3, -3, 0, -4, 0, 4, 0, 7, -5, 0, -6, -25, -2, 0, 5, -3, 2, -1, -8, 3, 3, -2, 5, -4, 2, 4, -2, 1, -1, 2, 7, 2, 1, 0, -2, 5, 4, 2, 6, 6, 7, -1, 11, 5, -18, 5, -2, 0, -8, -8, -3, 7, -9, -5, 3, 11, 8, -1, -8, -6, -6, 3, -4, 1, -9, 0, 5, -1, 8, 1, 9, -4, 1, -1, 3, 6, -5, -5, 6, 2, -1, 41, 2, 6, -12, -1, 1, -8, 2, -3, 0, -10, 5, 1, 2, -13, 5, 5, -3, -3, 5, 0, -3, -1, 4, -4, 8, 2, 1, 4, -10, 4, 2, -3, -6, -4, -3, 1, 0, -3, 1, 1, 4, -7, 4, 6, -5, 22, -4, -2, -5, -6, 2, 0, 1, 2, 6, 3, 1, -3, 0, -5, -10, -8, -2, 10, -1, -7, 0, 9, -3, -5, 6, -10, -5, 2, 6, -3, 0, 5, 8, -1, 7, -3, -2, -6, 3, -2, -3, -7, 0, 6, 2, -3, 0, 0, -6, -3, -1, 0, -2, -6, 5, 1, -2, -2, 9, 6, -1, -3, 2, 3, -5, -10, 3, 2, -8, -2, -1, 3, 0, -3, 4, -2, -5, -37, 3, 5, -1, 1, 0, 8, -1, 2, 8, 7, -1, 1, -1, -2, -14, -7, -4, -1, 3, -3, -4, -3, -3, 7, 0, 20, -5, 7, -6, 1, -2, 4, 2, 6, -4, -4, 16, -1, -5, 2, 3, 1, -2, -7, -1, -3, -8, -5, 12, 5, 2, 4, -6, -1, 2, -7, 12, -7, -3, 4, -3, 6, -6, -1, -6, 4, -7, 3, 1, -1, 3, -4, -4, 7, 0, 2, -4, 0, -1, 6, 8, -2, 0, 8, 3, 14, 6, 2, -2, -4, -1, 1, 9, -5, 2, -34, -3, -6, 5, 3, -6, 3, -7, -8, 6, -6, 7, 2, -2, 1, 0, 1, 3, 5, -6, 9, 2, 21, -6, 4, 3, 3, -6, 18, 2, 4, -6, 7, 4, 0, 4, -5, -1, 3, -5, 7, 2, -4, -7, 10, 4, -1, -12, -9, -2, -8, -1, 2, -6, 8, 1, 5, 0, -3, 3, -6, 0, 9, 2, -4], "explanation": ["Precision measures the accuracy of positive predictions. It is calculated by dividing the number of relevant instances retrieved by the total number of instances retrieved. This metric helps to understand the proportion of positive identifications that were actually correct."], "example": "If a search engine retrieves 100 documents and 80 of them are relevant, the precision would be 80/100 = 0.8 or 80%.", "whyItMatters": "Precision is crucial for evaluating the performance of classification models and information retrieval systems, ensuring that the predictions made are reliable and trustworthy.", "imageUrl": "https://upload.wikimedia.org/wikipedia/commons/thumb/2/26/Precisionrecall.svg/1280px-Precisionrecall.svg.png"}, {"id": "ecbadb2233ea", "title": "TF-IDF scoring", "slug": "tf-idf-scoring", "headline": "TF-IDF = (Term Frequency) * (Inverse Document Frequency)", "summary": "Write the formula for TF-IDF scoring", "source": "Write the formula for TF-IDF scoring", "sourceUrl": "", "articleUrl": "", "publishedAt": "2026-06-12", "category": "learn", "cohortScore": 0.5, "embedding": [-11, 0, 1, -2, 1, -1, 1, 7, 3, 4, 2, -8, 6, -6, -2, -3, -6, 4, -2, -4, 12, -4, 1, 1, 7, 6, -6, -8, -5, -23, 0, -2, 6, -2, 6, -1, -11, 6, -1, 2, -2, -6, 5, -1, -4, -2, -11, -2, -4, 5, -8, -5, -2, 8, 2, 4, 5, 0, 5, -1, 3, 7, -18, 11, 2, 2, -6, -1, 0, 10, -5, 6, 4, 5, 8, 2, -3, -7, -2, -2, 1, -1, -5, 0, 3, -4, 5, 2, 7, 0, 0, -2, 2, 0, -10, -11, 3, 8, 5, 40, -1, -6, -4, 0, 1, -7, 7, -8, -1, -5, -2, 1, 6, -11, 6, -2, 2, 9, 4, -6, -1, 0, 1, -2, 0, 8, 2, 6, -3, 6, -3, -7, -9, 1, 4, 0, -8, -5, -2, 9, 4, -3, -3, 5, -1, 18, -5, 0, -7, -5, 1, 9, 1, -3, 4, 9, 2, -8, 0, -3, -1, -3, 0, 12, -5, -7, -1, 5, -12, -2, -2, -6, -1, 5, 6, 4, -8, -1, 7, -2, 6, -3, -9, 4, 8, 5, -6, -8, 8, 3, -3, -4, 0, 4, -5, -6, -3, 1, -3, -6, 2, -1, 2, -1, 3, 1, 0, -2, 1, 3, 1, 0, -1, -2, -5, 2, -3, 0, -1, 3, -1, -4, -12, -39, 2, 1, 0, 4, -8, 4, -1, -1, 10, 5, 1, -9, -5, -5, -7, 0, -10, 5, 2, 2, -1, -4, 1, 5, 1, 18, -2, 9, -7, 2, 2, -2, 5, 5, -7, -3, 4, -7, -6, -3, 1, 4, -6, -8, -2, -1, -3, -2, 6, 3, 3, -2, 1, 1, -1, -5, 3, -5, -8, 4, -2, 7, -4, -2, 5, 4, -4, 6, 2, 1, 9, 0, 3, 12, -4, 0, -1, -2, -1, 7, 5, 2, -7, 6, 9, 8, 5, -2, 3, -1, 6, 9, 11, 0, 2, -39, -2, -3, 7, 3, -5, 5, -7, -10, -3, -11, 5, -1, -3, 4, -3, 3, -5, 7, -6, 4, 7, 25, -4, 0, -1, 5, 2, 11, 1, 8, -4, 10, 5, -2, 0, -2, -3, 6, -8, 8, -2, -3, -4, 5, 0, 3, -4, -9, -1, -5, 4, 2, 8, 9, 6, 4, 1, -1, 0, -3, -6, 3, 2, -2], "imageUrl": "https://upload.wikimedia.org/wikipedia/commons/2/2f/Jackson_Pollock%27s_passport_%28cropped%29.jpg", "imageLicense": "Public domain", "imageArtist": "Unknown authorUnknown author"}, {"id": "563af7871252", "title": "PageRank", "slug": "pagerank", "headline": "PageRank formula: PR(A) = (1-d) + d \u03a3(PR(C)/L(C))", "summary": "Write the formula for PageRank equation", "source": "Write the formula for PageRank equation", "sourceUrl": "https://en.wikipedia.org/wiki/PageRank", "articleUrl": "https://en.wikipedia.org/wiki/PageRank", "publishedAt": "2026-06-12", "category": "learn", "cohortScore": 0.5, "embedding": [-12, -1, 2, -4, -10, -3, 1, -1, 11, 1, 12, -3, 9, 0, -1, -2, 0, 3, -6, 0, 10, -8, -5, -12, 7, 2, -6, -5, -4, -24, -6, 1, 9, -3, -2, 3, 3, -1, -1, 3, -2, 1, 3, 6, 0, -2, 4, 0, -5, 1, -4, 6, -9, -3, 0, -3, 1, 1, 2, 8, 9, 7, -16, 5, -1, 4, -8, -5, -9, 15, -4, -5, 4, 7, 7, 3, -4, -1, 3, 0, -9, 3, -6, 0, 4, -4, 10, -2, 4, 1, 3, 0, -1, -2, -6, -8, -5, 4, 4, 42, -4, 6, 0, -2, -1, -10, 3, -2, 1, -8, 0, -2, 7, -14, 1, -8, 6, 2, 0, -4, -7, 0, -2, -6, 7, 6, -5, 12, -5, 11, 7, 1, 1, 0, -1, -3, -8, 1, -4, 1, 0, 2, 0, 1, -2, 20, -6, -6, -8, -1, 3, 4, 0, -1, 3, 1, 5, -2, -3, -1, -6, -2, 1, 10, 5, -4, 8, 2, -7, 3, 3, -1, 0, 4, 5, 6, 1, -3, 11, 2, 6, 0, -9, 2, -1, 7, -6, -4, -4, 0, 2, 0, -2, 2, -9, 1, -2, -5, 3, 2, 5, -6, -1, -3, 1, 1, 5, 0, -8, 9, -12, -5, -3, -7, 4, -4, 1, 4, 2, 10, 0, -5, -6, -33, -6, 7, -2, 3, -5, 5, -5, -5, 11, 10, 0, -5, -5, -2, -2, 1, -3, 0, -1, 10, -6, 2, -5, 10, 5, 13, 3, 1, -8, 1, 3, -9, 8, 5, -4, 0, 1, -5, -10, 0, 5, -5, 0, -1, -3, 2, -4, 1, 11, -5, 0, 6, 2, -2, 4, 2, 2, -15, -4, -1, -8, 6, -5, -5, -3, 1, -5, 4, 1, -2, 6, 4, 4, 11, -1, 2, 5, 2, -2, 4, -4, 7, 1, 2, -1, 8, 3, -6, 7, -1, 1, -3, 1, -2, -4, -34, 4, -1, 5, 3, -2, 9, -6, -12, 0, -5, 14, -4, -3, -1, -2, -4, -9, 6, 3, 12, -3, 23, 5, 5, -3, 4, -1, 1, -3, 2, 4, 16, -6, 6, 1, -2, 5, 3, 1, 3, -1, -4, 4, 12, 2, 0, -10, -7, -4, -5, -1, 1, -1, 3, 6, 2, 1, -1, 1, -8, -2, 5, 1, 6], "explanation": ["PageRank (PR) is an algorithm used by Google Search to rank web pages in their search engine results. It is named after both the term \"web page\" and co-founder Larry Page. PageRank is a way of measuring the importance of website pages. According to Google: PageRank works by counting the number and quality of links to a page to determine a rough estimate of how important the website is. The underlying assumption is that more important websites are likely to receive more links from other websites. Currently, PageRank is not the only algorithm used by Google to order search results, but it is the first algorithm that was used by the company, and it is the best known. As of September 24, 2019, all patents associated with PageRank have expired."], "example": "If a web page A has 3 incoming links from web pages C1, C2, and C3, with PageRanks of 0.5, 0.3, and 0.2 respectively, and C1, C2, and C3 have 1, 2, and 3 outgoing links respectively, then the PageRank of A would be calculated as follows: PR(A) = (1-d) + d [(0.5/1) + (0.3/2) + (0.2/3)], assuming a damping factor d of 0.85.", "whyItMatters": "Understanding the PageRank formula is crucial for webmasters and SEO professionals as it helps them optimize their websites for better search engine rankings.", "imageUrl": "https://upload.wikimedia.org/wikipedia/commons/5/55/Page_rank_animation.gif"}, {"id": "ae7e9b82987e", "title": "Discrete Fourier transform", "slug": "discrete-fourier-transform", "headline": "Discrete Fourier Transform (DFT) equation: X[k] = \u03a3(n=0 to N-1) x[n] * e^(-j*2\u03c0*k*n/N)", "summary": "Write the equation for discrete Fourier transform", "source": "Write the equation for discrete Fourier transform", "sourceUrl": "https://en.wikipedia.org/wiki/Discrete_Fourier_transform", "articleUrl": "https://en.wikipedia.org/wiki/Discrete_Fourier_transform", "publishedAt": "2026-06-12", "category": "learn", "cohortScore": 0.5, "embedding": [-11, 2, 9, -10, -2, 0, -1, 4, 2, -5, 4, -5, 4, -10, 0, 1, -6, 1, -9, 4, 16, -1, -2, -5, 5, 6, 11, -4, -2, -19, -1, 0, 7, -3, -2, -6, -2, 7, -2, 2, -1, -6, 9, -2, -3, 3, -10, -3, 3, -4, 0, 0, 1, 0, 1, -1, 6, 2, 6, -3, 5, 2, -17, 5, 6, 4, 1, -12, -2, 4, -3, 0, -2, -1, 2, -2, -2, -7, -1, 2, -6, 0, -2, -3, -5, 2, -3, -3, -1, 4, -4, 4, -8, -4, -10, -1, 0, 3, 3, 42, 2, 4, -3, 1, -6, -10, 4, -5, 3, -8, -4, 7, 6, -15, 2, -4, -1, 6, 0, 0, 2, 7, -2, -5, 12, 3, -3, 11, -1, 17, -1, -2, 3, -3, 1, 7, -4, -1, -9, 5, -5, -8, -8, 5, 5, 12, -7, -1, -1, 1, 3, 4, -9, 0, 3, 3, 1, -3, -6, -8, -6, -7, 2, 9, 3, 5, 4, 1, 0, -13, -4, -4, -2, -2, 8, 0, -1, 0, 6, 4, 0, -2, 0, -1, 5, 3, -7, 3, -3, 2, 1, -2, -2, 10, -5, 3, -8, -1, -1, 2, 8, 4, 4, 3, -3, -1, 10, -5, -7, 8, -7, -3, 6, -5, 2, 0, -5, 6, -3, 4, -3, -13, -10, -36, -8, 6, -2, 6, -3, 7, -2, -2, 16, 8, -1, -1, -6, -4, -7, -1, -2, -3, -1, -3, -5, 2, -3, 4, 3, 15, 1, 11, -4, 1, 1, -2, 4, 3, -10, -1, 3, -2, -5, 2, 1, -3, 4, 1, -3, -8, -1, -6, 8, -3, 1, 8, -3, -3, -2, -1, -1, -9, 0, 2, -2, 0, -3, -3, 4, 5, -3, 6, -2, 1, 9, 3, 3, 11, 2, -1, 14, 3, -3, 10, 0, 5, 6, 7, 6, 9, 2, -7, -2, -8, 2, 9, -2, -4, -2, -35, 1, -1, 2, 3, -1, 5, -2, -15, 2, -13, 0, -2, 3, 5, -8, 6, -5, 1, -1, 8, 0, 21, 0, -4, 0, 2, 8, 5, -4, 4, -3, 9, -2, 2, 2, -2, 6, 9, -1, 12, -4, 4, 1, 8, 5, 8, -13, 4, -7, 1, 8, 4, 3, 0, 5, -4, -6, -2, -2, -4, -1, 6, 1, 4], "explanation": ["The DFT equation provided converts a sequence of N complex numbers into another sequence of N complex numbers, representing the frequency components of the original sequence. This transformation is fundamental in signal processing for analyzing the frequency content of signals.", "The DFT equation X[k] = \u03a3(n=0 to N-1) x[n] * e^(-j*2\u03c0*k*n/N) shows that each output X[k] is a sum of the input sequence x[n] multiplied by complex exponentials. The term e^(-j*2\u03c0*k*n/N) represents the basis functions of the discrete Fourier transform, which correspond to different frequencies.", "Understanding and applying the DFT equation is crucial for tasks such as signal analysis, image processing, and solving partial differential equations numerically. The DFT allows for efficient computation of the frequency spectrum of discrete signals, which is essential in many scientific and engineering applications."], "example": "Consider a sequence x[n] = {1, 2, 3, 4}. To compute the DFT, we apply the formula for each k from 0 to N-1 (where N=4). For k=0, X[0] = 1 + 2 + 3 + 4 = 10. For k=1, X[1] = 1*e^(-j*2\u03c0*1*0/4) + 2*e^(-j*2\u03c0*1*1/4) + 3*e^(-j*2\u03c0*1*2/4) + 4*e^(-j*2\u03c0*1*3/4). Continue this process for k=2 and k=3 to obtain the full DFT.", "whyItMatters": "The DFT equation is fundamental for converting time-domain signals into their frequency-domain representation, enabling efficient analysis and processing of discrete signals.", "imageUrl": "https://upload.wikimedia.org/wikipedia/commons/thumb/3/31/DFT_2sin%28t%29_%2B_cos%284t%29_25_points.svg/1280px-DFT_2sin%28t%29_%2B_cos%284t%29_25_points.svg.png"}, {"id": "9c18dd9f1d92", "title": "Taylor series", "slug": "taylor-series", "headline": "Taylor series formula: f(x) = f(a) + f'(a)(x-a) + f''(a)(x-a)^2/2! + ", "summary": "Write the formula for Taylor series expansion around point a", "source": "Write the formula for Taylor series expansion around point a", "sourceUrl": "https://en.wikipedia.org/wiki/Taylor_series", "articleUrl": "https://en.wikipedia.org/wiki/Taylor_series", "publishedAt": "2026-06-12", "category": "learn", "cohortScore": 0.5, "embedding": [-9, -1, 6, -5, -7, 8, 0, 4, 8, 2, 2, -12, -3, -8, -3, -5, -5, 2, -13, -4, 6, 2, -5, -5, 9, 11, -4, 0, 0, -19, 2, 1, 4, -2, -5, 3, -3, 5, 1, -1, 1, -1, 4, 3, -7, -1, -3, 6, 0, -5, 4, 0, -10, 4, 1, -3, -5, 0, 5, 7, 11, 6, -13, 8, -7, 6, 2, 2, 0, 11, -3, -7, -6, 6, 6, 7, -4, -4, 0, -1, -4, -6, -2, 2, 2, -4, 8, -4, 0, 6, 3, -1, 6, -2, -1, -11, 4, 0, 2, 41, -4, 0, -4, 1, -6, -5, -3, 1, -1, -5, 3, -3, 2, -10, -3, -5, -1, 3, -2, -1, 3, 1, 7, 2, 7, 4, 2, 13, -5, 5, 4, 2, -1, 2, -1, 5, -9, -3, 4, 6, 10, -7, -1, -1, 4, 17, -3, 0, -8, 4, 0, 2, -1, 4, 8, 1, 4, -1, -9, 2, -14, -5, -5, 3, 6, -7, 11, 5, 3, -5, 1, -6, -6, -2, 9, -1, 1, -6, 9, -7, 2, -5, 3, 0, -2, -2, -10, 3, -5, -1, 1, 3, -8, -4, -6, -6, 2, 8, -1, 4, 5, -2, 7, -3, 5, 1, 10, 3, -8, 5, -6, -2, -2, -3, -9, 7, 0, -4, -6, -6, 9, -14, -2, -37, -5, -1, -5, 0, -5, 1, 1, -10, 6, 2, -3, -3, -6, 0, -9, 2, -1, 3, 3, 2, -4, -4, -7, -5, -1, 11, -3, 7, -5, 2, -7, -10, 12, 2, 2, 6, 9, -1, -11, -2, 10, -2, 5, 2, 3, -3, -4, 5, 3, 6, 5, 5, 0, -2, 3, -8, 7, -1, 1, -6, -1, 7, 4, 0, -3, 3, -7, -2, 8, -1, 7, 1, 3, 6, 0, 0, 9, -1, 0, 3, -7, 0, -1, 5, 3, 9, -1, -3, -2, -9, 1, -4, 5, -3, -7, -33, -7, 3, -3, -4, -3, 4, -1, -9, 5, -10, 9, 2, 1, 5, -5, 4, 0, 5, -2, 9, 1, 20, -7, 6, 4, 8, 0, 14, -4, 5, -1, 5, -1, 3, -3, 0, 14, 7, -4, 9, -7, -13, 0, 5, 3, -4, -8, -4, 4, -4, 5, 2, 4, 9, 2, -9, 5, 0, 1, -9, -4, 8, -2, 9], "explanation": ["The Taylor series formula is an infinite sum representing a function's approximation around a point 'a'. It includes the function's value and derivatives at 'a', multiplied by powers of (x-a) and divided by factorial terms."], "example": "For f(x) = e^x around a = 0, the Taylor series is f(x) = 1 + x + x^2/2! + x^3/3! + ...", "whyItMatters": "Understanding the Taylor series formula is crucial for approximating functions and analyzing their behavior near a specific point.", "imageUrl": "https://upload.wikimedia.org/wikipedia/commons/thumb/e/e4/Sintay_SVG.svg/1280px-Sintay_SVG.svg.png"}, {"id": "dac971378f77", "title": "Chain rule", "slug": "chain-rule", "headline": "Chain rule formula: h'(x) = z'(y(x)) * y'(x)", "summary": "Write the formula for chain rule in calculus", "source": "Write the formula for chain rule in calculus", "sourceUrl": "https://en.wikipedia.org/wiki/Chain_rule", "articleUrl": "https://en.wikipedia.org/wiki/Chain_rule", "publishedAt": "2026-06-12", "category": "learn", "cohortScore": 0.5, "embedding": [-17, 1, 7, 0, -9, -1, -1, 7, 2, 3, 3, -3, 6, -5, -9, -11, -5, 11, -5, 5, 13, -6, -8, -3, 14, 9, -2, 3, -1, -20, 0, -2, 0, -7, -8, -2, -3, 2, -4, -2, 0, 6, 9, 3, -1, 1, -8, -2, -2, -2, -5, 3, -4, -1, 1, 2, 2, 5, 3, 8, 3, 10, -14, 6, 3, -1, -5, 2, 3, 18, 0, -9, -3, 5, -1, -4, -6, -6, 1, -2, -6, -6, 2, -3, 3, -2, 2, -3, 4, 1, 0, 2, -3, -3, -6, -3, -3, -2, 0, 44, -1, -2, 3, 3, 1, 1, 1, -2, -1, -6, -2, 0, 6, -12, 3, -8, 3, 7, -1, -9, 0, 6, 7, 6, 4, 2, -3, 11, -4, 5, 6, -4, 2, 4, -7, 4, -6, -4, -1, -1, -1, -2, -8, -4, 3, 14, -6, -6, -8, 4, 3, 4, 2, -4, 0, 10, 6, -4, -2, 4, -7, -3, -2, 15, -4, -3, 9, 1, 0, -8, 3, 3, -4, -1, 9, -4, -2, -1, -1, -1, 7, -2, -7, 1, 7, 6, -13, -5, 0, 9, 0, -3, -3, -3, -6, -5, -6, -2, -4, 0, 6, 3, 7, 1, -4, -2, 10, -5, -9, 3, -2, 3, -1, 1, -1, 6, 5, 0, -2, 1, 0, -9, -3, -36, -6, 3, 0, 9, 1, -2, -3, -9, 8, 8, 7, -7, -10, -4, -3, 4, -3, 0, 6, -3, -9, -3, -7, 5, 2, 12, -1, 6, 3, 0, -9, -1, 7, 2, -5, 1, 2, 4, -11, -1, 1, -4, 2, 5, 4, -1, -1, -2, 0, 8, 3, 0, 3, -8, 0, 2, 3, -4, -6, -4, 6, 3, 4, -2, -3, 8, -4, 1, 1, -5, 6, 2, -7, 9, 2, -4, 3, -4, -3, 1, -2, 5, 7, 4, 3, 2, 1, 4, 5, -1, 1, 1, 7, -6, -6, -36, 3, -1, 4, -1, 1, 11, -9, -12, -3, 1, 6, 4, 1, 6, -11, 3, -6, 6, 5, 8, 8, 25, -3, 11, -3, 0, -2, 8, 1, 0, 4, 10, -3, 5, -3, -2, 3, 10, 0, -1, -2, -6, 1, 7, 8, -4, -5, -5, 3, -3, 1, -7, 3, 0, 4, 6, -5, -6, -2, -4, 3, 8, 1, 0], "explanation": ["The chain rule formula connects the derivative of a composite function to the derivatives of its constituent functions. It is essential for differentiating compositions of functions in calculus. The formula states that the derivative of the outer function z with respect to y, multiplied by the derivative of y with respect to x, yields the derivative of the composite function h with respect to x."], "example": "Let z(u) = u^2 and y(x) = 3x + 1. Then h(x) = z(y(x)) = (3x + 1)^2. To find h'(x), we first find z'(u) = 2u and y'(x) = 3. Then, h'(x) = z'(y(x)) * y'(x) = 2(3x + 1) * 3 = 6(3x + 1).", "whyItMatters": "Understanding the chain rule formula is crucial for solving complex differentiation problems involving composite functions in calculus.", "imageUrl": "https://upload.wikimedia.org/wikipedia/commons/e/e1/Doorway_in_Ben_Youssef_Madrasa.JPG", "imageLicense": "CC BY-SA 4.0", "imageArtist": "Ian Alexander"}, {"id": "493ae10fcbce", "title": "Euler's identity", "slug": "euler-s-identity", "headline": "Euler's identity: e^(i\u03c0) + 1 = 0", "summary": "Write Euler's identity e^(i\u03c0) + 1 = 0", "source": "Write Euler's identity e^(i\u03c0) + 1 = 0", "sourceUrl": "https://en.wikipedia.org/wiki/Euler%27s_identity", "articleUrl": "https://en.wikipedia.org/wiki/Euler%27s_identity", "publishedAt": "2026-06-12", "category": "learn", "cohortScore": 0.5, "embedding": [-12, 0, 3, -2, -7, 2, -2, 2, 7, 5, 3, -5, 2, -8, -9, -7, -7, 10, -12, 4, 8, -13, -5, -2, 2, 15, 4, -8, 0, -22, 2, 1, 4, 1, 5, -5, 1, 7, -5, -4, -1, -2, 4, 5, 5, 1, -7, -1, 0, -3, 2, 6, 1, -1, -8, 1, 4, 0, 1, 4, 8, 9, -18, 12, 1, 7, -5, -7, 2, 7, -7, -2, 0, 7, -1, 2, -2, 3, 0, -1, -9, 2, -2, 5, -2, 3, 2, -2, 6, 0, -4, -5, -5, 1, 2, -1, -3, 2, -1, 46, 1, 0, 2, 5, 2, -5, 3, -4, -4, -10, -5, -3, 7, -11, 3, -1, -1, 2, 3, -2, 7, 1, -2, -1, 11, -3, 2, 11, -1, 12, 0, -2, 1, 1, -5, 6, -10, 5, 3, 2, 6, -1, -7, 2, 6, 9, -4, -3, -9, -2, 5, 4, -4, -3, 0, 4, 0, -2, -4, 1, 1, -4, -3, 13, -2, -1, 3, 5, 4, -6, 6, -5, -2, -1, 13, 0, 1, 0, 6, 4, 0, -2, 1, 5, -2, 3, -8, 2, -5, -2, 0, 3, -6, 4, -9, -3, 2, 1, 0, -7, 9, 7, 7, 0, 5, 2, 0, -5, -6, -2, -5, -7, 8, 2, -3, -8, 3, -2, 4, -5, -5, -6, -9, -37, -8, 2, -5, 6, -10, 3, -1, 1, 0, 0, -8, -6, -1, -4, 2, 0, -2, 7, 4, -8, -2, 2, -3, 3, -1, 15, 7, 5, -1, -4, 0, -1, 7, 4, -1, 3, 0, 5, -5, 8, -1, -5, 7, -6, 2, -11, -5, 0, 12, 3, 7, 8, -1, 5, -6, -3, 1, -3, 0, 2, -3, 6, 1, 1, 5, 0, -5, 9, 0, 1, 6, 4, -1, 9, -1, 2, 7, 1, -1, -5, -5, 5, -5, 0, 0, 4, 6, 3, -4, -5, 7, 5, 11, -5, -8, -37, 4, -2, -1, 7, 2, -5, -8, -16, -9, -4, 2, 2, 3, 0, 4, -5, -11, 3, 2, 10, 1, 24, -3, -4, -3, 9, 2, 5, -2, -3, -2, 2, 2, -1, -2, -3, 4, 7, -1, 3, -6, 0, -3, 9, 0, 4, -2, 0, -5, 2, 5, 1, 4, -2, 9, -9, -5, -5, 2, -8, -2, 2, 2, 4], "explanation": ["Euler's identity is a remarkable equation that combines five fundamental mathematical constants: e, i, \u03c0, 1, and 0. It showcases the deep connections between different areas of mathematics, such as algebra, geometry, and calculus.", "Euler's identity is derived from Euler's formula, which states that e^(ix) = cos(x) + i*sin(x). When x is set to \u03c0, the formula simplifies to e^(i\u03c0) = cos(\u03c0) + i*sin(\u03c0). Since cos(\u03c0) = -1 and sin(\u03c0) = 0, this further simplifies to e^(i\u03c0) = -1. Adding 1 to both sides results in e^(i\u03c0) + 1 = 0.", "This identity is not only elegant but also surprising, as it links seemingly unrelated mathematical concepts. It serves as a testament to the beauty and unity of mathematics, demonstrating how different branches can come together in a single, simple equation."], "example": "Using Euler's formula, we can express e^(i\u03c0) as cos(\u03c0) + i*sin(\u03c0). Substituting the values, we get e^(i\u03c0) = -1 + i*0, which simplifies to e^(i\u03c0) = -1. Adding 1 to both sides gives us e^(i\u03c0) + 1 = 0.", "whyItMatters": "Euler's identity is significant because it encapsulates the beauty and interconnectedness of mathematics, illustrating how different concepts can converge in a simple yet profound equation.", "imageUrl": "https://upload.wikimedia.org/wikipedia/commons/thumb/7/71/Euler%27s_formula.svg/1280px-Euler%27s_formula.svg.png"}, {"id": "4fddac1e198b", "title": "Quadratic equation", "slug": "quadratic-equation", "headline": "Quadratic equation standard form: ax\u00b2 + bx + c = 0", "summary": "Write the quadratic formula", "source": "Write the quadratic formula", "sourceUrl": "https://en.wikipedia.org/wiki/Quadratic_equation", "articleUrl": "https://en.wikipedia.org/wiki/Quadratic_equation", "publishedAt": "2026-06-12", "category": "learn", "cohortScore": 0.5, "embedding": [-14, -1, -5, -1, -6, 4, -3, 2, 7, -1, 3, -4, 6, -5, 1, -3, -3, 6, -3, 0, 8, -6, -2, 0, 5, 6, -5, -1, 1, -22, 2, 3, 10, -1, 0, -6, -4, 5, -1, -6, 0, 0, 10, 3, -1, -1, -7, 0, 11, 2, -3, -1, -8, 2, 1, 4, 1, -6, 1, 5, 4, 1, -17, 8, 9, -1, -8, -6, -1, 10, -6, -6, 5, 2, -2, 0, -2, -4, 0, 0, -5, -2, -1, 4, 9, -1, 3, -4, 2, -1, 5, -2, -9, 0, -11, -14, -1, 2, -3, 39, 3, -6, -4, -5, -3, -8, 3, -2, -2, -6, -6, 2, 3, -10, -2, -3, 0, 2, 0, -6, 5, 0, 2, 1, 10, -4, -4, 6, -7, 13, 15, 2, 2, -3, -5, 4, 1, 5, 4, 0, 4, -2, -4, 3, -2, 10, -5, -6, 3, 4, 7, 6, 1, 2, 13, -5, 4, -5, -7, -6, -11, -8, -12, 15, 2, 0, 8, 8, 4, -4, 11, -5, -1, -1, 9, 0, -4, -3, 10, -5, 9, -6, -1, -2, 6, 3, -9, -2, -6, -7, 1, 2, -10, 7, -10, 0, 1, -11, 1, -4, 6, 1, 1, 0, 0, -1, 7, 1, -3, 10, -3, -8, 4, -3, -2, 2, 0, 1, -2, 6, 0, -5, -5, -34, 3, 1, -14, 7, -5, 6, -4, -8, 5, 7, -1, -4, -4, -6, -3, 2, -4, 2, 4, -9, -10, -1, -2, 1, 2, 19, 6, 7, 3, 1, 2, -1, 8, 4, -2, 3, 8, 0, -1, 5, -1, -1, 4, 3, 3, -4, -4, -4, 2, 8, 1, 4, -3, -1, -7, -5, 3, -2, 1, 0, 0, 1, -2, -8, 5, 8, -8, 6, -4, 2, 8, 5, -5, 7, -4, 6, 11, 7, -1, -6, -6, 4, 1, 4, 1, 4, 2, 4, -6, -4, -4, 7, 7, -1, 4, -36, -3, 6, 2, -2, -7, 2, -8, -13, -1, -5, 7, 3, 2, 3, -9, 2, -8, 4, -5, 6, 4, 22, 0, 3, 2, -1, 2, 8, 1, 3, -3, 14, -1, 1, -3, -7, 5, 2, -3, -6, -2, -4, 1, 2, 0, -6, -2, 3, 2, 1, 9, 2, 0, 7, 9, -5, -8, -2, 4, -6, 3, 15, -1, 8], "explanation": ["A quadratic equation is expressed in the standard form ax\u00b2 + bx + c = 0, where 'a', 'b', and 'c' are coefficients and 'a' cannot be zero. This form is essential for solving quadratic equations using various methods. The coefficients 'a', 'b', and 'c' represent the quadratic coefficient, the linear coefficient, and the constant term, respectively."], "example": "Consider the quadratic equation 2x\u00b2 + 3x + 1 = 0. Here, 'a' is 2, 'b' is 3, and 'c' is 1. This equation can be solved using methods like factoring, completing the square, or the quadratic formula.", "whyItMatters": "Understanding the standard form of a quadratic equation is crucial for applying different solving techniques and finding the roots of the equation.", "imageUrl": "https://upload.wikimedia.org/wikipedia/commons/2/28/Circle_radians_tau.gif", "imageLicense": "Public domain", "imageArtist": "Lucas Vieira"}, {"id": "6c6a1ac72fd2", "title": "Binomial coefficient", "slug": "binomial-coefficient", "headline": "Binomial coefficient formula: (n choose k) = n! / (k!(n-k)!)", "summary": "Write the formula for binomial coefficient n choose k", "source": "Write the formula for binomial coefficient n choose k", "sourceUrl": "https://en.wikipedia.org/wiki/Binomial_coefficient", "articleUrl": "https://en.wikipedia.org/wiki/Binomial_coefficient", "publishedAt": "2026-06-12", "category": "learn", "cohortScore": 0.5, "embedding": [-12, 4, 6, -5, -2, 3, 2, 6, 8, 2, 1, -7, -2, -3, -8, -3, -10, 1, -6, 3, 9, -2, -5, -8, 7, 9, 4, -3, -7, -18, 0, 7, 6, -9, -1, 4, -6, 5, -4, -1, 1, 1, 11, 2, 2, 3, 1, -4, -2, -4, 3, -4, -3, 1, 2, -2, 0, 6, 4, 0, 6, 2, -19, 5, 3, 0, -1, 2, -7, 11, -3, 3, 1, 5, 8, 4, -6, -13, -2, -3, -6, -2, -5, 7, 0, 4, -6, -4, 5, 2, 3, 3, 0, -4, -8, -1, -4, 2, 5, 41, 3, 0, -9, -1, -7, -5, -3, -2, 2, -3, 4, 1, 8, -12, -6, -4, -2, 0, 1, -5, 0, 3, 7, 2, 11, 2, -5, 7, -6, 5, 7, -2, -2, -5, -6, 2, -2, 0, -4, -1, 7, -7, 1, 1, 6, 13, -5, -1, -2, 1, -2, 3, -2, 0, 2, -6, 0, 0, -8, -2, -4, -4, 2, 11, -1, -2, 10, 3, -4, -6, 4, 4, -6, 0, 8, 1, -1, 2, 15, -4, 6, 2, 0, 1, 3, 0, -8, -5, -2, 1, -4, 1, -8, -2, -11, -6, -9, -5, 2, 0, 5, 0, 5, 3, 2, 2, 17, -8, 2, 2, -2, 1, 2, 6, 0, 0, -4, 3, 11, -6, 6, -14, 2, -36, 2, 3, 0, 5, -4, 10, -2, -4, 9, 9, -8, -5, -8, -7, -8, -6, -7, 0, 10, 6, -6, 4, 4, -4, 0, 13, 5, 12, 7, 5, 0, -1, 5, -1, -5, -3, -6, -9, -8, 2, 7, -4, -1, 1, -2, -5, -3, -4, 6, -3, 2, 6, -5, -2, -5, 0, -1, -4, 3, 7, -11, 0, -4, -9, -1, 3, -4, 1, 2, 1, 8, 3, -4, 11, 4, 1, 4, 4, -3, 4, -12, 4, 5, 6, 2, 7, 7, 0, -1, -12, -1, 0, 4, -3, 1, -29, 7, -6, 3, 5, -5, 5, -10, -9, 3, -2, 3, -1, -1, 7, -8, 6, -4, 2, 3, 17, -2, 17, 6, 4, -1, 3, 0, 8, 1, -3, 4, 13, -5, -1, -1, -3, 3, 7, -1, 2, -7, -8, -1, 14, 9, -1, -15, 0, 3, -9, 7, -4, 4, 9, 1, -5, 2, -6, -6, -4, 3, 13, 4, -3], "explanation": ["The binomial coefficient, denoted as (n choose k) or C(n, k), represents the number of ways to choose k elements from a set of n elements without regard to the order of selection. It is a fundamental concept in combinatorics and appears in the binomial theorem, which describes the algebraic expansion of powers of a binomial.", "The formula for calculating the binomial coefficient is given by (n choose k) = n! / (k!(n-k)!), where n! denotes the factorial of n, which is the product of all positive integers up to n. This formula allows us to compute the number of combinations efficiently."], "example": "To find the number of ways to choose 3 elements from a set of 5 elements (5 choose 3), we use the formula: (5 choose 3) = 5! / (3!(5-3)!) = 120 / (6 * 2) = 10. Thus, there are 10 ways to choose 3 elements from a set of 5 elements.", "whyItMatters": "Understanding the binomial coefficient formula is crucial for solving problems related to combinations and permutations in various fields such as mathematics, computer science, and statistics.", "imageUrl": "https://upload.wikimedia.org/wikipedia/commons/thumb/f/f6/Pascal%27s_triangle_5.svg/1280px-Pascal%27s_triangle_5.svg.png"}, {"id": "129cacf176cb", "title": "Poisson distribution", "slug": "poisson-distribution", "headline": "Poisson distribution formula: P(k; \u03bb) = (\u03bb^k * e^(-\u03bb)) / k!", "summary": "Write the formula for Poisson distribution probability", "source": "Write the formula for Poisson distribution probability", "sourceUrl": "https://en.wikipedia.org/wiki/Poisson_distribution", "articleUrl": "https://en.wikipedia.org/wiki/Poisson_distribution", "publishedAt": "2026-06-12", "category": "learn", "cohortScore": 0.5, "embedding": [-11, 0, 6, -5, -4, 7, 0, 0, 11, 8, 4, -13, 1, -8, -8, 3, -7, 3, -13, 4, 14, -8, -11, -8, 8, 9, -1, 6, 0, -19, -4, -4, 4, -5, -4, -1, -3, 2, 0, 3, -1, -1, -1, 2, 6, 1, -5, -5, -1, -3, 3, 2, -2, -1, 1, -8, 0, 5, 2, 7, -4, 8, -12, 9, 3, 2, -9, -3, 0, 6, -6, 2, -3, 14, 6, 4, -8, -9, -2, -2, -5, 1, -3, 9, -4, -2, 7, -5, 3, -1, 2, 8, -5, 1, -2, -1, 2, 1, 6, 42, -5, -1, 1, 5, 5, -2, -3, -1, 1, -4, -1, -2, -2, -11, -4, -5, 3, 5, 3, -5, -1, 0, 6, 5, 11, 2, 0, 6, -1, 12, 5, 2, 0, -3, -2, -1, -4, -1, 1, 7, 6, 0, -6, -2, 5, 11, -5, 0, -1, -8, -2, 7, 7, -7, 10, -11, -3, 6, -3, 6, -8, -4, 2, 15, -7, 3, 8, -4, 2, -5, 6, 10, 0, 6, 3, -2, -4, -3, 10, -4, 4, 3, 1, 2, -1, -3, -11, -1, 0, 6, 3, -3, 3, -5, -9, -6, -7, 1, -4, 1, 5, -3, -6, 1, -1, 3, 9, 1, -3, 1, -1, -8, 0, 7, -5, 8, -4, 1, 7, -3, -3, -10, 0, -33, -1, -1, -2, 0, -2, 4, 1, -2, 4, 11, -3, -3, -11, 2, -8, -1, -7, -3, 9, 3, -6, -5, 4, 8, 8, 12, -1, 5, -2, -1, 0, -6, 6, 4, -4, 1, 4, -5, -1, 1, 11, -11, -2, -6, -7, 0, 9, -3, 8, 5, 1, 7, -4, 4, -8, 0, 5, -9, -4, -3, -5, 9, -2, -5, -5, 1, -9, 1, -2, 0, 12, 0, 0, 8, 0, 7, 1, -1, -6, 3, -8, 3, 0, 9, 2, 1, 8, -5, 5, -5, 1, -3, 4, -8, -1, -33, 7, -1, 9, -6, 6, -1, -11, -3, -1, -3, 4, 2, -1, 6, -6, -1, -7, 4, 1, 12, -3, 17, -1, 2, -5, 10, 8, 7, -4, -2, 3, 8, -1, -5, -3, -3, 1, 2, -5, 6, -8, 4, -1, 12, 7, 0, -14, -1, 0, -9, 2, -6, 8, -3, 9, 3, -9, 0, -2, -1, 0, 10, -3, 4], "explanation": ["The Poisson distribution formula calculates the probability of observing k events in a fixed interval when events occur independently at a constant mean rate \u03bb. This formula is essential for understanding the likelihood of various outcomes in scenarios modeled by Poisson processes."], "example": "If a bookstore averages 3 sales per hour (\u03bb = 3), the probability of exactly 2 sales in the next hour (k = 2) is calculated using the Poisson formula: P(2; 3) = (3^2 * e^(-3)) / 2! = (9 * e^(-3)) / 2 \u2248 0.224.", "whyItMatters": "Understanding the Poisson distribution formula is crucial for accurately predicting event probabilities in fields like telecommunications, insurance, and traffic flow management.", "imageUrl": "https://upload.wikimedia.org/wikipedia/commons/thumb/1/16/Poisson_pmf.svg/1280px-Poisson_pmf.svg.png"}, {"id": "18936f0a165f", "title": "Normal distribution", "slug": "normal-distribution", "headline": "Normal distribution PDF formula", "summary": "Write the formula for normal distribution PDF", "source": "Write the formula for normal distribution PDF", "sourceUrl": "https://en.wikipedia.org/wiki/Normal_distribution", "articleUrl": "https://en.wikipedia.org/wiki/Normal_distribution", "publishedAt": "2026-06-12", "category": "learn", "cohortScore": 0.5, "embedding": [-9, 4, 7, -5, 2, 2, -5, -2, 9, 3, 4, -6, -1, -3, -5, -5, -8, 0, -9, 5, 15, -5, -7, -2, 10, 8, -10, -5, -8, -20, 1, -2, 4, -6, 3, -5, -4, 4, 7, 2, -6, 2, 1, -3, 6, -6, -8, -7, 4, 0, -5, 3, -1, 2, 0, -1, 6, 0, 6, 7, 0, 14, -19, 8, 9, -2, -13, 1, 4, 3, -7, -8, -1, 7, 9, -2, -3, -7, -8, -1, -8, 8, 0, 4, 3, -2, 11, -4, 6, -8, 6, 9, -5, 8, -5, -2, 4, -2, 8, 38, 0, -4, -1, 3, -4, -7, 2, 0, 0, -6, -1, -1, 1, -9, 2, -10, -1, -1, -1, -6, 5, 3, 1, 4, 11, 0, 2, 10, -7, 5, 2, 5, -5, -6, 0, 1, -6, -1, -2, 6, 4, 1, -10, -1, 5, 19, -7, -2, -1, 4, 5, 9, 8, -3, 13, -2, -3, 0, -5, -3, -7, -12, 2, 10, -1, -4, 4, -2, 2, -1, 0, -2, 5, 4, 7, 2, 2, -2, 5, -2, 1, 5, -1, -5, 0, -1, -2, 1, -4, 9, 6, -2, -3, 0, -6, 2, -3, 4, 0, -6, 5, 1, 5, -8, -1, 2, 9, -4, 2, 2, -4, -11, 7, 1, -8, 7, -4, 1, 1, 1, 3, -2, -6, -33, -1, 1, -1, -3, 4, 5, 4, -2, 7, 12, -4, -3, -8, -4, -5, 2, -3, 0, 7, 2, -5, -7, 3, 12, 5, 12, -9, 11, -3, 0, 2, -1, 2, 2, -5, -5, 2, -3, -8, 0, 5, -1, 1, -6, -4, -4, 1, -1, 7, -3, 2, 9, -3, 0, -5, -3, 5, -13, -2, 0, -5, 13, -10, -11, -5, 0, -4, 7, 0, -6, 10, -1, 1, 8, 1, 2, 1, 3, -7, 7, 4, 10, 2, 2, 1, 0, -2, 1, 7, -3, -4, 2, 11, -5, 4, -32, -3, 2, 5, 3, -1, 2, -4, -10, 3, -9, 11, 1, -1, 0, -7, 1, -1, 4, -1, 1, -5, 22, -5, -6, -2, 6, 0, 6, -2, 4, 5, 6, 3, 6, 1, -5, 1, 8, -8, 7, -7, -3, -1, 8, 3, -7, -8, -8, 0, -14, -1, -5, 2, 10, 6, 2, -1, -6, 1, -3, -7, 13, 4, 0], "explanation": ["The normal distribution, also known as Gaussian distribution, is a fundamental concept in probability theory and statistics. Its probability density function (PDF) is crucial for understanding the distribution of continuous data.", "The formula for the normal distribution PDF is given by:", "f(x) = (1 / (\u03c3\u221a(2\u03c0))) * exp(-((x - \u03bc)\u00b2 / (2\u03c3\u00b2)))", "In this formula, \u03bc represents the mean of the distribution, \u03c3 represents the standard deviation, and exp denotes the exponential function. The constant (1 / (\u03c3\u221a(2\u03c0))) is the normalization factor that ensures the total area under the curve equals 1.", "Understanding the normal distribution PDF is essential for various applications in statistics, such as hypothesis testing, confidence intervals, and data analysis. It helps in determining probabilities and making inferences about population parameters based on sample data."], "example": "For a normal distribution with a mean (\u03bc) of 50 and a standard deviation (\u03c3) of 10, the PDF at x = 60 is calculated as follows:\n\nf(60) = (1 / (10\u221a(2\u03c0))) * exp(-((60 - 50)\u00b2 / (2 * 10\u00b2)))\n       = (1 / (10\u221a(2\u03c0))) * exp(-((10)\u00b2 / (200)))\n       = (1 / (10\u221a(2\u03c0))) * exp(-0.5)\n       \u2248 0.024", "whyItMatters": "The normal distribution PDF formula is fundamental in statistics for calculating probabilities and making inferences about population parameters.", "imageUrl": "https://upload.wikimedia.org/wikipedia/commons/thumb/7/74/Normal_Distribution_PDF.svg/1280px-Normal_Distribution_PDF.svg.png"}, {"id": "caec657610a4", "title": "Conditional probability", "slug": "conditional-probability", "headline": "P(A|B) = P(A \u2229 B) / P(B)", "summary": "Write the formula for conditional probability P(A|B)", "source": "Write the formula for conditional probability P(A|B)", "sourceUrl": "https://en.wikipedia.org/wiki/Conditional_probability", "articleUrl": "https://en.wikipedia.org/wiki/Conditional_probability", "publishedAt": "2026-06-12", "category": "learn", "cohortScore": 0.5, "embedding": [-15, -3, -5, -3, -12, 2, 6, 3, 13, 4, 1, -11, 6, -1, -9, 3, -7, 7, -4, 6, 5, -10, -6, -7, 5, 10, 2, 9, -1, -19, 0, 3, 3, -8, 3, -7, -5, 2, 2, 1, 3, -3, 5, 2, -5, -5, -3, -6, -2, 2, 2, 0, -2, 2, -3, -3, -2, 9, 1, 6, 2, 9, -14, 9, 3, 0, -11, -2, -2, 12, -6, 6, 4, 14, 1, -1, -3, -9, -1, 1, -10, 1, 0, 6, 3, -5, 0, -3, 1, -6, 5, 7, -6, 1, 1, 4, 7, -2, 9, 45, -8, -2, -10, -1, -1, -10, -1, -3, -6, -2, -1, -3, 6, -8, -4, 3, 9, 7, 3, -7, -3, -4, 1, 3, -3, 0, -1, 14, -6, 9, 7, -3, -2, -1, 1, -6, -4, 0, 0, -3, 4, -5, 0, -4, 5, 13, -9, 1, -6, -4, -1, -1, 4, -3, 6, -3, 2, -1, 0, 0, -2, -5, -4, 13, -5, -1, 4, -5, 0, -3, -2, 2, 1, -3, 4, 4, 0, 2, 10, 1, 7, -1, -2, -5, 0, -2, -6, -1, -3, 3, 5, -6, -6, 1, -6, -5, -5, -5, -6, 3, 7, 2, -5, -2, 2, 0, 8, 0, -2, 0, 7, -5, -4, 3, 0, 3, 3, 8, 3, 3, 0, -2, 6, -34, 1, 2, -4, 0, 2, -6, -1, -7, 7, 6, -9, -6, 5, -5, -9, 0, -2, -1, 1, -5, -5, -2, -3, 5, 4, 15, 1, 7, 5, 0, -2, -6, 6, 5, 2, -8, 1, -11, -2, 1, 8, -6, -3, -4, -8, 3, 7, 2, 13, 4, 1, 7, -6, 2, -5, 1, 6, -9, 8, 4, -2, 7, 4, -1, 0, 0, -10, 1, 2, 2, 11, 2, 0, 4, 5, 14, 5, -3, -4, 6, -6, 6, 6, 8, -1, 7, 10, 2, 2, -5, 1, -5, 11, -9, 2, -34, 1, 0, 0, -2, 4, 4, -4, -12, -6, 0, 4, 5, 1, -7, -8, 1, -5, -2, -4, 9, 0, 17, -4, 5, -4, 7, 0, 5, -3, -6, -4, 3, -7, 1, 7, -3, 1, 1, -7, 0, -10, -2, 0, 18, 9, -4, -1, 1, 0, 1, 7, -4, 3, 2, -2, 2, -5, -1, 0, 1, 3, 13, -4, 1], "explanation": ["Conditional probability measures the likelihood of an event A occurring given that another event B has already occurred. It is expressed as P(A|B), which can also be written as PB(A). This formula helps us understand the relationship between events A and B."], "example": "Suppose we have two events: A is drawing a red card from a standard deck, and B is drawing a card from the same deck. If we know that we have drawn a red card (event B), the conditional probability of drawing a red card that is also a heart (event A) is P(A|B) = P(A \u2229 B) / P(B). In this case, P(A \u2229 B) = 1/52 (since there is 1 heart in a deck of 52 cards) and P(B) = 1/2 (since there are 26 red cards in a deck of 52 cards). Therefore, P(A|B) = (1/52) / (1/2) = 1/26.", "whyItMatters": "Understanding conditional probability is crucial in many fields, such as statistics, finance, and decision-making, as it helps us make informed predictions and decisions based on known information.", "imageUrl": "https://upload.wikimedia.org/wikipedia/commons/thumb/3/3a/Standard_deviation_diagram_micro.svg/1280px-Standard_deviation_diagram_micro.svg.png"}, {"id": "3ac5a8f41e29", "title": "Expected value", "slug": "expected-value", "headline": "Expected value formula: E[X] = \u03a3 [x * P(x)]", "summary": "Write the formula for expected value E[X]", "source": "Write the formula for expected value E[X]", "sourceUrl": "https://en.wikipedia.org/wiki/Expected_value", "articleUrl": "https://en.wikipedia.org/wiki/Expected_value", "publishedAt": "2026-06-12", "category": "learn", "cohortScore": 0.5, "embedding": [-12, 0, 12, -5, -1, -3, 4, 2, 11, 4, 4, -8, -1, -6, -5, -4, -11, 0, -11, 7, 12, -7, -7, -6, 7, 9, -2, 2, -5, -19, -4, -3, 4, -9, -2, 0, -4, 1, 5, 5, -1, -3, 1, 2, -3, -3, -9, -3, 2, -1, 0, 2, -3, -5, -4, 3, 0, 6, 5, 5, 2, 10, -13, 3, 8, 1, -9, -5, 3, 7, -7, -1, 5, 12, 5, 0, 2, -6, -4, -5, -10, 2, -5, 9, 3, 0, 9, 3, 10, -2, -1, 7, -9, -2, 1, 0, -1, 3, -2, 45, 1, 3, -2, 3, 1, -12, -5, 0, -4, -11, 1, -3, -3, -11, -6, 2, 2, -2, 0, -8, -3, 0, 0, 4, 7, 0, 0, 17, -6, 12, 4, -2, -4, 4, 1, 2, -2, -1, 3, 1, 7, -7, -10, -2, 3, 15, -4, 0, 1, -6, -1, 3, 1, -3, 7, -2, 3, -1, -4, -4, -14, -5, 0, 10, -4, 4, 4, -1, 1, -5, 7, 2, -2, -3, 8, 5, -3, 0, 9, -3, 2, -2, 1, 1, 0, 0, -5, -1, -1, 5, 4, -2, 1, 5, -10, -3, -3, 0, -1, -2, 8, -2, -1, 2, -3, 0, 1, 3, -3, 2, -1, -7, 3, 1, -6, -3, 3, 8, 9, 0, -2, -7, -5, -38, -1, 1, -1, 1, -3, 2, -3, -5, 5, 3, -1, 0, -6, -2, -6, -6, -9, -2, 9, -2, 0, -4, -2, 6, 1, 13, 1, 8, -3, -2, -2, 0, 8, 5, 1, -6, 10, -2, -5, 0, 6, -6, 3, -5, -3, -1, -2, 2, 8, 5, 2, 3, -7, 3, -3, 2, 12, -7, 0, 7, 0, 4, -2, -4, -6, 5, -6, 2, 1, -4, 12, -2, -3, 8, 1, 2, 3, -1, 7, 0, 1, 0, 4, 10, 3, 2, 7, -3, 4, -8, -5, 1, 8, -10, -4, -36, 4, -3, 0, 1, 0, -1, -6, -17, 3, -4, 2, 6, 6, 0, -7, 0, -4, -1, 5, 8, 1, 27, -1, 1, 0, 4, -1, 15, -3, 1, -2, 9, 0, 7, 4, 2, -4, 4, -7, 8, -1, -1, -4, 14, 4, 2, -7, -6, -1, -8, 2, -5, 4, 1, 7, -3, -3, -4, -1, 1, -1, 5, 0, 3], "explanation": ["The expected value formula for a discrete random variable X is the sum of the products of each outcome x and its probability P(x). This formula captures the weighted average of all possible outcomes, where the weights are the probabilities."], "example": "For a fair six-sided die, the expected value E[X] is calculated as follows: E[X] = (1*1/6) + (2*1/6) + (3*1/6) + (4*1/6) + (5*1/6) + (6*1/6) = 3.5", "whyItMatters": "Understanding the expected value formula is fundamental in probability theory as it helps in predicting the average outcome of a random variable over many trials.", "imageUrl": "https://upload.wikimedia.org/wikipedia/commons/thumb/3/3a/Standard_deviation_diagram_micro.svg/1280px-Standard_deviation_diagram_micro.svg.png"}, {"id": "00e04f41a82c", "title": "Hessian matrix", "slug": "hessian-matrix", "headline": "The Hessian matrix is denoted by H or \u2207\u00b2", "summary": "Write the Jacobian matrix for f: R^n \u2192 R^m", "source": "Write the Jacobian matrix for f: R^n \u2192 R^m", "sourceUrl": "https://en.wikipedia.org/wiki/Hessian_matrix", "articleUrl": "https://en.wikipedia.org/wiki/Hessian_matrix", "publishedAt": "2026-06-12", "category": "learn", "cohortScore": 0.5, "embedding": [-6, 1, -4, 3, -4, 3, -1, 11, 6, -3, -2, -5, 3, 1, 2, -3, -2, 10, -3, 2, 8, -7, -1, -6, 4, 10, -3, 4, -3, -24, 4, -4, 12, -1, 5, 1, -4, 0, -9, -4, -2, 1, 1, 8, 0, -3, -9, -5, -4, -6, -3, 0, 0, -1, 16, 3, 2, -5, 2, 6, 10, 1, -20, 5, 7, 3, 0, -7, 1, 15, -1, -2, -7, 2, 4, 0, -6, -5, -2, -3, 3, 5, 2, 0, 4, -5, 5, -8, 1, 5, -4, -2, 0, -1, -5, -6, 4, 5, 1, 43, 0, -5, 4, -2, -2, -5, -7, -1, 7, -2, -5, -1, 6, -8, -4, -8, 5, 9, -8, 1, -5, 4, 5, -1, 3, -2, -5, 11, 3, 5, -6, 11, 1, -5, -1, 1, -3, -3, -3, -1, -2, 3, -7, 2, -2, 12, -10, -4, -5, 1, 1, 7, 2, -6, 5, 6, 1, -2, -14, -1, -10, -6, -1, 13, -3, 1, 5, 6, 2, -8, 8, 1, 5, 0, 6, 3, -5, -7, 6, -5, 2, -1, -1, -2, 9, 2, -6, -8, -1, 3, -3, 0, 0, -4, -1, -3, 0, 5, -4, 4, 3, 5, 3, 8, 1, -6, 4, -4, -12, 7, -7, -5, 2, -1, -6, 13, 2, -2, -7, 3, 3, -7, -7, -36, -4, -1, -3, 2, -6, 11, -1, -1, 5, 7, 0, -5, -1, 6, 0, 5, -2, 1, -2, -4, -5, -3, 4, 6, -2, 18, 2, 8, 1, 9, 4, -2, 7, 3, -5, 6, 0, 4, -7, 4, 3, -3, 0, -4, -8, -4, -9, -4, 2, 12, -1, 8, -6, 0, -1, -4, -3, -7, 3, 1, -9, 4, -3, 2, -9, 2, -2, -10, 0, -4, -2, 1, -2, 9, -5, 1, 8, -1, -4, -5, 1, 5, 9, -1, -1, 1, -1, -1, 1, -7, -1, -5, 8, -3, -2, -32, -1, 8, 2, -5, -3, 5, -9, -10, -3, 0, 10, 3, 3, 9, -3, 1, -1, -2, -7, 3, 4, 23, -12, 4, 0, 4, -2, 5, -2, 3, 0, 14, 5, 7, 8, -5, 1, 10, -1, 6, 3, -4, -1, 8, 0, 7, 0, -2, -2, 7, 6, 4, 8, 1, -4, -5, -5, -4, 5, -8, 2, -1, -5, 2], "explanation": ["The Hessian matrix is a fundamental concept in multivariable calculus and optimization. It is a square matrix containing second-order partial derivatives of a scalar-valued function. The Hessian matrix provides valuable information about the local curvature of the function, helping to determine whether a critical point is a local minimum, maximum, or saddle point.", "The Hessian matrix was developed in the 19th century by the German mathematician Ludwig Otto Hesse. Hesse originally used the term \"functional determinants\" to describe this matrix. Over time, the term \"Hessian\" became more commonly used.", "The Hessian matrix can be denoted in several ways, including H, \u2207\u00b2, \u2207\u2297\u2207, or D\u00b2. Each notation represents the same mathematical concept, but they may be used in different contexts or by different authors."], "example": "For a function f(x, y) = x\u00b2 + y\u00b2, the Hessian matrix is given by H = [[2, 0], [0, 2]].", "whyItMatters": "Understanding the Hessian matrix is crucial for analyzing the behavior of multivariable functions and optimizing them in various applications.", "imageUrl": "https://upload.wikimedia.org/wikipedia/commons/f/f8/Sierpinski-carpet.gif", "imageLicense": "CC BY 4.0"}, {"id": "6174706a0044", "title": "Lagrangian L(x,\u03bb) = f(x) - \u03bbg(x)", "slug": "lagrangian-l-x-f-x-g-x", "headline": "How do we find the path an object naturally takes?", "summary": "Write the formula for Lagrangian L(x,\u03bb) = f(x) - \u03bbg(x)", "source": "Write the formula for Lagrangian L(x,\u03bb) = f(x) - \u03bbg(x)", "sourceUrl": "https://en.wikipedia.org/wiki/Lagrangian_mechanics", "articleUrl": "https://en.wikipedia.org/wiki/Lagrangian_mechanics", "publishedAt": "2026-07-03", "category": "learn", "cohortScore": 0.5, "embedding": [-11, -6, 3, -2, -1, -1, 3, 2, 2, 5, 4, -10, 0, -7, 2, -6, -5, 12, -11, -1, 8, -5, -5, -11, 3, 11, 7, 4, 0, -23, 0, -5, 3, -5, -1, 7, -3, 7, -2, 4, 8, 0, 3, 2, 3, -1, -6, 2, -2, 0, -4, 3, -2, -7, 2, 8, 3, -3, 8, 8, 1, 2, -13, 8, 7, 5, -1, -3, 2, 14, 0, -2, -4, 5, 9, 3, -1, -6, 0, -4, -1, 5, -9, 9, 1, -1, 9, -7, 3, 4, 0, 3, 0, 4, -5, -8, -2, 1, 6, 45, -4, 3, 4, 9, 2, -3, -4, -2, 2, -2, 0, -1, 2, -11, -4, -1, -4, -1, -7, 2, -1, -1, 4, 2, 5, -4, -4, 9, 5, 10, 4, 2, -8, -3, -5, 4, -4, 1, 2, 8, 0, -3, 1, 0, -1, 8, -6, -7, -5, -1, -3, 5, -2, -6, -2, 2, -3, 0, -11, 0, -14, -6, 0, 16, -7, 0, 11, 0, 2, -5, 7, 6, -6, -3, 9, 0, -12, 2, 1, 3, 2, 0, -7, 0, 4, -2, -5, -1, -3, 6, 4, 4, -2, -4, -8, -6, -3, 2, -2, 4, 5, 2, -3, -5, 1, -5, 6, -4, -3, 6, -4, -6, 3, -4, 1, 5, 1, -7, -3, -2, -6, -9, -1, -38, -1, -6, 1, 5, -6, 1, -1, -8, 5, 11, -4, 0, -2, 1, -2, 0, -1, -4, 4, -5, -7, -5, -4, -2, 2, 24, 0, 9, -6, 5, -2, -4, 11, 2, -3, 9, 4, 8, -2, -3, 5, -1, 5, -3, 4, -1, -1, 7, 0, 3, 5, 1, 1, -6, 3, -1, 4, -7, 3, -5, 0, 3, 3, 3, -2, -2, -8, 2, 2, 4, 1, 5, 1, 5, -4, 2, 12, -3, -5, 5, -3, -2, -4, 3, -6, 1, -6, -5, -1, -4, -3, -5, 3, -4, 0, -37, -1, 7, 8, -6, 1, 10, -10, -3, 0, -4, 5, 4, -1, 4, -7, 5, 0, 1, 0, 6, 4, 21, -7, 5, -1, -3, -6, 12, -7, -5, 8, 10, -1, 10, 0, 1, 5, 5, -6, 2, 2, 3, -1, 7, -4, 2, -1, -7, 4, -4, 8, -1, 6, 2, 4, -5, -6, -9, -2, -2, 1, 8, -9, 5], "imageUrl": "https://upload.wikimedia.org/wikipedia/commons/thumb/8/80/Composition_C_%28No.III%29_with_Red%2C_Yellow_and_Blue_-_Mondrian_%281935%29.jpg/1280px-Composition_C_%28No.III%29_with_Red%2C_Yellow_and_Blue_-_Mondrian_%281935%29.jpg", "imageLicense": "CC BY-SA 4.0", "imageArtist": "Egrabczewski", "explanation": ["Imagine you're throwing a ball; it doesn't just go straight up but follows a curved path. Why does it curve?", "Think of the ball's path as a journey it takes, with different forces acting on it. The Lagrangian helps us figure out this path by balancing the ball's energy and the forces acting on it."], "example": "If a ball is thrown with a certain speed and angle, the Lagrangian helps predict its curved trajectory.", "whyItMatters": "The Lagrangian formula (L(x,\u03bb) = f(x) - \u03bbg(x)) calculates the path by balancing energy and forces."}, {"id": "db60497c368e", "title": "convolution (f * g)(t) = \u222bf(\u03c4)g(t-\u03c4)d\u03c4", "slug": "convolution-f-g-t-f-g-t-d", "headline": "How do different shapes combine to create new patterns?", "summary": "Write the formula for convolution (f * g)(t) = \u222bf(\u03c4)g(t-\u03c4)d\u03c4", "source": "Write the formula for convolution (f * g)(t) = \u222bf(\u03c4)g(t-\u03c4)d\u03c4", "sourceUrl": "https://en.wikipedia.org/wiki/Convolution", "articleUrl": "https://en.wikipedia.org/wiki/Convolution", "publishedAt": "2026-07-03", "category": "learn", "cohortScore": 0.5, "embedding": [-5, -3, 1, 0, -4, 6, -3, 0, 7, -3, 1, -15, 5, 8, 4, -3, -5, 1, -8, -5, 6, -5, -5, -5, 0, 7, 2, -4, -1, -28, -1, 9, -3, -6, -4, -1, 0, 5, -4, 2, -3, -1, -4, -3, 2, -3, -12, 3, -6, 0, -1, -7, -3, 3, 0, 4, 0, 7, 4, 4, 1, 8, -12, 11, -5, 3, -3, -1, 5, 16, 3, 3, -1, 4, -1, 3, -5, 1, -5, 2, -6, 8, 5, 5, -1, -4, 0, -2, 2, -1, 2, -1, -3, 1, -7, -4, -2, 1, 7, 44, -5, -2, 5, 0, -3, -5, 1, -5, -6, 1, -4, -6, -2, -5, -6, -5, 0, 2, -2, 2, -2, -1, 2, -5, 2, 3, -6, 10, 5, 8, 1, 10, 0, -1, -2, 2, 0, -3, 0, 1, 0, 2, 5, 4, 9, 14, -12, -3, -6, 0, 1, 5, 0, -8, 6, 1, 2, -6, -3, 1, -7, -2, -5, 14, -1, -10, 2, -2, 3, -5, 6, 1, 0, -1, 8, 6, -10, -3, 4, -1, 4, -6, -5, -2, 2, -7, 4, 0, -3, 5, 2, 4, -1, 0, -10, -6, -2, 1, -4, 1, -3, 3, 2, -1, 1, -2, 8, 0, 1, 9, -2, -5, 0, 1, 1, 4, 3, 1, -5, 0, -6, -14, -7, -40, -4, 8, 1, -1, -8, 2, 2, 2, 2, 6, 0, -6, -8, -2, -5, 2, 6, 2, 0, -3, 2, 7, -6, 5, 7, 22, -1, 5, 1, 0, 3, -6, 8, 7, -1, 7, 16, 0, -7, -7, -1, 2, -4, -1, 3, -8, 1, -4, 0, -4, -4, -1, -4, -5, 0, -6, 5, -4, 1, 3, 1, 4, -4, -1, 4, -4, -8, 0, 1, 2, 9, 4, 1, 12, -4, 3, 3, 0, -2, 6, -1, -3, 4, 7, 2, 9, -1, 9, -4, 2, -2, 4, 11, -4, -1, -38, 3, 4, 7, 4, -3, 1, -8, 0, -8, -8, 4, 6, -7, 4, 1, 9, -6, 5, -2, 3, 3, 26, -8, 2, -2, 4, -5, 11, 1, 2, -2, 13, -1, 5, 4, -3, 5, 1, 0, 1, 1, -2, 2, 7, 1, -1, 4, -10, -3, -3, 1, -4, -2, 1, 1, 0, 3, 0, 11, 0, -6, 3, -7, -6], "imageUrl": "https://upload.wikimedia.org/wikipedia/commons/thumb/b/ba/ResBlock.png/1280px-ResBlock.png", "imageLicense": "CC BY-SA 4.0", "imageArtist": "LunarLullaby", "explanation": ["Imagine you're mixing paints. You start with a small amount of blue and gradually add white paint. The resulting shade changes as you mix.", "Convolution is like mixing paints. It combines two functions (like colors) to create a new function (a new shade). The formula f * g)(t) = \u222bf(\u03c4)g(t-\u03c4)d\u03c4 shows how much of each function is combined at each point."], "example": "If f(t) represents the amount of blue paint and g(t) represents the amount of white paint, the convolution f * g)(t) gives the total amount of paint mixed at time t.", "whyItMatters": "Convolution helps us understand how combining different functions (like mixing paints) results in a new function (a new shade)."}, {"id": "a821aad1e108", "title": "Write the Bellman equation for reinforcement learning", "slug": "write-the-bellman-equation-for-reinforcement-learning", "headline": "Predicting tomorrow's weather with today's clues", "summary": "Write the Bellman equation for reinforcement learning", "source": "Write the Bellman equation for reinforcement learning", "sourceUrl": "https://en.wikipedia.org/wiki/Temporal_difference_learning", "articleUrl": "https://en.wikipedia.org/wiki/Temporal_difference_learning", "publishedAt": "2026-07-03", "category": "learn", "cohortScore": 0.5, "embedding": [-11, 1, 7, 3, 4, 4, 4, 0, 6, 1, -3, 1, 1, 7, 6, 5, -8, 6, 1, -2, 8, -4, -2, -7, -7, 5, -1, 2, -2, -20, -1, -4, 2, 0, -2, 1, 0, 1, 0, 7, -3, 4, -1, -3, -4, -6, 1, -6, -5, -5, -3, -7, -6, 2, 6, 3, 6, 7, 1, 4, -4, 1, -18, 5, 3, 6, -8, -1, 0, 9, -1, 5, 6, 5, 2, 9, -7, -5, -1, -9, 5, 0, -5, -2, 0, 0, 1, 0, 5, -2, -4, 1, -1, 3, -4, 3, 3, 3, -9, 44, -2, 1, -1, 5, 5, -6, -2, -7, -4, -4, -7, -5, 6, 0, 2, 4, 10, 5, 7, 3, -3, -1, 7, 2, 1, -9, -2, 19, -6, 1, 5, -3, -4, 3, 8, -1, -2, -5, -4, 4, -2, 7, 2, -6, -11, 12, 5, -8, -8, -5, -8, -2, 6, -3, 5, 7, -1, 1, -6, 2, -3, -2, -7, 7, -10, -5, -1, -2, 3, 0, 4, 1, 0, 1, 5, 5, -12, -1, 0, 3, 2, -10, 4, -1, -1, -2, 3, -10, -2, -2, 0, -5, 3, 4, -8, -3, 1, -3, -6, -4, -7, -6, -3, -7, 1, 0, 3, -1, 10, 0, 3, -3, 4, -4, -3, 3, 6, 1, -3, 0, 4, 5, 3, -37, -5, 4, -2, 7, 0, 9, -4, 6, 3, 4, -9, -3, -4, 4, -1, 4, 4, -3, 6, -4, 3, 0, -15, -2, 2, 20, 3, -3, 3, 1, 0, -5, -5, 10, 2, 12, 1, -5, -6, 0, 6, 0, -4, -12, -1, 0, 5, -10, -5, 5, -1, 7, -5, -6, -6, -3, 7, -2, -1, 4, -1, -4, 0, 0, 0, 7, -6, 1, 2, -4, 3, -2, 7, 4, -5, 4, 0, -5, 0, 11, -5, 9, 6, 1, -7, 3, -3, 5, 6, -3, 1, -2, -4, 9, 2, -38, 1, 3, 0, 0, 1, 5, -1, -8, -2, -2, 2, 3, 4, 0, -7, 9, -8, 4, -5, 0, 9, 26, -5, 7, 6, 1, -4, 9, 0, 4, -3, 5, -5, 1, 16, -3, 3, 3, -2, -2, 9, 7, -1, 10, 4, 1, -7, -10, 1, -3, 0, 2, -5, 1, 4, -3, -8, -1, -7, 1, -4, 9, -10, 1], "imageUrl": "https://upload.wikimedia.org/wikipedia/commons/5/54/Feed_forward_neural_net.gif", "imageLicense": "CC BY-SA 3.0", "imageArtist": "Paskari at English Wikipedia", "explanation": ["You want to know if you'll need an umbrella tomorrow, but you can't wait until tomorrow to find out.", "Imagine you're guessing tomorrow's weather by looking at today's sky. You make a guess, then wait for a bit to see if your guess was right. If it was wrong, you adjust your guess based on what you just learned. This way, you get better at guessing without waiting for the whole week to pass."], "example": "Today is partly cloudy, so you guess there's a 50% chance of rain tomorrow. After a few hours, it starts to rain. You now know your guess was off, so you adjust your future guesses to be more accurate.", "whyItMatters": "You improve your guesses by learning from new information as it comes in, not just waiting for the end result."}, {"id": "1537e324af91", "title": "Stochastic gradient descent", "slug": "stochastic-gradient-descent", "headline": "Policy Gradient Theorem Equation", "summary": "Write the policy gradient theorem equation", "source": "Write the policy gradient theorem equation", "sourceUrl": "https://en.wikipedia.org/wiki/Stochastic_gradient_descent", "articleUrl": "https://en.wikipedia.org/wiki/Stochastic_gradient_descent", "publishedAt": "2026-06-12", "category": "learn", "cohortScore": 0.5, "embedding": [-16, -1, 0, -5, -8, 2, -1, 4, 7, 8, 4, -4, 7, 5, -1, 3, -4, 5, -2, 3, 9, -6, -4, -10, 5, 9, 0, 3, -5, -26, 5, -2, 3, -2, 8, 2, -4, -5, -7, 1, 2, 4, -6, -1, 0, -9, -7, -9, -7, -6, 2, 1, 2, -6, 1, 2, 8, 7, -1, -1, 8, -1, -27, 8, 3, 7, -1, -1, -2, 10, -4, 3, 5, 2, 2, 5, -2, 3, -3, 2, -3, 0, -1, 1, 3, -8, 4, -5, 3, 4, -1, -3, 4, -6, -3, 1, -1, 1, -3, 41, -2, 3, 1, 8, 0, -1, -2, -1, -4, 2, -11, 3, 2, -7, 4, -3, 8, 12, -3, -4, 0, -3, 0, -2, 2, -8, -6, 15, 3, 9, 2, 0, 3, -5, -2, -1, -1, -1, -2, 6, -1, 3, 0, -5, -5, 19, 0, 0, -7, -3, 4, 0, 5, -4, 3, 2, 0, 2, -7, 1, -7, -5, -2, 12, -3, 0, 8, 1, -1, -2, 9, 4, 3, 2, 5, -4, -10, -3, 0, 2, 6, -11, -9, -2, 3, 5, -2, -8, -3, 5, 0, -1, 0, 3, -5, -7, 1, -7, -1, -4, -2, -3, -4, 6, 2, 0, 4, -1, 0, 1, -3, -3, -1, -2, 1, 4, 1, 0, 1, 3, 0, 3, -8, -36, -7, -1, 0, 3, -13, 5, -2, -3, 5, 12, 2, -1, 3, -1, -4, 4, 7, -1, 2, -2, -2, 4, -8, 7, 1, 17, -4, 7, 1, -6, 3, -4, -3, 10, 1, 3, 1, 3, -9, 6, 10, -8, 2, -3, -2, -5, 3, -12, 0, 4, 0, 4, -4, 5, 1, -3, 6, -4, 4, 0, 2, 8, -4, 1, -5, 6, -1, -4, 6, 0, 4, 10, 2, 3, -1, -3, 6, -1, -6, 7, -1, 7, 3, -4, 2, 5, -5, 5, 5, -5, 0, -3, 5, 5, 1, -38, -2, 1, 3, 2, -2, 11, -10, -12, -2, -6, 9, -2, 0, 3, -4, 6, -10, 3, -7, 10, 2, 22, -4, 7, -4, 0, -5, 10, -4, -6, -4, 4, 2, 8, 9, -3, -1, 6, -6, 2, 1, 2, 1, 0, 2, -1, -5, -4, 0, 1, 2, -3, -3, 12, 4, -6, -7, -10, -1, -7, -3, 8, -3, 6], "explanation": ["The policy gradient theorem provides a way to optimize the parameters of a policy in reinforcement learning. It establishes a connection between the expected return and the gradient of the policy's parameters.", "The policy gradient theorem states that the gradient of the expected return with respect to the policy parameters can be expressed as an expectation over the gradient of the log-probability of the taken actions. This gradient can be estimated using samples from the environment.", "In reinforcement learning, this theorem allows for the optimization of a policy by adjusting its parameters in the direction that maximizes the expected return. This is done through stochastic gradient descent, which iteratively updates the policy parameters based on sampled gradients."], "example": "Consider a reinforcement learning agent playing a game. The agent's policy determines the probability of taking certain actions given the current state. Using the policy gradient theorem, the agent can estimate the gradient of the expected return with respect to its policy parameters and update them to improve its performance in the game.", "whyItMatters": "Understanding the policy gradient theorem is crucial for implementing and improving reinforcement learning algorithms that aim to optimize policies in complex environments.", "imageUrl": "https://upload.wikimedia.org/wikipedia/commons/4/47/Diophantus-II-8-Fermat.jpg", "imageLicense": "Public domain"}, {"id": "f0e9f5981db2", "title": "Variational autoencoder", "slug": "variational-autoencoder", "headline": "ELBO formula in variational inference", "summary": "Write the formula for ELBO in variational inference", "source": "Write the formula for ELBO in variational inference", "sourceUrl": "https://en.wikipedia.org/wiki/Variational_autoencoder", "articleUrl": "https://en.wikipedia.org/wiki/Variational_autoencoder", "publishedAt": "2026-06-12", "category": "learn", "cohortScore": 0.5, "embedding": [-9, 7, 7, 0, -4, 1, 3, 3, 7, 7, 2, -12, 4, 0, 8, -4, -4, 7, -5, 5, 8, -7, -2, -6, 2, 8, 4, 5, -3, -26, 5, -1, 9, 3, 4, 0, -6, 1, -6, 4, 4, -2, 1, 2, -2, -6, 0, 2, -10, 4, -1, -3, 0, 4, 7, 4, 2, 1, 7, 11, -1, 7, -18, 10, 8, 1, -6, 1, 3, 8, -2, -4, -1, 5, 3, 8, 1, -1, -6, -3, -6, 1, -4, 4, 5, -4, 3, -8, 0, 1, 6, 5, 4, 2, -4, -3, 4, 7, 0, 41, 2, 3, 0, 4, -2, -8, -1, -9, 2, 2, 0, -4, 8, -10, 0, 3, 9, -2, 1, -6, -5, -1, -1, -2, 3, -2, -8, 16, -4, 8, 0, 4, -2, 0, -5, -1, 1, 5, -1, 4, -3, -2, 8, -1, 0, 11, -7, -9, -8, -5, 5, 6, -3, 3, 10, 3, -2, -1, -11, -2, -4, -6, 6, 9, -8, 0, -3, -1, 2, -3, 12, 6, -1, 2, 2, -1, -9, 4, 2, 4, 1, -5, -5, 2, -3, -1, -3, -4, 1, 1, -1, -3, 1, -2, 2, -7, 1, -2, -6, -3, 3, 0, -3, -5, 5, 1, 0, 7, 5, 4, -5, -5, -4, 3, -2, 7, 0, -3, 2, -1, -4, -7, -1, -39, 1, 1, -6, 0, -11, 10, -5, 8, 6, -3, 0, -2, -2, -1, 3, -1, -7, -3, 8, -7, -2, -2, -6, 3, 5, 19, -3, 1, -2, 2, 5, 3, 5, 10, 0, 7, 0, -4, -2, 0, 1, -6, -10, -11, -1, -3, 5, -8, 2, 4, 4, 1, -6, -3, 2, -5, 5, -9, -2, 7, -2, -3, -3, 2, -4, -1, -9, -1, 0, -1, 6, -2, 7, 4, -4, 6, -1, -11, -1, 2, -4, 5, 3, 5, 3, 11, -1, 4, 3, -2, -2, -7, 6, 2, -6, -36, -3, 1, 8, -5, 8, 4, -8, -10, 0, -8, 1, 3, 0, -1, 2, 7, -12, 4, -7, 2, 0, 26, -7, 1, 3, 3, -2, 5, -11, -6, 2, 6, 0, 5, 11, -7, 4, 12, -9, 6, -1, 3, -1, 11, 1, -1, -5, -8, -2, 1, 3, 1, 2, 6, 5, -1, -4, -9, -4, 0, -7, 6, -4, 0], "explanation": ["The ELBO (Evidence Lower Bound) formula is central to variational inference as it provides a lower bound for the log-likelihood of the observed data. This bound is used to optimize the parameters of the variational distribution.", "The ELBO formula is expressed as: ELBO = E_q[log p(X|Z)] - KL(q(Z)||p(Z)), where E_q denotes the expectation with respect to the variational distribution q(Z), log p(X|Z) is the log-likelihood of the data X given the latent variable Z, and KL(q(Z)||p(Z)) is the Kullback-Leibler divergence between the variational distribution q(Z) and the prior distribution p(Z).", "Understanding and calculating the ELBO is crucial for training variational models like VAEs. By maximizing the ELBO, one can indirectly maximize the log-likelihood of the observed data while also ensuring that the variational distribution stays close to the prior distribution."], "example": "In a VAE, suppose X represents images and Z represents latent variables. The ELBO can be computed by taking the expectation of the log-likelihood of the images given the latent variables and subtracting the KL divergence between the variational distribution of the latent variables and the prior distribution.", "whyItMatters": "Maximizing the ELBO helps in learning meaningful latent representations and improves the generalization of the model.", "imageUrl": "https://upload.wikimedia.org/wikipedia/commons/4/4a/VAE_Basic.png"}, {"id": "5068e7b0264a", "title": "Write the reparameterization trick z = \u03bc + \u03c3\u2299\u03b5", "slug": "write-the-reparameterization-trick-z", "headline": "How can you predict the weather without getting wet?", "summary": "Write the reparameterization trick z = \u03bc + \u03c3\u2299\u03b5", "source": "Write the reparameterization trick z = \u03bc + \u03c3\u2299\u03b5", "sourceUrl": "https://en.wikipedia.org/wiki/Reparameterization_trick", "articleUrl": "https://en.wikipedia.org/wiki/Reparameterization_trick", "publishedAt": "2026-07-03", "category": "learn", "cohortScore": 0.5, "embedding": [-9, 4, 5, 9, 1, -2, 4, 0, -3, 6, -3, -5, 3, 2, 0, -3, 2, 8, -4, -1, 11, 4, -3, -3, 6, 1, 4, 2, -4, -22, -3, -5, 1, -1, -2, -4, 0, 1, -4, 1, -1, 4, -5, -3, 1, -14, 7, -1, -2, 4, -1, 3, -9, 4, 8, 7, 1, -2, 3, -3, -6, 4, -12, 3, 6, 1, -6, -6, 4, 5, 2, 5, -1, 5, -4, -1, -6, 2, -4, 0, -1, 0, 0, 0, 5, 0, -4, 1, 6, -3, -6, -4, -4, -3, -5, 2, 9, 6, -4, 42, -9, 3, -3, 1, 2, -6, -1, -9, -6, 0, -7, -4, 5, -5, 1, 2, 7, 7, -3, -2, 2, -4, 7, 8, 7, -2, 2, 13, -2, 9, 3, -1, -10, -4, 1, -2, -1, 1, -4, 7, -2, 3, 1, -3, -3, 6, -5, -1, 1, -12, -5, 0, 1, -6, 15, 0, 2, -1, -1, 2, -5, 2, -4, 9, -5, -4, 7, 3, 5, -7, 4, -2, 0, 1, 12, -1, -9, 1, 5, 8, 1, -4, 1, 1, -2, -1, 0, -4, -4, 0, -4, -10, -3, 4, -3, 2, 1, 0, 1, -11, 3, 4, 2, -6, 3, 4, 11, -2, 3, 9, 3, -9, -1, -9, -1, 5, 4, 0, -4, -4, 4, -7, -11, -38, -4, 6, -3, 15, -14, 8, -6, 9, 0, 8, -11, -1, -1, -1, 2, -2, -1, -2, 0, 1, 4, -2, -6, 1, 1, 13, -1, 8, -3, 2, -3, 1, -1, 4, 5, 5, 6, -6, -6, 10, 10, 0, 1, -10, 0, -5, 7, -6, -1, -3, -3, 4, -4, 1, 1, -10, 6, -1, -4, 10, 2, 2, -6, -3, 1, 0, -5, 10, 2, -6, 6, -4, 0, 8, -3, 2, -6, -1, -2, 4, 2, 6, 7, 8, -2, 3, -4, -1, 2, -3, -2, -2, 3, 7, -6, -40, -2, -6, 9, 0, -4, 8, -6, -14, 6, -11, -1, 1, 4, 10, -5, 4, 4, 2, -3, 8, 4, 27, 0, 4, 4, 5, -10, 10, -2, -3, -7, 6, 2, 1, 2, 0, 7, 2, -6, 0, 4, 4, -3, 9, 0, 6, -1, -6, 0, -5, 1, -1, -2, 0, 7, -4, -3, -6, -2, 1, -5, 8, -11, 3], "imageUrl": "https://upload.wikimedia.org/wikipedia/commons/3/36/Astronaut_Riding_a_Horse_Hiroshige_%28SD3.5%29.webp", "imageLicense": "Public domain", "imageArtist": "VulcanSphere", "explanation": ["Imagine you're planning a picnic and want to know if it will rain. You don't want to check the forecast every minute because it takes time and you can't change your plans quickly.", "Think of the weather like a roller coaster, where rain is a sudden drop. Normally, predicting rain is hard because it's random. But with the reparameterization trick, you can smoothly ride the roller coaster, making it easier to predict rain by adjusting your picnic plans slightly."], "example": "If there's a 70% chance of rain, instead of checking the weather every hour, you adjust your plans a bit each time you check, making it easier to decide when to cancel the picnic.", "whyItMatters": "The reparameterization trick allows you to make small adjustments to your plans based on the latest weather forecast, making it easier to predict rain and avoid getting wet."}, {"id": "9429e508bcf1", "title": "Write the contrastive loss function for SimCLR", "slug": "write-the-contrastive-loss-function-for-simclr", "headline": "Contrastive loss function: L = (1/2N) \u03a3 [max(0, margin - y_i * (z_i - z_j))^2 + max(0, y_i * (z_i - z_j) - margin)^2]", "summary": "Write the contrastive loss function for SimCLR", "source": "Write the contrastive loss function for SimCLR", "sourceUrl": "", "articleUrl": "", "publishedAt": "2026-06-12", "category": "learn", "cohortScore": 0.5, "embedding": [-11, -2, -2, -3, 0, 0, -1, 8, 9, 0, 5, -10, 3, -3, 0, -6, 0, 4, -4, -2, 8, -5, -4, -9, 2, -2, 0, 5, -4, -26, 1, -1, 0, -3, 0, 0, -4, 0, -3, 3, 5, 3, 1, 5, -4, -4, -5, -8, 3, -1, 1, 1, 3, -1, 3, 2, 5, 10, 1, -1, 7, 4, -15, 5, -6, 5, -4, -1, 1, 16, 1, -6, 3, 5, 4, 0, -1, -4, -1, -8, 3, 1, -5, -2, 6, -1, 4, -3, -3, -3, 0, 0, 3, 1, -10, -4, 4, -3, 4, 39, 1, 3, -5, 2, 3, -6, 1, 1, 1, -9, -9, -1, 3, -7, -6, 3, 8, 4, -1, -2, 0, 4, -1, -2, 6, 5, 1, 8, -6, 7, 1, 0, 1, 5, 1, -1, -8, -3, 0, 1, 3, 0, -1, -2, -3, 12, -8, -5, -6, -1, 5, 4, -3, -7, 5, 8, 0, -1, -8, -5, -8, -7, 0, 15, -7, -1, 3, 5, 5, -1, 7, -1, -2, -6, 12, 3, -10, 3, 10, 3, 1, -1, -3, 5, 6, 2, -4, -7, 4, 3, -3, -3, -9, 5, -11, 6, -1, -1, -8, 1, 14, 0, -3, -2, 4, -4, 5, -10, 5, 8, -5, -2, 9, 2, 1, 2, 4, 3, 4, 3, -1, -8, -9, -38, -6, 5, -4, 9, -8, 2, -5, 5, -4, 11, 7, -5, -3, -3, -1, 1, -9, -4, -2, -6, 2, -5, -5, 2, 2, 16, -7, 5, -3, 3, 3, 5, 10, -3, 0, 0, 0, -6, -3, 7, 6, -2, 1, 0, -5, -10, 6, -11, 10, 2, 0, 1, 0, 4, -2, -7, 0, -15, 0, 2, -8, 8, -6, 6, 4, 7, -5, 0, 0, 1, 4, -2, -5, 8, 2, 3, 5, -4, -5, 3, 0, 4, -1, 3, 8, 4, 3, -2, 2, -13, -3, 2, -4, -2, -5, -37, 2, 1, 4, -1, 1, 5, 0, -11, -1, -3, 9, -1, -2, 3, -4, -1, 0, 5, 6, 6, 3, 20, -11, -3, 3, 6, -4, 7, -7, -2, 3, 16, -1, 1, 13, -3, 6, 7, -5, 6, -2, 6, 0, 13, 5, 6, 3, -11, -1, -10, 12, -2, -5, 1, 3, -3, 0, 0, 2, -1, 1, 4, -5, -1], "imageUrl": "https://upload.wikimedia.org/wikipedia/commons/thumb/b/b8/Ionic_frieze_from_the_Erechtheum%2C_dimensions_130_x_50_cm%2C_in_the_Glyptothek.jpg/1280px-Ionic_frieze_from_the_Erechtheum%2C_dimensions_130_x_50_cm%2C_in_the_Glyptothek.jpg", "imageLicense": "CC BY-SA 4.0", "imageArtist": "Neoclassicism Enthusiast"}, {"id": "c85909556566", "title": "Write the triplet loss formula: max(d(a,p) - d(a,n) + margin, 0)", "slug": "write-the-triplet-loss-formula-max-d-a-p-d-a-n-margin-0", "headline": "Can you tell friends apart even if they've changed a lot over time?", "summary": "Write the triplet loss formula: max(d(a,p) - d(a,n) + margin, 0)", "source": "Write the triplet loss formula: max(d(a,p) - d(a,n) + margin, 0)", "sourceUrl": "https://en.wikipedia.org/wiki/Triplet_loss", "articleUrl": "https://en.wikipedia.org/wiki/Triplet_loss", "publishedAt": "2026-07-03", "category": "learn", "cohortScore": 0.5, "embedding": [-10, -2, 4, -1, 0, 2, 3, 4, 8, -3, 16, -3, 1, -5, 4, 0, 0, 5, -6, -3, 6, -6, -6, -1, 8, 7, -2, 1, -9, -22, 2, -2, 4, -6, 0, 8, -4, 2, -1, 5, 0, 4, -2, 0, -5, 1, -2, -5, 0, 1, 0, -1, 0, 8, 5, 4, 0, 6, -3, 4, 11, 5, -15, 6, 8, 2, -6, 2, -2, 15, -5, -5, 0, 7, 0, 4, 0, -5, -6, -3, -3, -1, -2, -3, 0, -5, 8, -1, -1, -4, 0, 4, 3, -5, -12, -2, 3, 1, 2, 46, -2, -2, 0, 1, 2, -6, 6, -5, 8, -5, -6, 4, 6, -11, 1, 1, 5, 2, -1, -3, -3, 2, 3, 1, 5, 2, -2, 12, -5, 5, 4, 2, -7, 1, -4, 0, -4, -1, 3, -6, 2, -2, 8, 3, 5, 17, -8, -8, -2, -2, -1, -7, 2, -12, 5, -1, 10, -4, -6, -3, -6, -9, -5, 11, 5, -6, 7, 3, 2, -5, 2, -5, -2, -2, 6, -2, -5, -5, 10, 3, 1, 1, -8, 5, -6, 0, -5, -2, 0, 0, 2, -9, -8, 4, -8, 0, -1, 0, -5, -3, 9, -7, -1, -2, 5, 4, 5, -8, 10, -1, 3, -5, 2, 2, 4, 3, 3, 1, 2, 7, 7, -6, -4, -41, -3, 3, -1, 8, -2, 4, -6, 0, 7, 8, 0, -3, -1, 2, 0, 0, 3, -8, 1, -5, 1, -4, -5, 6, 2, 20, -2, 4, -2, 0, 7, -2, 4, 7, 0, -6, -3, -12, -6, -6, -2, 4, -4, -7, -5, -3, 5, -2, 15, 6, -3, 1, -1, 0, -2, -4, 3, -5, -6, 1, -6, 0, -4, 1, 0, -5, -9, -1, 3, -1, 5, -2, -6, 6, 1, -1, 5, -6, -5, 4, -5, 7, -1, 6, 6, 0, 1, 4, 1, -4, -7, 0, 3, 0, -3, -35, -1, -5, -1, -3, 4, -2, 4, -4, -3, -4, 6, -1, -8, 1, -4, 2, -1, 4, 9, 11, 2, 21, -2, 5, 4, 0, 2, 10, 0, -1, -3, 10, -2, 4, 4, -2, 2, 3, -3, 9, -12, 2, 2, 14, 10, 1, 1, -7, -5, -5, 8, -4, -3, 6, 8, -9, 2, 3, -6, -6, 1, 8, -5, 0], "imageUrl": "https://upload.wikimedia.org/wikipedia/commons/e/e0/3dcurves.jpg", "imageLicense": "CC BY-SA 3.0", "imageArtist": "Darko Kadvanj, student", "explanation": ["Imagine you have a photo album with pictures of your friends. Over time, some friends change their hairstyle, gain weight, or even grow older. You want to easily recognize them even if they look different.", "Think of your friends' photos as points in a space. Triplet loss helps you place them closer together if they're the same person and farther apart if they're different people. It's like drawing invisible lines connecting friends' photos."], "example": "You have three photos: A, B, and C. Photo A shows your friend Tom in his 20s, photo B shows Tom in his 30s, and photo C shows Tom in his 40s. Triplet loss helps you understand that photos A, B, and C are closer together than photo C and any other photo of a different person.", "whyItMatters": "Triplet loss ensures that photos of the same person stay close together, making it easier to recognize them even if they change over time."}, {"id": "cf3ebfc72b35", "title": "BLEU", "slug": "bleu", "headline": "Ever wondered how computers know if a translation makes sense?", "summary": "Write the formula for BLEU score", "source": "Write the formula for BLEU score", "sourceUrl": "https://en.wikipedia.org/wiki/BLEU", "articleUrl": "https://en.wikipedia.org/wiki/BLEU", "publishedAt": "2026-07-03", "category": "learn", "cohortScore": 0.5, "embedding": [-13, -1, -4, -8, 3, -7, 2, 5, 10, -4, -1, -7, 2, 1, 0, -8, -4, -5, 2, 1, 6, -2, -1, 0, 1, 4, 2, 1, -4, -25, -4, 0, 6, 2, 4, 3, -4, -1, 4, -4, 1, -1, 8, 1, 4, -5, -2, 5, -4, 4, -6, -1, 0, 3, 1, 4, 3, 11, 4, -1, 0, 11, -15, 10, -4, 7, -7, -9, -6, 9, -1, -5, 3, 9, 3, -1, -4, -1, -3, 3, 2, -2, -1, 6, -3, 0, 2, 10, 8, -1, -1, 4, -4, 5, -8, -9, -2, -1, -2, 42, -1, -12, -1, -2, 1, -7, 5, -7, -4, -3, -4, 1, 4, -2, 3, 6, 2, 0, 9, -8, -9, 2, -1, -5, 4, -5, 2, 4, -5, 7, 5, -6, -11, 0, 1, 3, 1, -3, 3, 2, 6, 5, 6, 4, -11, 15, 1, -1, 3, 1, 2, 5, -3, -7, 2, 5, 12, -4, -6, -5, -8, -6, -4, 9, 1, 1, -1, 1, 3, -6, 1, 2, -10, 4, 0, -3, -4, -2, 2, -2, 6, -3, -2, 2, 1, 0, -2, -9, 6, 2, -1, 5, 0, 5, -4, -1, -6, -3, -2, -6, -2, 2, -6, 0, 3, 1, 8, -1, 8, 5, 4, -6, 0, 0, 3, 2, 0, 0, 4, 5, -4, -3, -9, -41, 0, 2, -1, 11, -4, 5, -3, 10, 9, 12, -6, 0, -5, 3, -6, -2, 0, -2, -2, -5, -5, -3, -7, -6, -3, 17, -1, 9, 0, 3, 0, -5, -5, 8, 3, -2, 9, 2, -3, -1, -5, -1, -4, -12, 3, 4, -6, -4, 10, 0, 6, 0, 2, -6, -5, -11, 4, -1, -1, 2, -2, 2, 0, 0, -5, 6, -1, 9, 2, 6, 10, -3, -7, 7, 4, 9, -7, -2, 3, 6, -1, 0, -4, 5, 1, 8, -2, 1, 6, -1, -4, 0, 1, -6, 3, -37, 3, 2, 4, 4, -9, 2, -7, -7, 3, -2, -7, 1, -8, 2, 3, 9, 2, 6, -2, 0, 1, 26, 0, 0, 4, 8, -8, 7, 0, -3, -3, 3, 2, -1, 2, -11, 1, 5, 2, 7, 3, -4, -5, 10, 10, -4, 1, -2, -5, -2, 5, 1, -1, 0, 7, 1, -7, -2, 2, -7, -7, 12, 6, -5], "imageUrl": "https://upload.wikimedia.org/wikipedia/commons/d/d5/Inkwell15.jpg", "imageLicense": "CC BY 3.0", "imageArtist": "The original uploader was Palmiped at English Wikipedia.", "explanation": ["Imagine you're using a translation app to understand a foreign movie's subtitles. You want to make sure the subtitles are accurate and readable.", "Think of BLEU as a scorecard that compares the app's translation to a set of professional translations, giving you a sense of how good it is."], "example": "If the app's translation closely matches the professional ones, it gets a high BLEU score, indicating better quality.", "whyItMatters": "BLEU score helps you quickly gauge the accuracy of machine translations."}, {"id": "540decbdad4a", "title": "Perplexity", "slug": "perplexity", "headline": "Perplexity = 2^H", "summary": "Write the formula for perplexity from cross-entropy", "source": "Write the formula for perplexity from cross-entropy", "sourceUrl": "https://en.wikipedia.org/wiki/Perplexity", "articleUrl": "https://en.wikipedia.org/wiki/Perplexity", "publishedAt": "2026-06-12", "category": "learn", "cohortScore": 0.5, "embedding": [-8, 0, 1, -2, -5, -1, 6, 0, 4, -1, 4, -7, 6, -4, 2, 1, -9, 2, -15, 1, 10, -4, -3, -8, -2, 9, -5, 5, -10, -26, 3, -5, -1, 1, 6, -2, -3, 1, -6, 2, 3, 0, 5, 8, -1, -4, -9, 10, -2, -5, -5, 4, -2, -2, 6, 2, 4, 4, 0, 7, 2, 10, -14, 5, 8, -2, -5, -10, 3, 7, -3, 3, 0, 3, 0, -5, -16, -3, -3, 1, -4, -2, -3, 0, 4, -3, 8, 2, 4, -2, 1, 3, 0, 1, 2, -5, 2, 5, 8, 40, 3, -2, -2, -2, 1, -11, 1, -10, -3, -5, 0, -4, 6, -12, 3, 5, 5, -1, -4, 0, -2, -4, 6, 2, 3, 3, -6, 14, -5, 5, 3, 5, 5, -4, -2, -4, 0, 10, 9, 2, 7, -4, 2, -2, 0, 7, -12, 2, -7, -2, 3, -3, 0, -6, 8, 2, 6, -2, -1, 3, 5, -2, 5, 10, 0, -1, 13, -1, 5, -3, 4, 3, -4, 3, 6, 4, -12, 1, 8, -2, 3, -1, -7, 1, 2, -5, 1, 2, 0, 4, 0, -6, -8, 11, -5, 1, 0, 5, -7, 1, 3, -1, -4, -3, 6, 3, 10, -4, -2, 4, 5, -7, -8, 1, -1, 2, -1, 4, 4, 0, 0, -9, -9, -40, -6, -3, -10, 6, -5, 4, -5, -2, 4, 5, 6, -11, -1, 0, 1, 5, 3, 4, 1, 2, 4, 4, -6, -3, -5, 18, -4, 7, 0, 2, -3, -11, 7, 5, -1, 2, 5, -3, -9, -3, 6, -5, -2, -4, -2, -6, -5, -4, 5, 8, 1, 2, -1, 6, 0, -5, 1, -7, -1, -1, -5, 2, -1, -14, 1, 1, -4, 5, 2, 2, 6, 4, 0, 7, 0, 2, 0, -2, 1, 10, 5, 0, 6, 3, -2, 1, -2, 1, -1, 0, -2, 1, 6, -7, -5, -35, -3, -3, 9, 0, -5, 3, -11, -13, -5, -1, 6, 3, -2, 1, 1, 2, -6, 7, 2, 6, 0, 28, 5, 2, 2, 7, 5, 5, -2, -2, -3, 5, 0, 5, 1, -3, 1, 9, -6, 4, -11, -2, -4, 13, 3, 2, 1, -4, -3, -1, 5, 1, 3, 6, 8, -7, -4, 2, -5, -2, -2, 5, -9, -5], "explanation": ["Perplexity measures uncertainty in a probability distribution. It is calculated as 2 raised to the power of the information entropy (H). Perplexity quantifies how well a probability distribution predicts outcomes."], "example": "For a fair coin (N=2 outcomes), H = log2(1/0.5) = 1. Perplexity = 2^1 = 2.", "whyItMatters": "Understanding perplexity helps in evaluating models' performance in predicting outcomes, crucial for applications like speech recognition.", "imageUrl": "https://upload.wikimedia.org/wikipedia/commons/c/c1/Gosper_6.gif", "imageLicense": "CC BY-SA 4.0", "imageArtist": "Guillaume Jacquenot"}, {"id": "2f2a62e941a5", "title": "Write the attention score formula before softmax: e_ij = a(s_i, h_j)", "slug": "write-the-attention-score-formula-before-softmax-e-ij-a-s-i-h-j", "headline": "How do we know what's important in a sentence?", "summary": "Write the attention score formula before softmax: e_ij = a(s_i, h_j)", "source": "Write the attention score formula before softmax: e_ij = a(s_i, h_j)", "sourceUrl": "https://en.wikipedia.org/wiki/Attention_(machine_learning)", "articleUrl": "https://en.wikipedia.org/wiki/Attention_(machine_learning)", "publishedAt": "2026-07-03", "category": "learn", "cohortScore": 0.5, "embedding": [-8, 1, 5, -7, 4, 5, 9, 1, 12, -3, 5, -1, 3, 5, 2, 3, 1, 3, -9, -4, 9, -3, 1, -2, 4, 7, -1, -1, -6, -24, 0, -2, 8, -2, -4, 2, -4, -3, 2, 6, 0, 4, 1, 2, -4, -8, -1, -10, -2, -1, -5, -5, -2, 1, 11, 1, 3, 6, 5, -1, 4, 6, -17, 3, 4, -1, -9, -6, -6, 17, -5, -3, 3, 11, 2, 5, -5, -1, 8, -4, -5, 0, -4, 1, 8, -1, 3, 7, 8, -6, -1, -4, -2, 1, 0, -4, -7, 2, -3, 39, -1, -4, -8, -7, 3, -11, 2, 1, -4, -4, -5, -7, 1, -4, 4, 2, 12, 4, 5, -8, -2, 0, 5, -6, 7, 4, -3, 9, -2, -3, 7, -7, -9, 3, -4, 0, 2, 0, 9, -4, 2, 1, 3, -1, -7, 23, -10, -6, -3, -5, 1, 1, 7, -7, 4, -1, 1, -6, -4, -4, -3, -2, -8, 11, -3, -4, 0, -2, -1, -2, 7, -4, -4, 7, 5, 0, 2, 10, -1, -1, 4, -2, -5, -2, 0, -1, -1, -6, 1, 0, -5, 0, -2, 5, -9, 3, 1, 2, -7, -2, 1, 4, 0, -4, 7, 4, 3, 2, 9, 1, -7, -2, -1, 1, -3, -2, -3, 5, 3, -2, -2, -3, -9, -42, -2, 7, -7, 0, -3, 9, -1, 4, 6, 11, -5, -3, -12, 0, 2, -5, -3, 3, 3, 7, -3, 4, 1, -1, -3, 14, 0, 5, -4, -1, 1, -1, -5, 0, -5, -2, 11, -7, -2, -1, -3, -3, -1, -8, -4, 2, 0, -2, 8, 7, -4, 1, 1, -1, -3, -12, -4, -15, -1, 1, -2, 2, -6, -9, 0, 3, 0, -1, 4, -7, 8, -4, -1, 8, -2, 4, -1, 2, 0, 4, 5, 2, -4, 8, 7, 6, -2, 0, 8, -6, -1, 3, 1, -4, -3, -35, 5, -1, -4, 6, 0, 3, -12, -7, 2, -2, 8, -2, -1, -10, 0, 5, 3, 8, -4, 4, 2, 19, -1, 8, 2, 4, -2, 6, 0, 6, 5, 13, 10, 4, 3, -7, 1, 9, 6, 6, 0, -1, -6, 14, 7, 4, -6, -12, -2, -4, 0, -1, 3, 1, 7, 5, 3, 0, 1, -10, -1, 8, 6, -5], "imageUrl": "https://upload.wikimedia.org/wikipedia/commons/3/35/Human_losses_of_world_war_two_by_country.png", "imageLicense": "Public domain", "explanation": ["Imagine you're reading an email full of information, but you want to quickly find the key points without reading everything word for word.", "Think of each word in the email as a person at a party. Some people are more important to the conversation than others. We want to figure out who those important people are so we can focus on them."], "example": "In the email, the word \"urgent\" next to \"meeting\" highlights the importance of the meeting over other less significant details.", "whyItMatters": "The attention score formula helps us identify which words (or people at the party) are most important to focus on."}, {"id": "2ea65b2d3808", "title": "Write the multi-head attention formula: MultiHead(Q,K,V) = Concat(head_1,...,head_h)W^O", "slug": "write-the-multi-head-attention-formula-multihead-q-k-v-concat-head-1-head-h-w-o", "headline": "Ever wondered how machines understand the importance of words in a sentence?", "summary": "Write the multi-head attention formula: MultiHead(Q,K,V) = Concat(head_1,...,head_h)W^O", "source": "Write the multi-head attention formula: MultiHead(Q,K,V) = Concat(head_1,...,head_h)W^O", "sourceUrl": "https://en.wikipedia.org/wiki/Attention_(machine_learning)", "articleUrl": "https://en.wikipedia.org/wiki/Attention_(machine_learning)", "publishedAt": "2026-07-03", "category": "learn", "cohortScore": 0.5, "embedding": [-8, -5, 0, -4, -6, 1, 8, 0, 7, -4, 0, -8, 4, 1, 7, 1, -10, -2, -1, -2, 8, 3, -6, -4, 0, 2, 1, -3, -6, -22, 0, 2, 7, -1, -5, 4, 0, 0, 1, 8, 4, 2, -1, 2, -4, -5, -6, -2, -6, -3, -3, -3, 1, 4, 7, 3, 1, 6, 7, -1, 6, 6, -16, 3, 3, -3, -10, -2, -6, 16, -2, -5, 5, 6, 4, 1, -6, -1, 3, -3, -2, 3, -4, -4, 1, 5, -5, 0, 0, -7, -3, -4, -3, -3, 4, -1, -3, 1, -1, 42, 4, -5, -7, -7, 2, -6, 4, -6, -4, 0, -4, -7, 8, -4, 0, 1, 4, 1, 7, -11, 5, -4, 0, -2, 7, 1, 5, 11, 4, 2, 9, 2, -3, -6, 0, -2, 1, 1, 1, -1, 4, -3, -1, -2, -2, 19, -7, -5, -4, 1, -4, 5, 4, -7, 1, -1, 1, -7, -5, 1, -3, -3, -6, 10, 0, -8, 2, -2, 2, -8, 10, 2, -4, 9, 2, -3, -12, 7, 2, -2, 4, -1, -6, -2, -3, 4, -2, -1, -3, 3, 0, 2, -1, 1, -9, 0, -1, 0, 0, -3, -3, 1, -3, 0, 3, 2, 3, 1, 11, 0, -7, -6, -4, 0, -5, -3, 0, 7, 6, -4, 0, -13, -12, -43, -7, 4, -2, 2, -3, 5, 5, 4, 3, 5, -5, -5, -9, -5, 2, 0, 3, 1, 2, 9, -1, -2, -9, 0, 1, 20, 4, 5, 4, 2, 1, 0, -1, 8, -4, -4, 0, -3, 2, -6, 0, -7, 0, -2, 2, -2, -3, -4, 7, 2, 1, 0, 5, -5, -1, -9, 2, -10, 1, 3, 4, 0, 0, -1, 3, 0, 0, 3, -3, -6, 11, 6, -4, 5, -4, 7, 0, 4, 4, 4, -1, 1, 3, 7, 3, 7, -2, 4, -3, -11, -2, 6, 3, -3, -4, -39, 3, 1, 3, 3, 4, -2, -9, -2, 4, -6, 11, -1, -6, -2, 2, 7, 0, 3, 7, -2, 4, 27, 1, 7, -8, -1, 2, 9, 4, -2, -3, 13, -4, 2, 5, -7, 5, 12, 5, 5, 5, 2, -12, 9, 8, 1, -12, -6, -2, -3, 2, 0, 1, 8, 9, 4, 1, 4, 4, -2, -4, 6, 2, -2], "imageUrl": "https://upload.wikimedia.org/wikipedia/commons/thumb/b/b9/%D7%A7%D7%9C%D7%A3%2C_%D7%A0%D7%95%D7%A6%D7%94_%D7%95%D7%93%D7%99%D7%95.jpg/1280px-%D7%A7%D7%9C%D7%A3%2C_%D7%A0%D7%95%D7%A6%D7%94_%D7%95%D7%93%D7%99%D7%95.jpg", "imageLicense": "CC BY-SA 4.0", "imageArtist": "Mushki Brichta", "explanation": ["Imagine you're reading a long email and trying to find the key points quickly. You don't read the whole thing word for word; instead, you focus on the most important parts.", "Think of each word in the sentence as a person at a party. Some people are more important to the conversation than others. The machine decides who to 'listen' to more by assigning importance, like deciding who's talking about the party's theme."], "example": "In an email, the machine might 'listen' more to the words \"meeting,\" \"deadline,\" and \"budget\" because they are key points.", "whyItMatters": "Multi-head attention helps machines focus on the most important parts of a sentence, like picking out the key points in an email."}, {"id": "26ba38969211", "title": "the L1 unit ball is a diamond shape and the L2 unit ball is a circle", "slug": "the-l1-unit-ball-is-a-diamond-shape-and-the-l2-unit-ball-is-a-circle", "headline": "Why does a ball look different in various dimensions?", "summary": "Why the L1 unit ball is a diamond shape and the L2 unit ball is a circle", "source": "Why the L1 unit ball is a diamond shape and the L2 unit ball is a circle", "sourceUrl": "https://en.wikipedia.org/wiki/Ball_(mathematics)", "articleUrl": "https://en.wikipedia.org/wiki/Ball_(mathematics)", "publishedAt": "2026-07-03", "category": "learn", "cohortScore": 0.5, "embedding": [-2, -8, -2, 3, 1, -5, 6, -1, 3, 1, 8, -10, 2, -3, 5, -7, 1, -8, -14, 2, 8, 0, -1, -2, 0, 10, -4, 3, -1, -33, 11, 8, -2, -4, -1, -5, 4, 5, -5, 1, 2, -1, -1, -8, 2, -3, 2, 10, 6, 2, 2, -1, 0, 0, 1, 7, 7, 9, 3, 8, 2, -7, -13, 8, -2, 0, -3, -8, 0, 4, 6, -5, 6, 3, 3, -6, -9, -6, -4, 7, -7, 1, -8, -4, -6, -2, -3, -8, 7, -3, -3, 6, -12, 0, -6, 2, 0, 3, 1, 42, -4, 1, 10, 5, 1, -2, -1, -4, 0, -2, 7, 4, -7, 1, -8, -7, -1, -1, 1, -4, -9, 3, -2, -13, -6, -1, 0, 6, 4, 4, 2, -1, -7, -12, 1, 8, 6, 3, 8, 4, -2, -6, 4, -4, -3, 2, -9, 0, 6, 9, -4, 1, -7, -2, -3, 1, -5, -3, -5, 2, -3, 4, 1, 7, -3, -10, -1, -10, 1, 0, 4, 5, -4, -1, 10, 3, -7, -9, 2, 3, 8, -2, 3, -2, 4, -7, -9, 3, 3, 5, -2, 4, -4, 8, -6, -8, -3, -1, -3, -2, 2, 7, 0, 3, 2, -2, 12, -6, 0, 2, -5, -3, -11, -8, 3, 3, 6, -4, 0, 1, -7, -2, -7, -35, -2, 1, -7, 8, -5, 3, 2, 0, -2, 6, -2, -11, -7, -5, -2, -1, 2, -4, 2, 1, 7, -4, 0, -2, -2, 19, -2, -4, 6, -1, -1, -2, 5, 7, -1, 1, -4, -6, -3, -3, 3, 4, -2, 3, 3, 2, 9, 0, 2, -2, 2, 4, -3, 6, -3, -2, 1, 3, 7, -1, 0, 6, -12, 0, 3, -5, -7, 1, -1, 3, 7, 0, -4, 9, 3, 9, 9, 6, 6, 5, 0, 3, 3, 6, 1, -2, 2, 9, -5, -3, 0, -2, 7, -5, -4, -34, 0, 4, 9, -4, 3, 1, 0, 4, -4, -1, -6, 5, -2, -6, -6, 9, -6, 9, -1, 6, 2, 24, -4, 3, 3, 3, 4, -3, 4, 2, 5, 11, 5, -6, 6, -1, 4, 0, 2, 0, 4, -12, -2, 11, 5, 1, 5, 7, -7, -5, 0, -8, 2, -8, 5, -8, -2, 7, 0, 8, 8, 3, -1, 8], "imageUrl": "https://upload.wikimedia.org/wikipedia/commons/thumb/2/24/Aphaia_pediment_Paris_W-XI_Glyptothek_Munich_81.jpg/1280px-Aphaia_pediment_Paris_W-XI_Glyptothek_Munich_81.jpg", "imageLicense": "Public domain", "explanation": ["Imagine you're playing with clay. In 1D, you stretch a piece of clay into a line segment. In 2D, you flatten it into a disk. In 3D, you mold it into a sphere. What happens when you try to play with clay in 4D?", "As you increase the dimension, the shape of the ball stretches out more. In 1D, it's a line. In 2D, it's a disk. In 3D, it's a sphere. In 4D, it becomes a hyperball, which looks like a diamond when projected into 3D space."], "example": "If you tried to create a 4D ball with clay in 3D space, you'd get a shape that looks like a diamond when viewed from the side.", "whyItMatters": "A ball's shape changes with dimensions because it stretches differently in each dimension. In 4D, a ball's projection in 3D looks like a diamond."}, {"id": "3d292de0dd64", "title": "Regularization (mathematics)", "slug": "regularization-mathematics", "headline": "L1 regularization results in sparse solutions", "summary": "Why L1 regularization produces sparse solutions \u2014 the diamond corners touch axes", "source": "Why L1 regularization produces sparse solutions \u2014 the diamond corners touch axes", "sourceUrl": "https://en.wikipedia.org/wiki/Regularization_(mathematics)", "articleUrl": "https://en.wikipedia.org/wiki/Regularization_(mathematics)", "publishedAt": "2026-06-12", "category": "learn", "cohortScore": 0.5, "embedding": [-5, -2, -1, 5, 1, 2, -3, -3, 8, -5, 5, 0, 4, 2, 8, 4, 2, 3, -6, -1, 2, -10, 1, -3, -3, 2, 2, -7, -3, -34, 7, 4, 9, 4, 3, 7, -2, 8, -8, 3, 1, 2, -5, -2, -2, -8, -4, 3, -1, -2, -5, -4, 3, -2, 5, 2, 2, 3, 1, 7, 5, -4, -16, 9, 11, 5, 2, -9, -1, 5, 1, 0, 8, 2, 7, -1, -2, -3, -5, -2, 4, 2, -3, 0, -5, 0, 6, -9, 2, -3, -4, 0, -5, 1, -4, -9, 8, 7, -5, 46, -7, 8, 6, 1, 3, -2, -6, -6, -7, 2, 3, -3, 3, -2, 2, -9, 0, 2, 7, -5, -4, 3, -2, -7, 6, -6, 0, 14, 2, 3, 2, 5, -8, -2, 1, -2, 3, 2, 3, 8, -4, 0, 9, -1, -9, 7, -8, 0, -3, -5, 1, 1, -7, 7, 0, 1, -1, -6, -7, 3, -1, -1, -3, 13, -6, -9, 3, -4, 0, 0, 5, -1, 3, 1, 2, 4, -9, -1, -2, 4, 1, -7, 3, 0, 2, -6, 2, -2, -3, -6, -1, -6, -5, 4, 1, -4, -1, -2, -6, -1, 7, -1, -4, -2, 6, -4, 2, 0, 0, 8, -10, -8, 4, -3, 1, 3, 5, 2, 0, 8, 0, -3, -12, -34, -1, 1, 2, 0, -11, 10, -1, 11, -1, -5, -5, -3, 1, 3, -4, 1, 8, -2, 2, 1, 4, -3, -2, -1, 3, 21, -1, -2, 2, -6, 3, 0, 3, 1, 5, 15, -2, -6, -2, 1, -2, -3, -10, -11, 3, -2, -4, -4, 2, 1, -2, 4, -9, -2, 2, -10, 1, 1, 1, 2, -8, -1, -12, 6, 8, 3, -8, 4, -2, 1, 9, 0, 3, 3, 1, 9, 6, 0, -5, 8, 4, 3, -4, 5, 6, 11, -2, 0, 1, -2, 1, -12, -8, 3, 0, -32, -1, 8, 3, -3, 7, 7, -1, -1, 5, -10, 6, 4, 0, 2, -2, 8, -10, 8, -15, -2, 4, 23, -7, -1, 6, -2, -11, -3, -6, -2, 6, 4, 4, -5, 13, -6, 2, 0, 0, 4, 3, 3, -1, 6, -2, 5, 6, 4, -5, 0, 2, 6, -1, -2, 3, -7, 2, -2, 1, 2, -3, 5, 0, 0], "explanation": ["L1 regularization, also known as Lasso, adds a penalty equal to the absolute value of the magnitude of coefficients to the loss function. This penalty encourages the coefficients to be zero, leading to sparse solutions where only a subset of features contributes significantly to the model."], "example": "In a linear regression model with L1 regularization, if there are 10 features and the regularization parameter is high, the model may end up with only 3 non-zero coefficients, effectively selecting only 3 features out of the 10.", "whyItMatters": "Sparse solutions are beneficial for model interpretability and can lead to better generalization by reducing the risk of overfitting.", "imageUrl": "https://upload.wikimedia.org/wikipedia/commons/thumb/0/02/Regularization.svg/1280px-Regularization.svg.png"}, {"id": "965fa8417c95", "title": "the Lp norm ball shape changes as p goes from 1 to 2 to infinity", "slug": "the-lp-norm-ball-shape-changes-as-p-goes-from-1-to-2-to-infinity", "headline": "How does the shape of a ball change as we measure distance differently?", "summary": "How the Lp norm ball shape changes as p goes from 1 to 2 to infinity", "source": "How the Lp norm ball shape changes as p goes from 1 to 2 to infinity", "sourceUrl": "https://en.wikipedia.org/wiki/Lp_space", "articleUrl": "https://en.wikipedia.org/wiki/Lp_space", "publishedAt": "2026-07-03", "category": "learn", "cohortScore": 0.5, "embedding": [-5, -6, 0, -3, -5, 6, 6, -3, 6, 3, 9, -8, 0, -2, 0, -2, -5, -1, -17, 4, 7, -5, 1, -4, 3, 10, -2, -4, -1, -36, 5, 1, 1, -7, -3, -4, -1, -3, 4, 10, 2, 0, 0, -9, 0, -5, 0, 6, 2, -1, -5, -1, 1, 1, 7, 8, 3, 9, 8, 0, 7, -2, -17, 11, 5, 2, -6, -6, -4, 5, 1, 7, 1, 1, 8, -4, -6, -4, 0, 4, 0, -1, -7, -2, -4, -1, 0, -7, 1, -1, -1, 3, -10, 1, -2, -2, -2, 0, 9, 43, -9, 4, 0, 5, 0, 1, 0, -6, 5, 3, 3, 2, -5, 1, -6, -3, -3, 5, 3, -5, -8, 12, -5, -5, 0, 3, 1, 12, 5, 9, 4, -2, -6, -8, 3, 4, 2, 5, 11, 6, 0, -1, 7, -1, 0, 14, -9, 0, 6, 0, 0, -2, -10, -7, 4, -1, 4, 0, -7, -5, -13, -2, 0, 12, 0, 0, 7, -10, 4, -1, 1, -1, 2, -1, 9, 3, -7, -8, 10, -4, 3, -3, -1, -4, -3, -3, -4, 4, 6, 5, 6, -3, -8, -4, -4, -5, -2, 2, -2, -4, 2, 4, 2, -1, 3, 3, 9, -2, -1, 9, -3, -13, -11, -8, 2, 3, 3, -4, -4, 4, -9, -1, -5, -33, -1, -4, -5, 12, -2, -3, -1, 3, -1, 8, -2, -6, 1, 2, 0, 3, 4, -7, 1, -5, 9, -11, 1, 1, -1, 14, -5, 4, 3, -4, 0, -5, 3, -1, -2, -3, -2, -6, 0, -1, -1, 1, 1, -6, 0, 5, 5, -1, 3, -1, 0, 3, -7, 1, -5, 3, 1, -1, 7, 1, -1, 7, -2, 1, 4, -1, -4, -2, -2, 4, 5, 1, -4, 4, -3, 6, 7, 2, 2, 13, 0, 5, -1, 3, -2, -1, -3, 0, -5, 2, -2, -2, 3, -2, -4, -35, -2, 3, 6, -7, 7, 5, 1, 2, -6, -6, -1, 3, 0, -5, 1, 3, -1, 12, -6, 1, 1, 27, -9, 1, -6, 5, 2, -1, 1, -4, 2, 7, 2, 1, 14, -1, 3, -3, -1, 6, -9, -4, -4, 11, 4, -2, 2, 6, -2, -4, 1, 2, 1, -7, 9, -6, 0, 4, 0, 5, 0, 5, -9, 10], "imageUrl": "https://upload.wikimedia.org/wikipedia/commons/thumb/2/21/Mandel_zoom_00_mandelbrot_set.jpg/1280px-Mandel_zoom_00_mandelbrot_set.jpg", "imageLicense": "CC BY-SA 3.0", "imageArtist": "Created by Wolfgang Beyer with the program Ultra Fractal 3.", "explanation": ["Imagine you're measuring how far apart two friends are standing. If you use a simple ruler, you're measuring straight-line distance. But what if you want to consider how far apart they are in a more complex way, like walking through a park?", "The Lp norm is like choosing different ways to measure distance. With p=1, it's like walking straight through obstacles. As p increases, it's like considering the longest path, even if it's winding. The ball shape changes from a diamond to a circle to a square as p goes from 1 to 2 to infinity."], "example": "If your friends are 3 meters apart straight-line (p=1), they might be 5 meters apart if you consider the winding path through the park (p=2), and 10 meters apart if you consider the longest possible route (p=infinity).", "whyItMatters": "The Lp norm measures distance in different ways, changing the shape of the ball that represents all possible distances."}, {"id": "0d2b5e596528", "title": "Norm (mathematics)", "slug": "norm-mathematics", "headline": "L\u221e norm equals max absolute value", "summary": "Why L\u221e norm is the max absolute value \u2014 the unit ball becomes a square", "source": "Why L\u221e norm is the max absolute value \u2014 the unit ball becomes a square", "sourceUrl": "https://en.wikipedia.org/wiki/Norm_(mathematics)", "articleUrl": "https://en.wikipedia.org/wiki/Norm_(mathematics)", "publishedAt": "2026-06-12", "category": "learn", "cohortScore": 0.5, "embedding": [-2, -10, -5, -6, -2, -3, 11, 7, 9, 6, 9, -5, 5, 3, -1, 0, 2, 5, -14, 1, 8, -5, 1, -8, 9, 5, -5, -2, 4, -34, -2, 4, 7, -5, -4, -6, -3, -7, -1, 5, 3, 2, 3, -13, 1, -3, -4, 4, -7, 4, -4, 3, 0, 0, 4, 5, 2, 7, -3, -1, 5, -5, -16, 7, -1, -6, 0, -8, -8, 3, 1, 1, 6, 0, 8, -1, -7, -7, 0, 2, 3, -3, -6, -1, 1, 0, 3, -7, 4, 4, 0, -2, -3, 2, 2, -2, -3, 4, 2, 47, -4, 1, -4, -7, 1, 0, 0, 1, -3, -10, -5, 3, -3, -2, -1, -3, 4, -2, -4, -4, 0, 3, 2, -1, 2, 3, -3, 12, 2, 10, 2, -6, 0, -5, -1, 2, 6, 3, 5, 7, 3, -3, 0, -4, -5, 5, -7, -5, 5, -3, 3, -1, -4, -8, 6, 6, 1, 2, -9, -7, -14, -2, -2, 12, -8, -2, 11, -1, -1, 0, 4, -5, -4, 4, 11, 4, -6, -1, 1, 2, 3, -6, -1, 4, 3, -1, -6, 5, 5, -2, -3, 3, -8, -4, -6, -7, 3, -2, 3, -6, 5, 3, 0, -2, 7, 2, 1, -6, 2, 7, -2, -3, -2, -5, -4, 4, 3, -4, -6, 0, 5, 8, -13, -37, -1, -4, -12, 10, -8, 6, -5, 0, -2, 4, -1, -10, -2, 1, 2, 2, 3, -7, 6, -6, 5, -9, 6, 4, -3, 17, -3, 7, 5, 0, 3, -2, 12, 0, -2, 0, -6, -1, 2, 1, -2, -3, -6, 1, 3, 5, 2, -6, 5, 2, -2, 1, -4, 9, -1, 1, -2, 2, 8, 6, -4, 3, 0, 3, 4, 2, -2, -2, 5, 7, 5, -3, -2, 5, -1, 6, 8, 2, 1, 6, -3, 7, -3, 7, -1, 3, 2, 0, 1, -4, -1, -2, -2, -4, -7, -33, -8, 7, 0, -10, 4, -2, -3, -8, 2, -9, 7, 2, -2, -6, 0, -1, -2, 13, -6, 1, 8, 22, -8, 2, 5, -4, 4, -4, -8, -1, 7, 13, 3, -1, 9, -6, 7, 4, 1, -4, -1, -3, 1, 7, 5, 3, 2, 1, -4, 2, 3, 4, 0, -5, -1, -7, 3, 3, 1, 4, 9, 3, 2, 7], "explanation": ["The L\u221e norm is defined as the maximum absolute value of the vector components. This norm measures the greatest deviation from zero among all components of the vector."], "example": "For the vector (3, -7), the L\u221e norm is 7, since 7 is the absolute value of the component with the greatest magnitude.", "whyItMatters": "Understanding the L\u221e norm is crucial for analyzing vector spaces and functions in various mathematical and engineering applications.", "imageUrl": "https://upload.wikimedia.org/wikipedia/commons/thumb/1/1f/James_Abram_Garfield%2C_photo_portrait_seated.jpg/1280px-James_Abram_Garfield%2C_photo_portrait_seated.jpg", "imageLicense": "Public domain", "imageArtist": "Unknown; part of Brady-Handy Photograph Collection."}, {"id": "51970effa4dc", "title": "Chebyshev distance", "slug": "chebyshev-distance", "headline": "Chebyshev distance is named after Pafnuty Chebyshev", "summary": "Why L1 distance is called Manhattan distance \u2014 grid-like paths", "source": "Why L1 distance is called Manhattan distance \u2014 grid-like paths", "sourceUrl": "https://en.wikipedia.org/wiki/Chebyshev_distance", "articleUrl": "https://en.wikipedia.org/wiki/Chebyshev_distance", "publishedAt": "2026-06-12", "category": "learn", "cohortScore": 0.5, "embedding": [-2, -3, -2, 2, -4, 1, -1, 4, 7, -5, 2, -4, 0, 7, 3, -1, -6, 6, -7, 0, 16, -9, 6, -4, 6, 14, 3, 0, 0, -28, 4, 3, 10, -1, -4, 6, -2, 3, -7, 5, 3, 4, 8, 5, -6, -5, -5, 1, -7, -3, 0, -1, 4, 1, 8, 7, 10, 4, -2, 1, 4, -7, -20, 2, 5, -1, 6, -6, -2, 8, -2, 1, 1, 3, 7, -5, -3, -3, -3, -1, 2, -1, -12, 2, -4, 8, -3, -3, -1, 1, -7, -5, -1, 6, -8, -8, 3, 2, 6, 49, -4, 8, -4, -1, 6, -1, 2, -11, -3, -2, 4, -4, -1, 2, 3, -2, 6, 3, 4, 0, -7, 6, 1, 0, -6, -4, 2, 6, 6, 4, 4, 1, -7, 3, 1, 5, 3, -2, -1, 4, 0, 1, 8, 1, -1, 9, -10, 2, -2, -5, 4, -2, -1, -12, -6, 4, 8, 2, 0, 6, -4, 0, 4, 11, 3, -13, 3, 6, 1, -6, 1, -4, 2, 3, 3, -1, -11, 0, 2, 5, 2, -5, -2, -5, 4, 1, -6, 0, -1, 6, -2, 1, 8, -2, -3, -5, -5, 2, 3, -7, 3, -2, -4, -3, -6, -12, 6, -8, 4, 7, -2, -2, -5, -1, 3, -8, 1, 4, 0, 8, 0, 2, -15, -38, -4, -2, -4, -3, -9, -2, 5, -3, 5, 9, -2, -4, 0, -3, 4, 5, 1, -6, -2, 4, 13, -4, -2, -6, 1, 18, -1, 4, -3, 0, 0, -1, -4, -3, -2, 7, -9, -3, -2, -8, -5, 3, 0, -7, 2, -2, -7, 4, 4, -4, -3, 3, -5, 2, -4, -4, 1, 0, 1, -3, -5, -1, -1, 9, -1, -6, -2, 3, 2, 2, 13, -3, -3, 11, -4, 7, 4, 0, -5, 10, 4, 9, -2, 1, -3, 9, 4, -1, 0, 1, 2, -2, -9, 6, -1, -33, 5, 5, 2, -6, 3, 1, -3, 1, 0, 2, 7, 4, -7, -5, -1, 6, 0, 1, -1, 5, 0, 23, -6, 0, -1, 0, 5, -3, -3, -3, 1, 3, -2, 0, 11, 5, 4, 3, -3, -2, -3, -3, -2, 13, 4, -4, -5, -4, 0, -2, -1, 0, 3, -1, 4, 1, -5, -9, -7, -1, -2, 8, -5, 5], "explanation": ["Chebyshev distance is a metric used in mathematics to measure the distance between two points in a coordinate space. It is defined as the greatest of their differences along any coordinate dimension. This metric is particularly useful in situations where movement is restricted to grid-like paths, such as in chess or urban grid layouts."], "example": "In chess, the minimum number of moves needed by a king to go from one square to another equals the Chebyshev distance between the centers of the squares. For instance, moving from f6 to e2 requires 4 moves, which corresponds to the Chebyshev distance of 4.", "whyItMatters": "Understanding Chebyshev distance helps in analyzing movements and optimizing paths in grid-like environments, such as chess or urban planning.", "imageUrl": "https://upload.wikimedia.org/wikipedia/commons/thumb/7/74/Tallinn_Digital_Summit._Introduction_for_elementary_school_children_to_coding_through_a_robotics_programme_%2836662719824%29.jpg/1280px-Tallinn_Digital_Summit._Introduction_for_elementary_school_children_to_coding_through_a_robotics_programme_%2836662719824%29.jpg", "imageLicense": "CC BY 2.0", "imageArtist": "EU2017EE Estonian Presidency"}, {"id": "24cd7fe5ff90", "title": "The elastic net combines L1 and L2: \u03bb\u2081|w| + \u03bb\u2082w\u00b2 gives both sparsity and stability", "slug": "the-elastic-net-combines-l1-and-l2-w-w-gives-both-sparsity-and-stability", "headline": "Why do we sometimes need both a scalpel and a hammer in surgery?", "summary": "The elastic net combines L1 and L2: \u03bb\u2081|w| + \u03bb\u2082w\u00b2 gives both sparsity and stability", "source": "The elastic net combines L1 and L2: \u03bb\u2081|w| + \u03bb\u2082w\u00b2 gives both sparsity and stability", "sourceUrl": "https://en.wikipedia.org/wiki/Elastic_net_regularization", "articleUrl": "https://en.wikipedia.org/wiki/Elastic_net_regularization", "publishedAt": "2026-07-03", "category": "learn", "cohortScore": 0.5, "embedding": [-8, -6, -1, 3, -3, 6, 0, 5, 3, -7, 2, -5, 6, 2, 3, -2, 0, 8, -12, 7, 8, -4, 3, -7, -4, -1, 0, -2, -1, -30, 4, -2, 6, -2, 4, 0, -1, 2, -3, 4, 7, 6, -2, -2, 7, -5, 2, -4, -1, 5, -5, -1, 6, 3, 3, 5, -3, 1, 0, -2, 9, -1, -13, 10, 8, 0, 0, -10, 1, 3, 5, 2, 5, 8, 2, 0, 2, -5, 5, 3, 6, -3, -4, 0, 0, -6, 0, -11, -7, 1, -8, 1, 2, 2, 2, -5, 1, 11, -1, 53, -3, -1, 5, -1, 10, -3, 1, -2, -6, 4, 9, 2, 3, -3, -4, 1, -3, 1, 2, -8, -10, 4, 0, -5, 1, -5, 1, 11, 8, -2, 0, 0, 2, 0, -7, 1, -1, -1, -3, 5, 1, -3, 2, -2, -6, 13, -4, -1, -2, -5, -9, 2, -4, 1, -2, 1, -6, -7, -3, -2, -1, -6, -9, 13, 1, -7, 4, -1, -1, -3, 7, -5, 3, 1, 2, 0, -7, -3, -1, 3, 4, -2, -2, 5, -2, 1, -3, 0, 6, 0, -2, -4, -2, 7, -3, -11, 3, 0, -8, 3, 5, 2, 2, -2, 7, 3, -2, 1, -3, 6, -4, 0, 4, -2, -4, -3, 4, 3, 4, 5, 4, 5, -9, -44, 2, 0, -5, 9, -4, 6, -2, -7, -7, 3, 7, -4, -3, 0, 1, 3, 0, -11, -1, 1, 8, -3, -2, 3, -3, 20, -10, 7, -2, -5, 2, -5, -2, 4, 5, 9, -7, -3, 2, -7, -3, -2, -4, -7, 1, -8, -6, -2, 3, 3, -6, 6, -2, -3, 2, -2, -3, -4, 2, 2, -3, 1, 1, 2, 3, 0, -2, 4, -9, 0, 9, 2, 3, 4, -4, 0, 7, -1, -3, 9, -3, 0, 1, 6, -6, 7, -2, 2, -4, 1, 5, -6, -7, -2, 1, -34, 5, 7, 3, -5, 1, 2, -5, 6, -3, -8, 3, 3, 1, 1, 4, 15, -9, 7, -7, -3, 6, 21, -3, 2, 6, 4, -2, 1, -1, 2, 0, 1, -2, 2, 5, -6, 4, 8, 0, 7, -2, 5, 1, 10, -5, -2, -1, 2, -3, -2, 8, 8, -2, -4, 1, 1, -3, -3, 1, 1, 2, -6, 2, -5], "imageUrl": "https://upload.wikimedia.org/wikipedia/commons/thumb/4/48/Egyptian_capital_%28SM_5257z%29.png/1280px-Egyptian_capital_%28SM_5257z%29.png", "imageLicense": "PDM-owner", "imageArtist": "Hessemer, Friedrich Maximilian\n\nFriedrich Maximilian Hessemer (Q1461066)", "explanation": ["Imagine you're trying to fix a broken vase with a delicate touch but also need to hammer in a loose piece. You need both precision and strength.", "The elastic net method in statistics is like using both a scalpel and a hammer to fix a vase. It combines the precision of the lasso (L1 penalty) and the strength of ridge regression (L2 penalty) to find the best balance in data analysis."], "example": "If the lasso helps remove unnecessary details (like a scalpel trimming excess), and ridge regression smooths out the data (like a hammer smoothing out rough edges), the elastic net uses both to get a clearer picture.", "whyItMatters": "The elastic net method uses both L1 and L2 penalties to balance precision and stability in data analysis."}, {"id": "1fd0a08246eb", "title": "the L1 norm is not differentiable at zero", "slug": "the-l1-norm-is-not-differentiable-at-zero", "headline": "Absolute value's kink makes it non-differentiable at zero", "summary": "Why the L1 norm is not differentiable at zero \u2014 the absolute value has a kink", "source": "Why the L1 norm is not differentiable at zero \u2014 the absolute value has a kink", "sourceUrl": "https://en.wikipedia.org/wiki/Absolute_value", "articleUrl": "https://en.wikipedia.org/wiki/Absolute_value", "publishedAt": "2026-07-03", "category": "learn", "cohortScore": 0.5, "embedding": [-5, -2, -6, -6, -9, 1, 3, 7, 8, 0, 12, -4, 3, 3, -1, -7, -3, 4, -18, 7, 9, -3, 7, -4, 1, 6, 1, 1, 6, -34, -4, 1, 2, -3, -2, -3, -2, 0, 1, 5, 3, -3, 7, -9, -2, -5, -4, 8, -1, 6, -4, 1, 5, 1, 0, 5, 3, 3, 2, -2, 7, -2, -15, 11, 9, 2, 2, -8, -5, -1, 0, -2, 2, 1, 9, -5, -3, -5, -2, 0, 5, -3, -4, 0, 0, 0, 4, -9, -2, 0, -4, 1, -2, 1, 0, -3, 0, 10, 1, 52, -8, 9, -4, -4, 1, -3, -3, 0, -2, 0, 1, -1, 4, -4, -3, -5, 3, 0, 6, -2, -1, 1, 2, -2, 0, 3, -4, 16, 2, 6, 4, -6, 3, -6, 1, 3, 1, 10, 6, 2, -4, -4, -3, 1, -7, 4, -10, -4, 4, 4, -2, 2, -7, -6, 3, 3, 0, -1, -7, -6, -7, -3, -10, 10, -4, 0, 9, 1, -2, -5, 11, -10, -5, -3, 12, -5, -8, 1, 0, 5, -2, -1, 3, 0, 6, 1, -4, 3, 4, -2, 1, -7, -7, -2, 0, -3, 3, -3, -2, -2, 7, 6, 3, -3, -2, 4, 0, -2, 0, 10, -4, -7, -5, -5, -4, 3, 2, -2, 1, -1, -8, 4, -2, -39, 1, -5, -6, 7, -4, 5, 4, 0, 4, 0, -1, -11, -3, 4, 6, 1, 1, 0, 0, -13, 7, -8, -2, 3, -2, 17, -6, 10, 1, 2, 4, 2, 6, -1, 1, 0, -3, -2, 2, 2, -3, 1, -1, -3, 4, -5, -3, -6, 9, -2, -3, -4, -1, 3, 3, -1, -4, 3, 9, 5, -2, 4, -4, -1, 4, -3, -1, 3, 3, 4, 10, 4, -1, 4, 1, 0, 9, 4, 3, 6, 0, 5, -1, -3, -4, 3, -3, 4, 2, -3, -1, -2, -1, 5, 0, -34, -4, 2, -4, -2, 4, 0, -11, -10, 4, -7, 6, 3, 2, 2, -5, 5, -10, 6, -11, 7, 8, 25, -2, -2, 1, -3, 1, -2, -3, -2, 6, 7, 2, 1, 2, -2, -3, 4, -2, 3, 4, 0, -3, 9, 5, 2, 1, 5, -6, 4, 0, 3, -1, 3, 4, -5, -1, -5, -3, 0, 4, 5, -4, 1], "imageUrl": "https://upload.wikimedia.org/wikipedia/commons/4/4d/Lorenz-SZ42-2.jpg", "imageLicense": "Public domain", "explanation": ["Imagine you're measuring the distance from your home to a friend's house. You want to know how fast you're getting closer as you walk.", "The distance changes smoothly until you reach your friend's house, but there's a sudden stop at the exact point of arrival. This stop is like the kink in the absolute value function at zero."], "example": "As you walk towards your friend, the distance decreases smoothly until you reach them. At that exact moment, there's an abrupt halt in the distance change.", "whyItMatters": "The absolute value function's kink at zero makes it non-differentiable there."}, {"id": "bb226867ee4e", "title": "Proximal gradient methods for learning", "slug": "proximal-gradient-methods-for-learning", "headline": "Why can't we always find the best path in a maze?", "summary": "Why proximal gradient descent is needed for L1 optimization", "source": "Why proximal gradient descent is needed for L1 optimization", "sourceUrl": "https://en.wikipedia.org/wiki/Proximal_gradient_methods_for_learning", "articleUrl": "https://en.wikipedia.org/wiki/Proximal_gradient_methods_for_learning", "publishedAt": "2026-07-03", "category": "learn", "cohortScore": 0.5, "embedding": [-10, -5, -1, 4, -3, 2, -3, 2, 13, 0, 7, -2, 2, 8, 2, 3, -3, 4, -3, -2, 4, -7, 2, -11, -1, 1, -3, -1, 3, -30, 6, -1, 3, 0, -5, 8, -3, 6, -8, 3, 0, 9, -4, 1, 8, -3, -2, -8, -10, 1, -1, -2, 4, -2, 0, 6, 5, 10, 2, 4, 2, 1, -14, 0, 8, -4, -3, -7, -2, 15, 1, 3, 7, 2, 5, 5, -1, -3, 5, 2, 4, -1, -6, -2, -3, -5, -1, 2, -3, -5, 1, -8, -4, 2, -1, -3, 3, 6, -7, 50, -7, 12, 0, 4, 0, -6, -2, -3, 0, -4, -2, -7, 8, -3, -1, 3, 3, 5, 2, 5, -2, -7, 6, -2, -2, -9, -7, 10, -1, 5, 3, -1, -3, 1, -2, 0, 3, -4, -3, -2, -6, 9, 13, -4, -10, 12, -3, -4, -6, -6, -5, -1, -1, -5, -3, 5, -2, -3, -7, 3, -5, -3, -2, 15, -5, -4, -1, -5, -3, 0, 2, -5, -2, -1, 1, -1, -14, -4, -8, 2, 4, -7, 0, -3, 4, -5, 5, -4, -1, -1, -7, -3, 2, -1, -4, -6, 1, -2, -2, 1, -2, 4, -1, 2, -1, 1, 3, -4, 8, 3, -9, -10, 4, -5, 1, -1, 3, 1, 5, 9, 0, 4, -7, -32, -6, -1, 3, -1, -8, 7, -1, -3, 5, 4, -4, -5, 6, 4, 0, 3, 1, 1, 2, 2, 2, 5, -9, -1, 2, 20, -4, 10, 2, -5, 3, -5, -2, 4, -3, 15, -6, 0, -1, -6, 3, 2, -11, -18, -4, -3, -1, 0, 3, 2, 3, 5, -13, 3, -2, -3, 2, -1, 9, -2, -6, -1, -4, 5, -2, 1, -1, 5, 6, 0, 5, 3, -3, 5, 2, 7, 6, -1, 2, 5, -3, 3, 0, 2, -1, 4, -6, 2, 5, -5, 1, -8, -4, 4, 5, -31, 0, 7, -4, -4, 6, 12, -3, 2, 6, 0, 7, 4, 4, 3, -3, 7, -1, 5, -8, 3, 9, 25, -8, 2, 3, -1, -7, 1, -4, -6, 6, 11, -4, 5, 13, -4, -1, -1, -2, 6, -1, 6, 2, 7, -1, 4, 5, -5, -3, -4, 2, 4, -3, 3, 4, -3, -5, -7, -2, 7, -2, 8, -1, -2], "imageUrl": "https://upload.wikimedia.org/wikipedia/commons/thumb/6/69/Th%C3%A9%C3%A2tre_D%E2%80%99op%C3%A9ra_Spatial.png/1280px-Th%C3%A9%C3%A2tre_D%E2%80%99op%C3%A9ra_Spatial.png", "imageLicense": "Public domain", "imageArtist": "Left intentionally blank", "explanation": ["Imagine you're trying to find the shortest route through a city with many one-way streets. You can't just follow the streets; you need a smarter way to navigate.", "Proximal gradient descent helps us find the best path by breaking down the problem into smaller, easier steps, even when the road map isn't smooth."], "example": "Instead of trying to find the shortest route in one go, you first follow the streets (simple steps), then adjust your path (gradually improving) until you reach your destination.", "whyItMatters": "Proximal gradient descent allows us to tackle complex problems by simplifying them into manageable steps."}, {"id": "4a063711c623", "title": "LASSO uses L1 to do feature selection by driving coefficients to exactly zero", "slug": "lasso-uses-l1-to-do-feature-selection-by-driving-coefficients-to-exactly-zero", "headline": "Why do some numbers disappear when solving complex problems?", "summary": "How LASSO uses L1 to do feature selection by driving coefficients to exactly zero", "source": "How LASSO uses L1 to do feature selection by driving coefficients to exactly zero", "sourceUrl": "https://en.wikipedia.org/wiki/Least_absolute_deviations", "articleUrl": "https://en.wikipedia.org/wiki/Least_absolute_deviations", "publishedAt": "2026-07-03", "category": "learn", "cohortScore": 0.5, "embedding": [-6, -1, -1, 0, -3, -3, 2, 8, 5, -4, 9, 2, 4, 5, -7, 2, 4, 4, -7, -1, 5, -8, 0, -7, 3, 4, 3, 0, -3, -36, 3, 1, 11, 2, -2, 10, 3, 7, -7, 2, 0, -1, -4, -2, -4, -2, 0, 2, -7, 0, -4, -7, 0, 8, 1, 5, 0, 6, 1, 3, 3, 0, -19, 5, 10, 2, -3, -8, -3, 14, 0, 2, -1, -1, 4, 2, -4, 0, 2, 5, 8, -3, -3, -3, 2, 1, -3, -6, 3, -8, -3, 2, 2, 2, -5, -4, 7, 5, 2, 43, -3, 5, -8, -2, -3, -9, -4, -7, -3, -1, 3, -4, -1, 0, 3, -1, -5, 4, 2, -1, 2, -4, 11, -3, 5, 1, -1, 16, -4, 4, 6, -1, -10, -3, -1, 2, 3, 8, -9, 2, -4, 3, 14, 1, -6, 12, -6, -3, 2, -7, 2, 1, -6, -9, -2, 2, -1, -5, -8, 4, -3, -4, -3, 6, -6, -6, 6, 3, -4, 5, 5, -6, -6, 2, 8, 1, -12, -1, 1, -1, -2, 0, 2, 3, 7, -1, 0, -3, -4, 2, -10, -8, 4, -5, 0, 2, 1, 0, -4, -2, 2, 5, 2, -5, 4, 1, 2, -2, 4, 12, -4, -7, 3, 0, -3, -1, 1, -5, 1, 3, 3, 0, -6, -39, -3, 2, -1, -7, -14, 8, -3, 3, 16, 0, -1, -14, -1, 3, -5, 1, 3, -7, 5, 1, 2, 5, -2, -2, -1, 18, -3, 4, 4, 0, 2, -4, 7, 0, -3, 11, -5, -5, 0, 4, -1, 2, -2, -8, 4, -4, 3, -10, 9, 7, 2, 7, -5, 4, -3, -7, 1, 0, 1, 1, -9, -4, -9, 2, 5, -1, -5, 9, 1, 2, 7, -2, 1, 7, 0, 4, -3, -5, 0, 10, 1, 2, 0, 6, 1, 11, -2, 0, 5, -3, -2, -5, -6, 3, -2, -27, -2, -2, 4, 5, 5, 4, -10, 0, 3, -6, 5, 6, -1, -2, 1, 4, -5, 11, -8, 3, 5, 22, -10, 3, 0, 0, -8, -4, -4, 4, 9, 15, -1, -6, 12, -5, -4, -2, 0, 9, 0, -3, -3, 10, -3, 4, -2, -1, -1, -5, 5, 1, -7, 1, 0, -7, 3, -3, -3, 5, 2, 6, 6, -6], "imageUrl": "https://upload.wikimedia.org/wikipedia/commons/7/74/Graph_showing_Wage_%3D_%CE%B10_%2B_%CE%B40female_%2B_%CE%B11education_%2B_U%2C_%CE%B40_0.jpg", "imageLicense": "CC BY-SA 3.0", "imageArtist": "Shailaja.k", "explanation": ["Imagine you're trying to balance a scale with weights representing different features of a dataset. Some weights are too heavy and throw off the balance.", "LASSO helps by making some weights lighter or even removing them entirely, simplifying the balance without losing the overall picture."], "example": "If you have weights of 1, 2, 3, and 4, LASSO might remove the 4, keeping just 1, 2, and 3 to balance the scale more effectively.", "whyItMatters": "LASSO uses L1 norm to drive some feature coefficients to zero, simplifying models."}, {"id": "c9d54f9d416a", "title": "Ridge regression uses L2 to shrink coefficients without eliminating them", "slug": "ridge-regression-uses-l2-to-shrink-coefficients-without-eliminating-them", "headline": "Why do some roads get smoother and straighter over time?", "summary": "How Ridge regression uses L2 to shrink coefficients without eliminating them", "source": "How Ridge regression uses L2 to shrink coefficients without eliminating them", "sourceUrl": "https://en.wikipedia.org/wiki/Ridge_regression", "articleUrl": "https://en.wikipedia.org/wiki/Ridge_regression", "publishedAt": "2026-07-03", "category": "learn", "cohortScore": 0.5, "embedding": [-2, 0, 4, 6, 4, -1, -3, 6, 4, -1, 8, -2, 5, -2, 2, 0, -5, 8, -5, -7, -1, -1, 5, 0, -2, 7, -5, -1, -3, -32, 9, 5, 3, 1, -4, 3, -6, 7, -3, 1, 3, 2, -2, -5, 0, 0, 4, 4, -4, 1, 0, -5, 1, 0, 0, 5, 3, 13, 1, 2, 0, -3, -21, 5, 7, 1, -2, -5, -7, 10, -2, 3, -4, 1, 4, 3, -1, 0, -2, -5, 10, 5, -1, -2, 3, -9, -2, -5, 6, -1, 2, -7, 3, -1, -1, 1, 3, 9, 8, 46, -9, 5, -4, 6, -2, -3, -1, -2, -6, 2, 2, -1, -1, -1, -4, -8, -2, 4, -3, 2, -6, 0, 2, -3, 4, -5, 0, 11, 4, 0, -6, 2, -10, -3, -4, -3, 3, 3, -1, 2, -5, 1, 8, -2, -6, 12, -3, -2, -2, -3, 1, 1, -8, -4, 4, 6, 1, -2, -5, 2, -1, -2, -11, 6, -9, -8, 3, 5, 2, 4, 7, -4, 7, -6, 3, 0, -8, 3, 0, 1, 2, 3, -4, 5, 1, -2, -10, 1, -4, 6, -4, -6, -3, 1, 1, 2, 1, 8, -6, -2, 3, 3, 2, -1, 1, 1, 7, -5, 4, 9, 1, -12, 7, -5, 1, 10, 6, 5, 0, 7, -1, -8, -7, -41, -4, 0, 1, 8, -7, 1, -1, -4, 4, 7, -1, -6, -5, 0, 1, -2, 4, -13, 8, 2, 3, -2, -5, 2, 7, 16, -16, 1, -1, -2, 2, 3, 3, 1, 0, 13, -1, -8, -4, -3, 0, 5, -1, -6, 1, -3, 4, -2, -1, 1, 0, 11, -2, 3, 3, -6, 4, 4, -5, -6, -10, 0, -8, 2, 3, -5, -12, -2, 6, 3, 12, -14, -5, 3, 1, -1, 4, -1, -5, 14, -3, 3, 4, 5, -3, 4, 1, 3, 8, 0, -4, -5, -7, 4, 4, -34, -4, 0, -5, -3, 5, 6, 1, -1, 5, -7, 13, 8, -4, 3, -3, 8, -6, 5, -5, -1, 1, 20, -3, 3, 4, -2, -6, 5, -4, -1, 4, 6, -1, -1, 7, -10, 3, 5, 3, 4, 4, -2, 0, 9, -3, 2, -3, 0, 3, 0, 4, 0, 0, 1, 2, -9, -1, -1, -5, 1, -7, 1, -1, -2], "imageUrl": "https://upload.wikimedia.org/wikipedia/commons/b/bf/Edge_computing_infrastructure.png", "imageLicense": "CC BY-SA 4.0", "imageArtist": "NoMore201", "explanation": ["Imagine you're driving a car on a winding mountain road. Over time, the road gets smoother and straighter as people drive over it, making it easier to drive.", "Just like the road gets smoother, ridge regression smooths out the bumps in a road map filled with lots of twists and turns (highly correlated variables). It does this by adding a tiny bit of extra weight to the turns (L2 regularization), making the overall path smoother and easier to follow."], "example": "If the road twists 10 times in one mile, ridge regression might add a small weight to each twist, making it 9.8 times instead of 10, smoothing out the path.", "whyItMatters": "Ridge regression adds a tiny bit of extra weight (L2 regularization) to smooth out the path (reduce the impact of highly correlated variables) without removing any twists (coefficients)."}, {"id": "12fbe06ef2b1", "title": "CUDA", "slug": "cuda", "headline": "CUDA enables parallel computation on GPUs", "summary": "What a CUDA kernel is \u2014 a function that runs on thousands of GPU threads in parallel", "source": "What a CUDA kernel is \u2014 a function that runs on thousands of GPU threads in parallel", "sourceUrl": "https://en.wikipedia.org/wiki/CUDA", "articleUrl": "https://en.wikipedia.org/wiki/CUDA", "publishedAt": "2026-06-12", "category": "learn", "cohortScore": 0.5, "embedding": [0, -2, 1, 2, 3, 2, -2, 5, 12, -1, -2, -2, 0, 3, 7, 2, 0, 2, 3, -9, 5, -4, -7, -10, 1, 3, 0, -8, -6, -29, 1, -1, 8, 4, 7, -6, 2, 8, 1, 7, -1, 10, -11, -3, 6, 1, -8, -1, 5, 5, -2, 2, -2, -3, -3, 4, 9, -2, 6, -4, 5, 2, -11, 9, 7, -5, 8, -10, 3, 8, -3, 4, 8, -1, 2, 0, -3, 2, -5, -1, -1, -1, -6, -1, -1, 2, -1, 7, 3, 1, -4, -6, 6, 1, -1, 6, 6, 5, 1, 42, -1, -2, -7, 2, 0, -2, 0, 1, -4, 0, 2, -9, 5, 2, 13, -7, -4, -3, -2, 9, -11, 6, -4, 3, 3, -4, -2, 10, 1, 3, 0, 10, -5, 1, 3, 5, 2, -1, -1, 8, -7, 6, 5, -3, 7, 9, 1, 5, -1, -6, 2, 5, -3, -5, -4, -5, 4, 1, -2, 6, -10, -4, -1, 15, -1, -9, -8, 1, 0, -4, -4, 1, 1, -8, 0, -6, -18, -1, -2, 0, 7, -4, -4, 0, 2, -10, 2, 1, -3, -3, -4, 2, -9, 0, -5, -10, 0, -2, -3, -5, -3, 6, -3, 8, -2, -6, -7, 1, -5, 9, 1, -4, 4, 6, -9, 0, -1, 12, 0, 0, 16, -1, 0, -36, -5, 1, 4, 2, -2, 7, -8, 7, 3, 4, -2, -7, -6, -4, 9, -7, -1, -5, -4, 2, 2, 8, -2, 0, 1, 18, 0, 2, -5, 0, -1, -2, -5, 8, 6, 14, 3, 1, 1, 0, 5, -1, -6, 1, -4, 8, 3, -2, 10, 1, -5, 5, 3, 0, -2, -7, 7, 0, 7, -4, -11, -5, 4, 7, -2, -5, -6, 6, -7, -2, 7, -8, -1, 6, -2, 3, -2, 1, 0, 8, 4, 0, 4, 0, -3, 7, 0, -4, -2, -9, 7, -8, -1, 5, 5, -33, -3, -1, 0, 2, 3, 6, -5, -7, 1, -7, 11, 5, 4, 0, 6, 11, -11, 2, 0, 0, 2, 16, -10, 2, -1, -6, -4, 6, 5, -4, -5, 5, -7, -2, 14, 5, 2, 9, 4, 8, -1, -1, -5, 1, 3, -6, -13, -7, -1, 0, -1, 10, -3, -3, -1, -9, -3, -7, -5, 6, -3, 3, 0, -6], "explanation": ["The CUDA platform includes a variety of tools such as drivers, runtime kernels, compilers, libraries, and developer tools. These components work together to help programmers accelerate their applications by leveraging the parallel processing capabilities of GPUs."], "example": "A CUDA kernel is a function that runs on thousands of GPU threads in parallel, enabling efficient execution of complex computations.", "whyItMatters": "Understanding CUDA and its capabilities is crucial for developers working in fields that require high-performance computing, such as scientific research and simulations.", "imageUrl": "https://upload.wikimedia.org/wikipedia/commons/thumb/8/88/Titan%2C_2013_%2849912802521%29.jpg/1280px-Titan%2C_2013_%2849912802521%29.jpg", "imageLicense": "CC BY 2.0", "imageArtist": "OLCF at ORNL"}, {"id": "87b1c7275fe9", "title": "a Triton kernel is", "slug": "a-triton-kernel-is", "headline": "Can your phone run faster with a different brain?", "summary": "What a Triton kernel is \u2014 Python-based GPU programming that compiles to PTX", "source": "What a Triton kernel is \u2014 Python-based GPU programming that compiles to PTX", "sourceUrl": "https://en.wikipedia.org/wiki/TRON_project", "articleUrl": "https://en.wikipedia.org/wiki/TRON_project", "publishedAt": "2026-07-03", "category": "learn", "cohortScore": 0.5, "embedding": [-6, 4, -1, 3, 4, -1, -6, 5, 0, 3, -1, -8, 9, -4, 2, -2, 4, -3, 6, -8, 2, -12, -8, -4, 3, 4, 2, -2, -2, -23, 5, 3, 5, 2, 3, -2, 2, 2, -9, 6, -5, 9, -9, 1, 1, -3, -4, -3, -4, -4, -4, 5, 3, -2, -4, 3, 8, 7, 3, -6, 2, 5, -9, 9, 8, -3, -2, -12, 4, 5, -11, 3, 6, -2, 0, 1, 1, 2, -2, 0, 3, -7, -11, -3, 2, 3, -6, 9, 0, 0, -2, 0, 3, 7, 0, 2, 9, 0, -9, 51, 4, 0, 1, 1, 8, -12, -2, -4, -4, -3, 4, -8, 1, 0, 9, 0, -10, -3, 1, 11, -8, 3, -7, -6, 1, -3, -5, 8, -4, -1, 5, 3, -5, 3, 6, 0, -3, 1, -2, 7, -2, 2, 12, 0, -4, 6, 0, 1, -5, 1, -4, 8, 1, -6, -2, -3, 11, -4, 0, 0, -4, -2, -3, 15, 4, -11, 0, 4, -4, -8, -3, 0, -1, -8, 2, -3, -17, 2, 1, 1, 6, 3, -1, -7, -2, -5, 2, -3, 3, 0, -3, 3, -11, -2, 1, -12, -7, 2, 1, -1, -3, 3, -1, 6, -1, -4, -9, -1, 0, 11, -2, -5, 7, 7, -9, -1, -5, 6, -3, 2, 5, 0, -5, -39, -2, 1, 0, 0, -8, 2, -5, 5, 2, 7, 6, 1, 0, -5, 4, -1, -3, -4, -9, 1, 1, -2, -10, 3, 1, 18, -4, 7, -3, -3, 1, -3, -11, 7, 8, 13, 4, -3, 1, -6, 5, 3, -7, -4, 3, 4, 3, 7, 8, 8, 1, 5, -4, -1, -11, -8, 4, 0, 7, -6, -9, 2, -2, 7, -3, 0, -4, 6, 4, 6, 8, -4, 5, 5, -1, 7, 3, 1, 2, 2, 4, 8, 5, -2, -6, 2, 2, -3, -2, -7, 6, -1, 3, 9, 5, -31, 1, -2, 2, 1, -3, 2, -4, -7, 4, -3, 5, 8, 1, 2, -3, 14, -5, -3, -1, 0, 3, 13, -2, -2, 7, 1, 5, 10, 5, -6, -1, -1, -4, -4, 5, -4, -1, 4, 0, 8, 2, 1, -6, 6, 0, -5, 1, -7, 0, -4, -5, -2, 1, 5, 7, -6, 0, -5, -4, 3, 0, 8, 9, 3], "imageUrl": "https://upload.wikimedia.org/wikipedia/commons/c/c5/MEGWARE.CLIC.jpg", "imageLicense": "CC BY-SA 3.0", "imageArtist": "MEGWARE Computer GmbH", "explanation": ["Imagine you're playing a high-definition video game on your phone, but it keeps freezing or lagging. Frustrating, right?", "This concept is like giving your phone a super-fast brain to handle games smoothly. It's called a Triton kernel."], "example": "Instead of your phone's old brain, you switch to a Triton kernel, and suddenly, the game runs seamlessly, even in 4K resolution.", "whyItMatters": "A Triton kernel upgrades your phone's brain for better performance."}, {"id": "bcce62209ff4", "title": "Triton differs from CUDA", "slug": "triton-differs-from-cuda", "headline": "Why does a super-fast computer sometimes run slower than a regular one?", "summary": "How Triton differs from CUDA \u2014 block-level programming vs thread-level programming", "source": "How Triton differs from CUDA \u2014 block-level programming vs thread-level programming", "sourceUrl": "https://en.wikipedia.org/wiki/CUDA", "articleUrl": "https://en.wikipedia.org/wiki/CUDA", "publishedAt": "2026-07-03", "category": "learn", "cohortScore": 0.5, "embedding": [-7, -2, -1, 4, 4, 0, -3, 3, 8, -2, 3, 2, 7, -1, 4, 2, -2, -5, 5, -6, 5, -9, -6, -7, 2, 2, -4, -6, -4, -32, 1, -2, 9, 0, 5, -1, 3, 3, -6, 1, -8, 8, -8, -5, 1, 3, 3, -3, -1, 3, -12, -2, 1, 0, -2, 2, 7, 5, 0, -6, 2, 4, -12, 5, 15, -4, 1, -7, 3, 7, -9, 2, 1, 4, -3, -5, 1, 8, 1, -2, -1, -12, -11, -4, -6, 1, -2, 10, 8, -4, -7, -1, 7, 4, -1, 3, 4, 4, -6, 47, -1, -4, -5, 4, 6, -5, 0, -2, -4, -1, 5, -1, 4, 0, 4, -1, -2, -2, 3, 12, -9, -2, -3, -7, -2, -12, -4, 11, -4, -2, 9, 4, -2, 4, 5, -5, -2, -1, -2, -2, -5, 8, 8, -5, -7, 7, -1, 5, -1, -1, -3, 2, -1, -11, -4, -1, 2, 3, 1, -6, -5, -1, -4, 8, 6, -4, -1, 3, -2, -5, -1, 1, -1, -10, 0, -2, -16, -7, 0, 3, 11, 4, 0, -3, 6, -7, 1, 0, -1, 4, -4, -5, -6, 2, -4, -10, 6, 4, -2, -1, 1, 7, -3, 11, -4, -5, -5, -3, 6, 10, -8, -7, 2, 5, -6, 0, 1, 7, 4, 5, 3, 1, -3, -37, -1, 1, 2, 11, -7, 0, -4, -1, 0, 6, -1, -2, -8, -1, 8, 2, 3, -4, -6, -1, 7, 4, -7, -2, -1, 18, -12, 10, 0, -8, -5, -5, -5, 4, 6, 14, 1, 3, 0, -6, 5, 5, -7, -4, 0, 5, -4, -2, 2, 3, 0, -1, -2, -2, -5, -5, 4, 3, 8, 1, -5, -3, 1, 5, 2, -1, -4, 4, -3, 0, 9, -9, -1, 2, -2, 2, 2, 3, 1, 5, 1, 3, 4, -3, -7, 6, 6, -2, 4, -5, 3, -2, 1, 2, 7, -33, -1, 3, -3, 0, 2, 2, -7, -5, 6, 0, 9, 6, 4, 4, 6, 8, -5, 4, 1, 1, 7, 21, -2, 1, 9, -1, 5, 5, 2, -1, -1, 8, -5, -6, 6, -1, 3, 2, 2, 1, 5, -1, -8, 4, 2, -7, -6, -4, 2, -3, -3, 1, -1, 5, 6, -11, 4, -7, -2, 6, 2, 5, 6, 1], "imageUrl": "https://upload.wikimedia.org/wikipedia/commons/6/63/Marchingcubes-head.png", "imageLicense": "CC BY-SA 2.5", "explanation": ["Imagine you're waiting for a friend who lives 10 miles away. If you walk, you get there in 1 hour. But if you teleport, you instantly arrive. Now, imagine a computer doing calculations. If it uses one method, it might take a long time. If it uses another method, it can finish much faster.", "Computers can do things in different ways. Sometimes, they use a method that lets them work on lots of small tasks at once, like a group of friends working together on a puzzle. This is called parallel computing. The other method makes them work on one big task at a time, like doing a puzzle alone. This is called serial computing."], "example": "If you have 10 friends helping you solve a puzzle, it takes 10 minutes. If you do it alone, it takes 100 minutes. In computers, using lots of small tasks (parallel computing) can finish a job much faster than doing one big task (serial computing).", "whyItMatters": "Parallel computing lets computers finish tasks faster by dividing them into smaller parts and working on them at the same time."}, {"id": "cfbd0145deb6", "title": "Thread block (CUDA programming)", "slug": "thread-block-cuda-programming", "headline": "Thread blocks can contain up to 1024 threads as of March 2010", "summary": "What a thread block is in CUDA \u2014 a group of threads that share shared memory", "source": "What a thread block is in CUDA \u2014 a group of threads that share shared memory", "sourceUrl": "https://en.wikipedia.org/wiki/Thread_block_(CUDA_programming)", "articleUrl": "https://en.wikipedia.org/wiki/Thread_block_(CUDA_programming)", "publishedAt": "2026-06-12", "category": "learn", "cohortScore": 0.5, "embedding": [-4, -6, -2, 1, 2, 2, 1, -2, 12, -1, -3, -4, 2, 7, 6, 5, -9, -4, 3, -7, 11, -2, -2, -5, 1, 4, -4, -10, -2, -29, -3, -4, 1, 0, 1, 1, 3, 6, 3, 6, -4, 14, -10, -3, -1, 4, -8, -2, 4, 3, -5, 2, -2, 3, -7, 4, 4, 2, 1, -3, 3, -1, -9, 7, 9, -1, 5, 2, 6, 2, -1, 2, 2, 1, -1, 1, -2, 3, 0, -5, -13, -2, 1, -3, -1, -1, 4, 10, -1, -1, -7, 2, 9, 0, -6, 0, 1, 5, -2, 48, -5, -3, -3, 7, -4, 0, 3, 2, -4, 3, 3, -7, 9, -5, 11, -9, 2, -5, 5, 11, -8, -2, 1, -2, -2, 0, 3, 10, 10, 0, -4, 11, -6, 6, 3, 2, 8, -2, 2, -10, -2, -3, 5, -8, -1, 12, 0, 3, 0, -3, -3, 7, -8, -6, 2, -2, 2, 3, -2, 3, -6, -1, -7, 8, 3, -11, -4, 4, 1, -6, -1, 4, -1, -3, 0, -4, -12, -2, 1, 0, 6, -1, -7, 2, 3, -4, 0, 2, -1, 0, -5, -3, -10, 12, -7, 1, 8, 0, -1, -4, -1, 4, -10, 11, -7, -2, -8, 2, 3, 3, -1, -3, 4, 1, -5, -4, 0, 7, 2, -6, 8, -7, 1, -35, -5, 9, 1, 7, -1, 5, -1, -1, 1, 9, -4, -10, -13, -2, 2, 5, 2, -5, 3, 2, -1, 4, 5, 6, 3, 11, -1, -2, -2, 1, 4, -1, -7, 6, 0, 1, 6, 6, -2, -7, 8, 0, -10, 7, -3, 7, 0, 5, 1, 2, -6, 2, 7, 0, 1, -9, 0, -1, 6, -5, -4, -4, 4, 1, 0, -9, -4, 0, -8, -3, 12, -7, -13, 2, -4, -3, 3, 0, -2, 7, 0, -1, 4, 2, 5, 7, 6, 4, -2, 1, 3, -8, 0, -1, 3, -35, 2, 6, 1, 1, 6, 10, -5, -11, 3, -3, 8, 4, 1, 3, 6, 2, -9, 8, 4, -4, 1, 17, -3, 5, 3, -3, 1, 0, 9, -3, -6, 9, -7, 1, 5, 0, 0, 6, 5, -3, -1, -11, -3, 6, 5, -7, -16, -4, 1, -4, -1, 3, -3, -1, 4, -9, -2, -6, -2, 2, 4, 4, 1, 0], "explanation": ["Thread blocks are a fundamental concept in CUDA programming that allows for efficient parallel processing. The increase in the maximum number of threads per block to 1024 with compute capability 2.x and higher enables more complex computations and better utilization of the GPU's resources. This change reflects the evolution of CUDA architecture to support more demanding applications."], "example": "In a CUDA program, a developer can define a thread block with 1024 threads to perform a large-scale matrix multiplication, taking advantage of the increased thread capacity for improved performance.", "whyItMatters": "Understanding the maximum number of threads per block is crucial for optimizing CUDA applications and fully utilizing the GPU's capabilities.", "imageUrl": "https://upload.wikimedia.org/wikipedia/commons/thumb/2/22/SocialNetworkAnalysis.png/1280px-SocialNetworkAnalysis.png", "imageLicense": "CC BY-SA 4.0", "imageArtist": "Martin Grandjean"}, {"id": "678bebdd6a77", "title": "Dynamic random-access memory", "slug": "dynamic-random-access-memory", "headline": "DRAM requires periodic refreshing to maintain data integrity", "summary": "What shared memory (SRAM) is on a GPU \u2014 fast local memory shared within a thread block", "source": "What shared memory (SRAM) is on a GPU \u2014 fast local memory shared within a thread block", "sourceUrl": "https://en.wikipedia.org/wiki/Dynamic_random-access_memory", "articleUrl": "https://en.wikipedia.org/wiki/Dynamic_random-access_memory", "publishedAt": "2026-06-12", "category": "learn", "cohortScore": 0.5, "embedding": [-5, 2, -1, 1, 7, 2, 1, 5, 3, -7, -3, -6, 3, 4, 1, 1, -5, -3, 9, -5, 4, -11, -3, -6, 3, 3, -7, -5, -3, -27, -2, 2, -4, 4, -2, -5, -1, 9, -9, 2, -3, 14, -6, -1, 1, 5, -2, -2, 3, -1, 5, 5, -1, 0, -7, 6, 11, 7, 2, -7, 2, 7, -8, 6, 9, 1, 7, -4, 3, -1, -5, 4, 3, 8, 7, -5, 2, 0, 2, 3, -6, -4, -6, -5, -1, -1, 0, 9, 3, -1, -4, -1, 6, 2, -8, 9, 7, 9, -3, 50, -1, 8, -3, 6, 0, -4, 0, 5, -11, 1, 7, -8, 4, 3, 18, -5, -7, -6, 4, 7, -11, 8, -2, -5, 1, -5, -2, 8, 7, 1, -5, 11, 0, 7, 4, 0, 1, -6, 5, -7, -5, 6, 9, -8, -1, 14, -1, 2, -8, 0, 0, 0, -6, -7, -3, 0, 0, 2, 1, 0, -6, 1, -4, 15, -2, -4, -2, 2, -2, -5, 1, 2, -3, -5, -1, -2, -7, -6, 0, 4, 4, 1, -8, -1, 1, -6, -2, 3, 1, -3, -6, -4, -7, 8, 0, -1, 0, -2, -4, -2, 1, 4, -4, 10, -6, -3, -7, -1, 1, 2, 0, -2, -6, 5, -7, -7, -1, 2, -1, 0, 15, -5, -3, -35, -4, 0, -5, 6, -1, 8, 0, 7, -5, 5, -1, -6, -9, 3, 1, 5, 0, -3, -4, -4, 3, -1, -4, 13, 1, 20, -6, 0, -4, -3, 1, -1, -9, 2, 2, 7, 8, 3, 3, -5, 6, -2, -5, -1, -4, 6, -4, 3, 5, 2, -8, 2, 9, 5, -5, -5, -2, -2, 5, -3, -2, -2, 1, 3, -2, -3, -7, 3, -3, 0, 7, -3, -5, 7, -5, 4, -2, -2, -2, 4, 2, 6, 10, 4, -1, 2, 9, -3, -1, -2, 2, -3, -10, 0, -1, -33, -5, -2, 2, 1, 0, 6, -2, -10, 6, -11, 10, 6, 4, -3, 11, 10, -2, 3, -1, -10, 2, 15, -2, 5, 0, 4, 5, 3, 6, -5, -2, 4, -3, 2, 3, -3, 2, 9, 6, -2, 3, -4, 0, 6, -5, -4, -11, -1, -1, -3, -4, 4, -5, -4, 3, -8, -5, -7, 7, 3, 4, -1, -3, -1], "explanation": ["DRAM stores data in capacitors that leak charge over time, necessitating a refresh circuit to restore the original charge periodically. This refresh process is essential to prevent data loss and maintain data integrity."], "example": "In a DRAM memory cell, the capacitor's charge representing a bit's value (0 or 1) gradually dissipates, requiring a refresh circuit to periodically rewrite the data and restore the capacitor's charge.", "whyItMatters": "Understanding the refresh requirement of DRAM is crucial for designing reliable memory systems that prevent data loss due to charge leakage.", "imageUrl": "https://upload.wikimedia.org/wikipedia/commons/thumb/9/9b/MT4C1024-HD.jpg/1280px-MT4C1024-HD.jpg"}, {"id": "4c9278bdd30a", "title": "2024\u2013present global memory supply shortage", "slug": "2024-present-global-memory-supply-shortage", "headline": "Global DRAM shortage began in 2024", "summary": "What global memory (HBM) is on a GPU \u2014 large but slow DRAM accessible by all threads", "source": "What global memory (HBM) is on a GPU \u2014 large but slow DRAM accessible by all threads", "sourceUrl": "https://en.wikipedia.org/wiki/2024%E2%80%93present_global_memory_supply_shortage", "articleUrl": "https://en.wikipedia.org/wiki/2024%E2%80%93present_global_memory_supply_shortage", "publishedAt": "2026-06-12", "category": "learn", "cohortScore": 0.5, "embedding": [-8, 4, 1, -1, 4, 3, -7, 3, 3, -4, 0, -1, 5, 2, 0, 2, -3, -11, 7, -5, 7, -9, 1, -4, -4, 4, -3, -4, -4, -26, -2, 5, 0, 0, -1, -10, 0, 8, -6, 6, -5, 12, -3, -6, 3, 0, -5, -2, 2, 1, 1, 9, 2, -7, -3, 4, 4, 1, 5, -2, 7, 1, -13, 5, 7, 5, 3, -4, -1, 2, -1, 1, 2, 4, 2, -3, 3, -2, 2, -4, 0, 3, -10, -8, -4, -3, -5, 7, -4, -4, -1, 3, 3, 4, -3, 5, 3, 4, -1, 50, 1, 5, -1, -3, 3, 2, -3, 4, -9, -4, 6, -10, 14, 2, 14, -12, -9, -6, 4, 7, -10, 5, 2, -6, 1, 0, -7, 15, 1, -4, -5, 4, -7, 3, 8, 3, 6, -5, 7, -6, -8, 5, 5, -6, -5, 11, 1, -1, -5, 2, 2, 2, 0, -2, 0, 1, 3, 4, -2, 4, -4, -3, 0, 15, -6, -6, -3, 4, -1, -3, 2, 7, 2, -3, 9, -9, -1, 0, -6, -1, 4, 2, -9, -4, 1, -11, 4, 4, 2, -4, -9, 2, -5, 10, 5, 1, -7, 1, 7, -11, 5, 4, -3, 5, 0, -1, -3, -5, -2, 5, 0, -2, 3, 6, -4, -1, 1, 1, -6, -3, 15, -7, -7, -37, -1, -4, -5, 3, 1, 7, -1, 10, 4, 2, -1, -3, -2, -3, -2, 5, -1, -2, -4, 1, 4, -2, 4, 7, 2, 21, -4, -5, -7, 1, 3, 2, -6, 9, 3, 6, 1, 5, 1, -8, 6, -2, -9, -2, -1, -1, -3, -2, 5, 3, -9, 2, 7, 1, -3, -7, -5, -2, 6, -2, -1, -9, 5, -6, -5, 0, -8, 5, -3, -4, 9, -1, -1, 9, -7, 2, -5, -4, -5, 8, -1, 4, 9, 7, 5, 3, 4, -8, 3, -4, -1, -4, -10, 3, -1, -28, 7, 0, 5, -1, -4, 6, 1, -4, 4, -10, 4, 4, 3, -5, 1, 8, -4, -1, 1, -9, 2, 18, -1, 1, -3, 3, 7, 1, 4, -1, -3, 4, -3, 2, 11, 1, 7, 10, 8, 0, -1, -1, 1, 7, 0, -6, -8, -2, 0, -1, -4, 8, -1, -8, 6, -3, -9, -7, -1, 8, 3, -3, -3, 0], "explanation": ["The global shortage of DRAM began in 2024 due to supply constraints and rapid price escalation in the semiconductor memory market. This shortage is attributed to a structural reallocation of manufacturing capacity toward high-margin products for AI data center infrastructure, leading to scarcity in consumer and enterprise PC markets. The shortage is expected to persist until at least 2030."], "example": "The shortage of DRAM has led to increased prices and limited availability for consumers and businesses relying on computer memory.", "whyItMatters": "Understanding the DRAM shortage is crucial for anticipating future market trends and preparing for potential impacts on technology and industries reliant on computer memory.", "imageUrl": "https://upload.wikimedia.org/wikipedia/commons/thumb/5/56/Average_price_of_DDR5-5200_2x16_GB_RAM_kits.png/1280px-Average_price_of_DDR5-5200_2x16_GB_RAM_kits.png"}, {"id": "6948d9cd7e77", "title": "Flashbulb memory", "slug": "flashbulb-memory", "headline": "Flashbulb memories are vivid but not always accurate", "summary": "Why memory coalescing matters \u2014 adjacent threads reading adjacent memory addresses", "source": "Why memory coalescing matters \u2014 adjacent threads reading adjacent memory addresses", "sourceUrl": "https://en.wikipedia.org/wiki/Flashbulb_memory", "articleUrl": "https://en.wikipedia.org/wiki/Flashbulb_memory", "publishedAt": "2026-06-12", "category": "learn", "cohortScore": 0.5, "embedding": [-8, 1, 3, 1, -1, 4, -3, -5, 8, -7, 2, 0, 9, 8, -1, 4, -5, 0, -1, -3, 3, -13, 4, 2, -10, 7, -7, -3, -7, -33, 5, 1, 6, -4, 0, -5, -1, 3, -6, -2, -2, 9, -8, -4, -6, -7, 4, 0, 0, -1, -4, 2, 7, 3, -1, 12, 7, 12, 8, 0, 9, 7, -9, 6, 9, -3, -1, -6, -3, 3, -7, 3, 0, 9, 3, -1, -5, 1, -5, -5, -3, -6, -3, -5, -3, 4, -3, -5, 2, -3, -2, -3, 1, 1, 1, 5, 8, 3, 5, 47, -4, 5, 10, -1, 0, -5, 2, -1, -12, 1, 7, -10, 2, 5, 11, 1, 2, -1, 3, 1, -9, 7, -6, -2, -6, -11, -3, 13, 3, -8, 2, 3, 0, 2, 0, 3, 8, -5, 3, -4, 1, 4, 10, 1, -7, 14, -1, 4, -1, 0, -2, 1, -3, -6, 0, 5, -1, 6, 5, 4, -4, -4, -8, 4, 2, -5, 1, -2, -5, -9, -1, -2, 7, -8, 1, -3, -6, -3, -3, 6, 3, 1, 0, 1, 4, -7, 0, 2, 0, 4, -7, -7, -1, 3, -3, -4, 1, 2, -2, -4, 5, 2, -10, 1, -1, -2, -5, -3, 5, 0, -2, -7, 6, 2, -10, -8, -3, 12, 2, -2, -3, -5, -10, -38, -5, -1, -3, 7, -7, 3, 4, 8, -5, -4, -8, -1, -6, 3, 4, -2, 7, -8, 8, -4, 0, 1, -3, 7, -1, 21, -2, 1, -1, -2, 2, -1, -3, 1, 8, 4, -1, 6, 1, -9, 5, 2, -11, -6, -7, -2, -8, 4, 3, 2, -10, 2, 2, 4, -6, -2, 0, -5, 4, 3, -6, -5, 0, 12, -2, 1, -6, 2, 3, 2, 6, -6, 3, 2, 1, 2, -3, -1, -2, 5, -4, 6, 2, 2, 0, 10, 1, 3, 1, 1, 1, -6, -8, 0, 4, -33, 6, -2, 3, 3, 3, 11, -2, 2, 5, -7, 5, 2, 2, -4, 8, 10, 2, 3, -6, -4, 1, 22, 1, -3, 2, 3, 2, 0, 2, -2, -1, 6, -2, -2, 8, 0, -1, 11, 3, 3, 1, -2, -1, 7, 4, -1, -4, -4, -2, 0, -2, 6, -3, 3, 5, -8, -3, -1, 2, 7, -3, 9, -2, -1], "explanation": ["Flashbulb memories are vivid and long-lasting memories of surprising events. However, they are not entirely accurate as the details of these memories can fade over time. Despite high confidence in these memories, they can be incomplete and sometimes incorrect."], "example": "A person vividly remembers hearing about the 9/11 attacks but later realizes they were not in the city at the time.", "whyItMatters": "Understanding the limitations of flashbulb memories is crucial for accurate memory recall and personal reflection.", "imageUrl": "https://upload.wikimedia.org/wikipedia/commons/thumb/a/a1/C-130J_135th_AS_Maryland_ANG_in_flight.jpg/1280px-C-130J_135th_AS_Maryland_ANG_in_flight.jpg", "imageLicense": "Public domain", "imageArtist": "USAF"}, {"id": "8c76088b9884", "title": "warp divergence kills performance", "slug": "warp-divergence-kills-performance", "headline": "Warp divergence causes threads to execute non-uniformly, leading to idle cycles and reduced throughput", "summary": "Why warp divergence kills performance \u2014 threads in a warp take different branches", "source": "Why warp divergence kills performance \u2014 threads in a warp take different branches", "sourceUrl": "", "articleUrl": "", "publishedAt": "2026-06-12", "category": "learn", "cohortScore": 0.5, "embedding": [-8, -4, 5, 0, 1, -2, -4, 5, 9, -7, 6, -1, 4, 5, -3, -2, -3, -1, -8, -1, 6, -4, -1, -4, -3, 4, -4, -2, -2, -31, -4, -2, -1, 2, 0, 1, 0, 0, -8, 4, 4, 8, -7, -2, 3, -1, -4, -5, 1, 6, -8, -4, 1, -1, 3, 1, 11, 13, 1, -6, 1, 4, -10, 5, 8, -3, 0, -12, -2, 6, -5, 6, 0, 9, 1, 1, -2, -4, 7, -5, 1, -5, -5, -4, -2, 2, -2, -2, 8, 0, -5, 5, 9, 1, 1, 5, 5, 0, 4, 45, 1, 5, 0, 4, 9, -1, 0, 3, -2, 2, 5, -7, 3, 6, 6, -2, -1, 0, -2, 3, -6, 2, 2, 1, 4, 0, 0, 15, -1, -9, 6, -5, 0, 6, 6, -1, 4, -1, 4, -4, -5, 4, 10, -3, -3, 12, 0, 0, -4, 1, -3, 0, -9, -14, -3, 7, 1, 11, -6, -1, -6, 2, -7, 9, -3, -3, -1, 8, -2, -2, -1, -4, 4, -6, 3, 0, -10, -2, 5, -2, 3, 0, -2, 2, 4, -9, -6, 5, -4, 2, -5, -13, -8, 5, -3, -3, 3, 1, -13, -5, -1, 6, -3, 10, -3, 2, -12, -4, 5, 4, -10, -11, 0, 4, -3, -2, 5, 12, 5, 1, 3, 2, -5, -36, -8, -1, -4, 8, -2, 1, -1, 5, -9, 3, 3, -5, -6, 4, 8, -5, 3, -8, 0, 1, 8, 3, -8, -1, 0, 16, -11, 10, -4, 0, 1, 2, -4, 1, 6, 5, -4, -4, 1, -10, 0, 2, -8, -1, 0, -5, -2, 2, 1, 3, 0, 6, 7, 0, 0, 2, 2, -4, 4, 2, 1, -3, -1, 10, 0, -2, -9, 1, -7, 2, 11, -7, -6, -2, -4, -5, 1, -3, -3, 8, -3, 9, 4, -4, 2, 7, 2, 6, -4, -2, 7, -8, 2, 7, 6, -32, -2, 1, -4, 2, -1, 7, -7, -4, 8, -1, 4, -10, 5, 6, 8, 15, -5, 3, -5, -7, 1, 20, 5, 2, 3, 0, 7, -1, 2, -9, -3, 2, -2, 1, 0, 13, 0, 5, 0, 5, 3, 6, -4, 11, 3, -6, -7, -3, 1, -1, -1, 4, -1, -5, 4, -11, -2, -1, -1, 8, -7, -1, -1, -3], "imageUrl": "https://upload.wikimedia.org/wikipedia/commons/f/f0/Graphite-and-diamond-with-scale.jpg", "imageLicense": "CC BY-SA 3.0", "imageArtist": "Robert M. Lavinsky"}, {"id": "df0151c74a4e", "title": "occupancy means in GPU programming", "slug": "occupancy-means-in-gpu-programming", "headline": "Occupancy = Active Warps / Max Warps", "summary": "What occupancy means in GPU programming \u2014 ratio of active warps to maximum warps", "source": "What occupancy means in GPU programming \u2014 ratio of active warps to maximum warps", "sourceUrl": "", "articleUrl": "", "publishedAt": "2026-06-12", "category": "learn", "cohortScore": 0.5, "embedding": [-2, -7, 2, 0, 0, 0, -3, 7, 9, -2, 2, -7, 0, 1, -3, 2, 2, 1, 1, -2, 9, -5, -7, -10, 0, 10, -6, -8, -1, -23, -11, 5, 8, 1, 0, -1, 0, 7, -5, 10, -4, 6, -3, -1, 5, -2, -3, -2, -1, 6, 2, 0, -2, 3, -1, 0, 8, 3, -5, -2, 6, 1, -11, 2, 7, -7, 4, -14, -1, 12, -1, 5, -2, 2, 8, 1, 5, 1, 4, -9, 5, -2, -8, 0, 0, 0, -4, -4, 2, 1, -3, -2, 4, -3, -6, -1, 12, 7, 4, 45, 6, -2, -3, 7, 3, -5, 4, 7, -6, 4, -8, -5, 4, 3, 14, 3, 0, -3, 0, 4, -8, 2, 0, -3, 5, -5, 3, 10, 4, 1, 0, 0, 0, 2, 4, 4, 9, 7, 3, 6, 0, 6, 13, -7, 0, 12, -7, 1, 0, -2, 4, 6, -3, -9, -3, 5, 2, 7, -6, -1, -4, -1, -7, 17, -6, -8, -4, 10, -2, 0, 1, -3, -1, 0, 5, 1, -15, 3, 1, -3, 4, -3, -10, 0, 1, -12, -8, -6, 3, -6, -10, -8, -10, 2, -4, 0, 2, 0, -5, -7, 4, 4, -5, 2, -1, -7, -6, -2, 0, 5, -4, -10, -4, 8, -4, 1, 2, 4, -2, -1, 6, -3, -4, -40, 0, 3, 2, 6, -4, 9, -4, 2, -7, 6, -1, 2, -1, -1, 5, -8, 3, -8, -4, 3, 6, -7, -4, 6, -2, 23, -7, 4, -4, 0, -3, -3, -6, 12, 4, 6, -3, -1, 0, -5, 5, -4, -4, 3, -2, 1, 8, 2, 2, -4, -4, 3, 5, -3, -6, -2, -2, 1, 5, 3, -3, -5, -2, 6, -3, -1, -7, 5, 0, 6, 4, -5, -9, 2, -2, -2, 3, -1, -4, 3, -6, 2, 3, 3, 0, 3, -3, -1, -1, -1, 9, -5, -3, 3, 6, -35, 1, 1, 1, -4, -3, 3, 5, -8, 2, -5, 5, -4, 7, 1, 7, 18, -11, -1, -8, -2, 4, 17, -5, 2, 0, 2, 8, 2, -6, -8, -2, 11, -5, -1, 10, 5, 4, 6, 0, 2, -5, 0, -1, 7, -1, 1, 2, -3, -2, -5, 0, 3, -4, -3, 3, -4, 4, -2, -1, 2, -2, 8, -3, 1], "imageUrl": "https://upload.wikimedia.org/wikipedia/commons/thumb/0/01/1237_E._Arques_Avenue.jpg/1280px-1237_E._Arques_Avenue.jpg", "imageLicense": "CC BY 4.0", "imageArtist": "Coolcaesar"}, {"id": "106399a018f6", "title": "Overdrawn at the Memory Bank", "slug": "overdrawn-at-the-memory-bank", "headline": "Overdrawn at the Memory Bank was shot on videotape due to budget constraints", "summary": "What bank conflicts are in shared memory \u2014 multiple threads accessing the same bank", "source": "What bank conflicts are in shared memory \u2014 multiple threads accessing the same bank", "sourceUrl": "https://en.wikipedia.org/wiki/Overdrawn_at_the_Memory_Bank", "articleUrl": "https://en.wikipedia.org/wiki/Overdrawn_at_the_Memory_Bank", "publishedAt": "2026-06-12", "category": "learn", "cohortScore": 0.5, "embedding": [-7, -4, -5, -4, 3, 1, 4, -4, 9, -6, 0, -5, 5, 7, 11, 0, -4, -7, 0, 3, 2, -9, 3, -6, -5, 5, 0, -4, -5, -29, 0, 2, -1, 2, 5, -1, -2, 6, -7, 0, -5, 14, -9, -8, -3, -3, 1, -1, 1, 3, -3, -4, 0, 3, -7, 6, 3, 12, 2, -3, 8, 2, -8, 4, 10, 4, 6, -2, 2, 1, -4, -1, 6, 6, 4, 0, 3, 0, 0, -2, -3, -1, 0, -4, -3, -2, 1, 4, -1, -7, -6, 3, 11, -2, -5, 3, 6, 5, -2, 56, 2, 2, 9, 4, 0, -1, -1, -2, -3, -1, 1, -7, 9, 1, 10, 5, -5, -5, 1, 4, -4, 5, -2, -1, -6, -12, -3, 11, 4, -6, -1, 3, -3, 1, 1, 2, -1, -8, 12, -9, -2, 1, 7, -1, -5, 12, 6, 2, -2, -4, -4, -1, -4, -7, -2, 5, -3, 3, 3, 4, -6, -2, -3, 6, 2, -7, 3, 1, -1, 2, -3, -1, -1, -1, -3, -4, -8, -2, -7, 2, 0, -5, -5, -1, 5, -4, 2, 3, 4, 3, -6, -7, -6, 3, -1, 0, 1, 3, -7, -1, 3, 9, -8, 11, -3, 2, -11, -6, 4, -1, 2, -3, -2, 7, -5, -8, 4, 10, 4, 2, 4, -1, 2, -41, -4, -3, -4, 5, -1, 8, -1, -6, 2, 2, -5, -8, -11, 3, 5, -3, 8, -8, -1, -4, 3, 5, -1, 7, 5, 20, -7, 1, 4, 2, 3, -3, -5, 0, 6, 5, 5, 4, -2, -10, -1, -2, -11, -1, 2, -5, -4, 3, 0, -3, -8, -2, 2, 8, -3, -2, 6, -2, 6, 3, -2, -2, -4, 10, -1, -4, -4, 1, 2, 2, 8, -6, -7, 3, 4, 10, -6, -5, -3, 7, -4, 1, 2, 3, 4, 6, 3, 7, -8, 1, -1, -6, -1, 4, 4, -33, 1, 0, -1, 1, 6, 4, 0, -4, 5, -2, 2, 3, 1, -2, 3, 4, -1, 4, -5, -6, 0, 15, -8, 0, -3, -1, 8, 10, -1, -5, -2, 1, -7, 0, 5, -1, -1, 7, 6, 3, 0, -3, -5, 11, 8, 1, -5, 1, 0, 2, -6, 4, 1, 1, 3, -7, -4, -5, 5, 5, 1, -1, -5, -1], "explanation": ["The film's budgetary constraints also influenced its critical reception. Overdrawn at the Memory Bank was featured in the eighth season finale episode of the comedy television series Mystery Science Theater 3000 in 1997. The film received mixed reviews from critics, which could be partially attributed to its budgetary limitations affecting production quality."], "whyItMatters": "Understanding the production choices of low-budget films can provide insight into their distribution and reception.", "imageUrl": "https://upload.wikimedia.org/wikipedia/commons/3/3e/Liveaudioequip.jpg", "imageLicense": "Public domain", "imageArtist": "PeterPan23 at English Wikipedia"}, {"id": "fbc397bc7200", "title": "Matrix multiplication algorithm", "slug": "matrix-multiplication-algorithm", "headline": "Ever wondered how computers speed up multiplying huge numbers?", "summary": "How tiling works in matrix multiplication \u2014 loading blocks into shared memory", "source": "How tiling works in matrix multiplication \u2014 loading blocks into shared memory", "sourceUrl": "https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm", "articleUrl": "https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm", "publishedAt": "2026-07-03", "category": "learn", "cohortScore": 0.5, "embedding": [-10, 2, 2, -2, -7, 3, 0, -2, 10, 0, 2, -1, 5, 3, 8, 5, -10, 2, 1, -11, 8, -12, -7, -8, -2, 5, -6, -8, 1, -32, 4, 3, 9, 0, 5, -4, -1, 8, -7, -4, -3, 10, -7, 3, 4, -1, -2, -3, 1, 1, -1, -1, 2, 5, 3, 3, 7, 9, 2, 0, 5, 0, -8, 14, 9, -9, 0, -5, 5, 10, -1, 7, 6, 6, 9, -1, -4, 2, 1, -4, -1, -10, 1, -4, -5, 1, -2, -2, 6, -5, -1, 7, -3, -1, -2, 2, 2, 8, -4, 47, -5, 4, 2, 1, -4, -4, -3, 0, -7, -3, 0, -4, 4, 1, 8, -3, -2, 1, 5, 0, -6, 5, -6, -3, 0, -5, -10, 16, 1, 6, 3, 6, -2, 4, 4, 1, 2, -5, 4, -5, -3, 9, 10, -4, -2, 13, 4, 4, 4, -3, -1, 3, -6, -12, 0, -2, 4, -1, -7, -1, -11, 6, -7, 15, 6, -5, 3, 2, 4, -10, 1, 4, -8, 2, 5, -1, -13, -4, 4, 2, 7, 1, -1, 1, 2, -8, 1, 4, -5, -6, -2, 2, -13, 1, -4, -5, 2, 7, -5, -2, 3, 0, -7, 8, 0, -1, 3, 0, 5, 9, 3, -8, 1, -3, -7, 0, 5, 5, 1, 2, 2, -9, -8, -37, -5, 3, -3, 3, -3, 4, -3, -3, 0, 3, -1, -1, -4, 3, -3, -2, 10, -4, 3, -1, 3, -4, -5, 6, -1, 17, -4, -2, 3, 2, 1, -5, -4, -2, 5, 7, 6, 1, 2, -5, -1, 0, -9, -3, 1, 0, -6, 5, 3, 0, -5, 0, 4, 3, -8, 1, -1, -2, 3, -1, -14, -5, 3, 4, 0, 1, -4, 0, -5, 4, 11, -2, -4, 1, -4, 6, 1, 0, -1, 6, 1, 2, 1, 4, -6, -1, 9, -5, -2, -1, 2, -3, -3, 1, -2, -34, 4, 3, -4, -8, -6, 2, 4, 4, 4, -10, 3, 6, 2, 3, 3, 5, 1, 4, -6, -1, 0, 26, -2, 1, 0, 5, 3, 1, -3, -4, -2, 2, -7, -1, 11, -2, 6, 6, 7, 0, -4, -5, 2, 6, 3, 1, -7, 2, -2, -3, -1, 7, -2, -5, 0, -9, 0, -3, 5, -1, -3, 0, 0, -1], "imageUrl": "https://upload.wikimedia.org/wikipedia/commons/0/0c/Fortunes-algorithm-slowed.gif", "imageLicense": "Public domain", "imageArtist": "Mnbayazit", "explanation": ["Imagine you're organizing a huge party and need to quickly calculate how many gift bags to prepare for all guests.", "Picture each gift bag as a square and guests as numbers. Instead of counting each guest individually, you group them into smaller teams (blocks) and multiply them together first. This way, you handle fewer numbers at a time, speeding up the process."], "example": "If you have 4 teams of 4 guests each, instead of multiplying 4 guests by 4 guests for each team, you multiply 2 guests by 2 guests for each team (2x2 = 4) and then multiply the results (4x4 = 16).", "whyItMatters": "Grouping numbers into blocks reduces the total number of calculations needed."}, {"id": "2db30563d2b0", "title": "Attention (machine learning)", "slug": "attention-machine-learning", "headline": "Why do we sometimes zoom in faster on a scene?", "summary": "Why flash attention is faster \u2014 it tiles attention to avoid materializing the N\u00d7N matrix", "source": "Why flash attention is faster \u2014 it tiles attention to avoid materializing the N\u00d7N matrix", "sourceUrl": "https://en.wikipedia.org/wiki/Attention_(machine_learning)", "articleUrl": "https://en.wikipedia.org/wiki/Attention_(machine_learning)", "publishedAt": "2026-07-03", "category": "learn", "cohortScore": 0.5, "embedding": [-5, 3, 3, 6, 6, 2, 8, -1, 9, -1, -1, 1, 4, 15, 2, 3, -3, -5, -9, -3, 4, -8, 3, -4, -2, -2, -4, -8, -3, -26, 2, 4, 10, 1, -11, -5, -2, 1, -4, -4, 2, 10, -9, 1, -6, -3, 1, -5, -2, -5, -5, -10, 2, 7, 2, 6, 0, 4, 5, -4, 10, 0, -10, 7, 9, -6, 0, -6, -5, 5, -7, 6, -3, 3, 6, -3, -4, -3, 6, -8, 7, -4, -3, -2, 2, 1, -5, -6, 6, -4, -4, -1, -6, -1, -1, 1, 4, 6, 1, 43, -2, 3, 11, 0, 5, -11, 4, 2, -9, 11, 3, -6, -4, 5, 7, 1, 3, 4, 3, -5, -2, 6, -4, -4, -2, -5, -5, 13, 0, -4, 8, -6, -2, 3, 2, 2, 12, -3, 0, -4, 4, 8, 5, -3, 3, 15, -2, 0, 1, -4, -2, 3, -1, -5, -1, -2, -1, 3, 0, 0, -8, 5, -4, 7, 3, -3, 1, -4, -8, -8, -5, -3, 0, 1, 5, 2, -11, -2, -2, 3, 9, -6, 0, 5, 0, -6, 0, 5, 3, 2, -1, 0, 3, 6, -10, -1, 1, 2, -10, -4, 2, -1, -3, 4, 8, 6, 0, -3, 2, 8, -14, -2, 0, 1, -8, -5, -5, 8, -2, 2, -3, 2, -11, -39, -2, -3, -2, 6, -7, 3, 3, 8, 2, -1, -7, -1, -9, 6, -5, -7, 2, -1, -3, 6, 12, 1, -4, 4, -1, 17, 0, -2, 1, 2, 3, -3, -5, -7, 2, 6, 0, -7, 3, -3, -4, 6, -8, -5, -4, -1, 2, 2, 2, 8, -10, 0, 1, -2, -5, 0, -4, -7, 5, 2, -8, -2, -6, 6, -1, -2, -3, -2, 2, -4, 17, -4, 1, 8, 0, 6, 3, -1, 1, 10, 9, 2, -2, 8, -9, 6, -6, -7, 3, -3, 5, -9, -10, -3, -5, -34, 10, 9, -6, -2, 0, 3, -2, 8, 3, -10, 9, 6, 5, -1, 7, 12, 4, 3, -5, -2, -2, 22, 0, -2, -3, 2, -7, 3, -6, 7, 6, 1, -4, 0, 4, 2, 4, -2, 4, 4, 0, 3, -3, 8, -4, 4, 3, -4, 1, -1, -5, 6, 0, 3, -3, -1, 0, 4, 6, 7, -4, 3, -2, 3], "imageUrl": "https://upload.wikimedia.org/wikipedia/commons/thumb/6/62/Attention_mechanism_overview.svg/1280px-Attention_mechanism_overview.svg.png", "explanation": ["Imagine you're watching a movie and suddenly a character you love appears on screen. You want to focus on them quickly to enjoy the moment.", "Think of your eyes as a camera that can zoom in on different parts of the scene. Instead of moving slowly to focus on the character, your eyes can quickly scan the entire scene and instantly zoom in on the character, like a camera with a fast zoom feature."], "example": "In the movie, your eyes quickly scan the entire scene (a 1920x1080 image) and zoom in on the character (a 32x32 pixel region) in less than a second.", "whyItMatters": "This is why flash attention is faster\u2014it quickly scans the entire scene and zooms in on important parts, avoiding the need to build a large matrix to focus on every detail."}, {"id": "971ea4810927", "title": "fused kernels do", "slug": "fused-kernels-do", "headline": "Why wait for a computer to finish one task before starting another?", "summary": "What fused kernels do \u2014 combine multiple operations into one kernel to avoid memory round-trips", "source": "What fused kernels do \u2014 combine multiple operations into one kernel to avoid memory round-trips", "sourceUrl": "https://en.wikipedia.org/wiki/AMDgpu_(Linux_kernel_module)", "articleUrl": "https://en.wikipedia.org/wiki/AMDgpu_(Linux_kernel_module)", "publishedAt": "2026-07-03", "category": "learn", "cohortScore": 0.5, "embedding": [-7, -3, 6, -3, -3, -1, 0, 0, 9, -3, 4, -3, 4, -5, 6, -3, -10, -2, 0, -12, 1, -10, -5, -1, -5, 5, 0, -5, -5, -27, 3, 3, -3, -4, -3, -1, 5, 7, -4, 5, 0, 3, -13, -2, -1, -7, -2, -7, 4, 5, 0, -2, 3, -3, 2, 5, 5, 13, 2, 4, 1, 3, -7, 1, 4, -1, 3, -9, 3, 13, -3, 10, 2, 7, -5, -1, -4, 2, -3, 7, 0, -3, -1, -2, -10, 5, -10, 1, 6, -3, 0, 1, 4, 0, 2, 4, 6, 3, 2, 43, 5, -2, 5, -1, -4, -8, 2, 1, -5, -6, 6, -8, 5, 0, 14, 3, -2, -2, 5, 1, -3, 4, 1, 2, -1, -7, -2, 11, -2, 1, 3, -4, -3, -4, -1, 5, -3, -4, 6, -8, 1, 9, 11, -3, 4, 15, 4, 0, -2, 7, -4, 3, -3, -10, -3, 1, 6, -4, -3, 2, -12, -3, -7, 15, 3, -6, 4, 5, -6, -3, -2, -7, 6, -11, -2, -3, -16, 1, -4, 2, 11, 1, -3, -4, 2, -8, -3, 1, -8, 0, -8, 4, 3, -2, -1, -12, 0, 5, 0, -2, -3, 1, -4, 1, -2, -2, -3, 0, 7, 5, 0, -4, -1, 1, -5, 2, -4, 8, 1, 2, 3, -2, 0, -38, -9, -4, -5, 4, -1, 7, 2, -8, 0, 7, -5, -3, -2, 0, 6, -2, 3, -3, 0, 2, 6, 7, -8, -1, 3, 15, -6, 6, -1, 2, 5, -2, -5, 3, 3, 11, -3, 1, 5, -5, 1, 0, -13, -1, -1, -2, 5, 8, 3, -4, -4, 5, -5, 6, -5, -5, 4, -3, 2, 1, -7, -7, 4, 11, 1, 2, -2, 2, -7, -2, 12, -2, -3, 7, 3, -1, 4, 1, -2, 11, -6, 3, 5, 1, -7, 5, 6, -1, -4, -5, 4, 1, 0, 11, -1, -35, 5, 2, -2, 5, 4, -3, -6, 0, 1, -7, 10, 0, 1, -2, 11, 18, -3, -3, -1, -4, 6, 16, -8, 2, 7, -3, 3, 3, 6, 0, -4, 1, -7, -1, 6, -2, 9, 10, 5, 0, -1, 1, -9, 6, 0, -2, -6, -6, -6, 1, -1, 6, -1, 1, 2, -5, 2, -7, 2, 9, -3, 11, 2, -4], "imageUrl": "https://upload.wikimedia.org/wikipedia/commons/9/9c/Continuous_Integration.jpg", "imageLicense": "CC BY-SA 4.0", "imageArtist": "Pratik89Roy", "explanation": ["Imagine you're cooking dinner. You need to chop vegetables, boil pasta, and toast bread. Doing each task separately takes a lot of time and effort.", "Think of a kitchen gadget that could chop, boil, and toast all at once. This idea is called combining multiple tasks into one step."], "example": "Instead of chopping vegetables (5 minutes), boiling pasta (10 minutes), and toasting bread (3 minutes) separately, a multi-functional gadget could do all three tasks simultaneously in 15 minutes.", "whyItMatters": "Combining tasks into one step saves time and effort."}, {"id": "bff3ed279ab5", "title": "kernel fusion reduces memory bandwidth bottleneck", "slug": "kernel-fusion-reduces-memory-bandwidth-bottleneck", "headline": "Can you imagine faster video games without waiting for loading screens?", "summary": "Why kernel fusion reduces memory bandwidth bottleneck", "source": "Why kernel fusion reduces memory bandwidth bottleneck", "sourceUrl": "https://en.wikipedia.org/wiki/AMDgpu_(Linux_kernel_module)", "articleUrl": "https://en.wikipedia.org/wiki/AMDgpu_(Linux_kernel_module)", "publishedAt": "2026-07-03", "category": "learn", "cohortScore": 0.5, "embedding": [-8, 1, 8, -4, 2, 5, -5, 4, 10, -1, 7, -2, 5, -2, 8, 0, 4, 0, -2, -10, -1, -10, -1, -5, -9, 0, -5, -5, -10, -25, 5, -1, 0, 2, -6, -8, 5, 7, -7, 2, 0, 11, -10, -1, 1, -2, 2, -6, 0, 5, -6, 0, 0, -4, 0, 6, 3, 11, 8, 0, 1, 1, -9, 2, 11, -2, 0, -8, 2, 6, -9, 14, 6, 7, 1, 2, -1, -1, 3, 1, 5, -4, -7, -8, -5, 4, -6, 1, 3, -1, -4, 4, 3, 1, 0, 9, 3, 3, -2, 39, 9, -3, 4, -2, 5, -7, 2, 0, -7, 0, 3, -8, 8, 5, 12, 1, -6, 1, 1, 0, -8, 5, -3, -7, 4, -6, -5, 13, -2, 2, 0, -6, -4, 1, -1, 3, 3, 0, 5, 0, -3, 7, 9, -4, -2, 15, 8, 3, -5, 5, -1, 4, -4, -6, -8, -7, -1, 2, -6, 3, -6, -3, 1, 11, -5, -4, 5, 4, -1, -2, -7, -5, -1, -5, 3, -7, -15, 3, -4, 0, 10, 4, -5, -2, 7, -15, 2, 1, -2, -2, -11, -6, -2, 0, 4, -5, -1, 9, -4, 0, 0, 2, -8, 4, -1, 7, -2, -6, 5, 3, 0, -9, 5, 8, -9, 3, -3, 7, 3, 7, 8, -1, -6, -35, -2, -5, 2, 4, -2, 5, 0, 2, 1, 4, 0, -6, 0, -1, 1, -3, 5, -7, -2, -3, 3, 4, -6, 4, -2, 20, -12, 0, -8, 0, 8, -3, -7, 0, 6, 12, -1, -3, 1, -6, 3, 5, -16, -5, 3, -1, 6, 1, 4, -3, -7, 7, -4, 8, -3, -2, 2, -2, 5, -1, -6, -11, -4, 12, -4, 3, -5, 1, 2, -1, 4, -7, 1, 11, 4, 0, 3, -3, -4, 12, 1, 5, 1, 1, -6, 1, 0, -4, 1, -8, 8, -7, -7, 5, 3, -34, 2, 4, -7, 4, 2, 1, -4, 0, 4, -5, 7, -3, -3, -1, 3, 16, -5, 3, -3, -1, 0, 20, -10, -2, 8, -5, 9, -2, 0, -4, -5, 5, -2, -5, 7, -1, 2, 9, 5, 8, -1, 5, -2, 7, 0, 2, -2, -3, -6, -2, -7, 12, 1, 6, 3, -7, 3, 0, -2, 5, -2, 3, 3, -3], "imageUrl": "https://upload.wikimedia.org/wikipedia/commons/thumb/0/0c/Google_Data_Center%2C_Council_Bluffs_Iowa_%2849062863796%29.jpg/1280px-Google_Data_Center%2C_Council_Bluffs_Iowa_%2849062863796%29.jpg", "imageLicense": "CC BY 2.0", "imageArtist": "Chad Davis", "explanation": ["Imagine you're playing an online game on your computer. Every time you switch levels, the game pauses and waits for the new level to load, making you wait longer and less fun.", "Think of your computer as a busy highway. Right now, it's like cars (data) taking separate roads (memory) to get to the destination (your GPU). If all cars took the same road, traffic jams (slowdowns) would be less frequent."], "example": "Currently, each level switch sends data down different memory paths. If all data went through one path, loading times would drop.", "whyItMatters": "Kernel fusion combines separate tasks into one, reducing the number of memory paths used and speeding up loading times."}, {"id": "615d90f21354", "title": "tensor cores are", "slug": "tensor-cores-are", "headline": "Why can computers crunch numbers faster than humans?", "summary": "What tensor cores are \u2014 specialized hardware for matrix multiply-accumulate on GPU", "source": "What tensor cores are \u2014 specialized hardware for matrix multiply-accumulate on GPU", "sourceUrl": "https://en.wikipedia.org/wiki/Tensor_(machine_learning)", "articleUrl": "https://en.wikipedia.org/wiki/Tensor_(machine_learning)", "publishedAt": "2026-07-03", "category": "learn", "cohortScore": 0.5, "embedding": [-7, 1, -2, 4, -5, 3, -2, 2, 10, -1, 7, -7, 3, 1, 4, 2, -1, -2, 4, -5, 2, -12, -6, -9, 1, -3, -7, -7, -5, -28, 6, 0, 15, 1, 0, -5, -1, 6, -8, 0, -3, 6, -7, 3, 7, 1, -4, 1, 0, 3, -1, -2, -4, 6, 8, -1, 5, 2, 3, -3, 3, 2, -8, 6, 8, -5, 2, -8, 0, 8, -4, 8, 9, -2, 5, -2, 4, 1, 0, 0, 6, -7, -7, -2, -3, 5, -1, 5, 1, -2, -5, 2, -2, 6, 2, 2, 8, 4, -3, 48, 2, 3, -4, 2, 5, -6, -3, 1, -11, -3, 6, -2, 5, 6, 13, -4, -5, 2, 0, 3, -7, 3, 3, -2, 0, -9, -9, 11, -1, 8, 4, 5, -4, 0, 5, 0, 1, 3, 4, 7, -3, 11, 9, -6, 0, 14, 0, -1, 5, -5, -1, 4, -6, -6, -8, 3, 5, -4, -7, -1, -8, -1, -4, 13, 5, -6, -1, 0, -3, -4, 4, -3, -2, 0, 6, -6, -14, -4, 2, 3, 4, 1, -2, -1, 0, -9, 1, -2, -2, -9, -7, 3, -13, 2, -7, -2, 0, 5, -7, 0, -1, -1, 1, 1, 3, 1, -7, -3, 3, 11, 1, -6, -2, 4, -8, -1, 3, 2, -3, 5, 7, -2, -7, -39, -1, -1, -4, 12, -11, 11, -5, 5, 8, 2, 5, -2, -5, -6, 2, -4, 0, -5, -3, -2, 7, -2, -5, -5, -2, 20, 0, 3, 3, -3, 3, -5, 1, 4, 6, 16, 1, -1, 1, -5, 1, 4, -8, -4, 2, -4, 2, 1, 4, 0, -8, 2, -1, 1, -10, -8, 3, -1, 6, 1, -10, -5, 0, 9, -2, -2, -3, 5, -2, 4, 10, 0, -1, 11, -4, 8, -1, 4, 1, 3, 2, 2, 5, 4, -7, 4, 3, -6, 3, -4, 3, -5, -3, 5, 0, -32, 1, 4, 0, -3, -7, 1, 0, 0, 0, -6, 7, 5, 1, 0, 4, 10, -4, -3, -3, 0, 3, 19, -3, -5, 3, 3, -2, 7, -2, -8, -6, 9, -7, -3, 11, 1, 2, 7, 0, 7, -5, -3, -3, 3, -3, -3, -4, 4, -6, 5, -1, 8, -2, 1, 0, -7, -6, -1, 1, 1, -1, -1, 0, -6], "imageUrl": "https://upload.wikimedia.org/wikipedia/commons/thumb/9/9a/NetApp_ONTAP_AI.jpg/1280px-NetApp_ONTAP_AI.jpg", "imageLicense": "CC BY-SA 4.0", "imageArtist": "Qdrddr", "explanation": ["Imagine you're trying to find the best route for a delivery truck in a city with hundreds of streets and intersections. You'd have to check countless possibilities to find the quickest path.", "Computers use special math tricks to quickly compare lots of routes at once, finding the best one much faster than checking each one individually."], "example": "Instead of checking 100 routes one by one, a computer can look at all 100 routes at the same time and pick the best one instantly.", "whyItMatters": "Computers can process many possibilities at once using matrix multiplication, saving time and resources."}, {"id": "95b109c547d4", "title": "tensor cores do 4x4 matrix multiply in one clock cycle", "slug": "tensor-cores-do-4x4-matrix-multiply-in-one-clock-cycle", "headline": "Tensor cores perform 4x4 matrix multiply using optimized GEMM (General Matrix Multiply) instructions in one clock cycle", "summary": "How tensor cores do 4x4 matrix multiply in one clock cycle", "source": "How tensor cores do 4x4 matrix multiply in one clock cycle", "sourceUrl": "", "articleUrl": "", "publishedAt": "2026-06-12", "category": "learn", "cohortScore": 0.5, "embedding": [-4, -1, -2, 1, -7, 4, -7, 0, 4, -4, 3, -7, 0, 1, 3, 1, -1, -2, 5, -8, 4, -10, -2, -3, 5, 4, -3, -2, -6, -31, 9, 0, 6, -1, -3, -2, 0, 5, -10, 1, 0, 8, -5, 4, 0, -1, -6, 2, 0, 4, 1, -4, -3, -1, 7, 4, 1, 4, 1, 0, -1, 6, -18, 7, 11, -1, 0, -8, -1, 13, -8, 7, 6, -3, -3, -1, 4, 3, 0, -1, -4, -8, -1, -6, -1, 8, -3, -1, 3, 1, -5, 0, -8, 3, 0, 3, 5, 5, 1, 44, -1, -1, -3, 9, -1, -2, 0, 1, -5, 2, 6, -4, 10, -6, 7, -5, -5, 3, 1, 4, -5, -4, 4, 0, -1, -3, -4, 12, 2, 4, 5, 7, -4, -3, 7, 3, 4, -3, 2, 1, -2, 3, 7, 0, 2, 18, -2, 0, 6, 2, -7, 4, -9, -5, -1, 2, 0, -2, -7, 4, -13, -5, 5, 11, 4, -9, -1, 5, -2, -8, 6, 1, 0, -7, 8, -8, -8, -3, 1, 5, 4, 0, 3, 3, -2, -3, -7, 1, -2, -15, -9, 4, -15, 7, -10, -2, 2, 1, -3, 7, 4, 4, 3, 6, -1, 2, -3, 0, 0, 10, -3, -4, 1, -1, -10, -2, 4, 2, -7, 6, 3, -4, -9, -38, 3, 1, -7, 11, -10, 6, -3, -3, 0, 6, 1, -2, -5, 2, 7, -3, 4, -5, -3, 3, 1, 1, -2, -7, -4, 14, 0, 4, 1, 4, -2, -2, 3, 6, 0, 12, 5, 3, -3, 1, 1, -1, -12, -2, 6, -4, 5, 3, 0, 0, -10, 0, 3, 0, -12, -7, -1, -4, 3, 6, -6, -1, 1, 10, 1, -4, -1, 3, -5, 4, 10, 3, 1, 11, -6, 2, 4, -1, -1, 4, -7, 1, 3, 2, -3, -1, 5, -2, 4, 1, 4, 2, 4, 3, -3, -33, 4, 5, 2, -3, -11, 1, -4, -5, 0, -7, 13, 8, 1, 2, 7, 9, -6, -7, -5, 1, 9, 19, 2, 1, 5, 3, 2, 12, 3, -2, -1, 2, 3, 1, 5, -5, 2, 10, 12, 0, -7, -6, -5, 4, -7, -3, -7, 1, -8, -3, -1, 6, 2, -2, 4, -9, -3, -2, 5, 3, -1, -1, -3, -5], "imageUrl": "https://upload.wikimedia.org/wikipedia/commons/thumb/3/3d/Measuring_a_qubit_leaves_no_room_for_error.jpg/1280px-Measuring_a_qubit_leaves_no_room_for_error.jpg", "imageLicense": "CC BY 4.0", "imageArtist": "FMNLab"}, {"id": "39575c84c4a1", "title": "Tesla Model Y", "slug": "tesla-model-y", "headline": "Tesla Model Y is the world's best-selling electric vehicle in 2023", "summary": "What the roofline model measures \u2014 whether a kernel is compute-bound or memory-bound", "source": "What the roofline model measures \u2014 whether a kernel is compute-bound or memory-bound", "sourceUrl": "https://en.wikipedia.org/wiki/Tesla_Model_Y", "articleUrl": "https://en.wikipedia.org/wiki/Tesla_Model_Y", "publishedAt": "2026-06-12", "category": "learn", "cohortScore": 0.5, "embedding": [-1, 0, 8, 2, 1, 5, 2, 6, 10, -4, 2, 1, 0, 3, 3, 1, -2, -2, -1, -5, 7, -9, -6, -6, 2, 1, 0, -1, -6, -30, -4, -7, 8, 2, -5, 3, -6, -2, 1, 3, -3, 5, -3, 1, 1, -2, 0, -2, -7, -1, -5, -3, 1, 4, 5, 9, 0, 5, 8, -1, -3, 6, -20, 0, 8, -5, -4, -5, -5, 5, 4, 3, -1, 4, -3, 7, -3, 5, -9, -4, 4, -1, -5, -2, -7, 3, -1, 0, 1, 4, -10, 1, 2, -1, -6, 5, 3, -1, -4, 48, 0, 8, 3, -2, -6, -1, -5, -2, -1, -2, 0, -4, 7, -5, 7, -1, 8, 7, 7, -4, -12, 11, 6, 0, 1, -2, 5, 12, -1, -2, 1, -1, -6, 4, -1, -1, -3, 4, -3, 2, -3, 9, 4, -6, -4, 15, -4, 0, -3, -2, 1, 8, 4, -14, 4, 4, 0, 2, -9, -1, -7, 5, -12, 15, -5, -7, 0, 0, -2, 4, 6, 1, 3, 2, 1, -1, -12, 3, -6, 4, 1, -5, -6, 0, 8, 0, -2, 1, 0, -2, -3, 1, 1, 7, -5, -8, -1, 0, 4, -4, -3, 5, -8, -1, -4, 0, -5, 6, 4, 5, -3, -5, -1, 1, -5, 4, 1, 1, -5, 4, 5, 3, -1, -41, -4, -4, 3, -1, -7, 7, -4, 7, 2, 5, 0, -7, 3, 3, 1, -5, 2, -12, 4, -4, 4, 0, -4, 6, -3, 18, -9, 3, -2, -3, 4, -5, 4, 7, -2, 4, 3, -7, 3, -5, -3, 1, -7, -6, -1, 1, -3, -4, 4, 4, -1, 3, -6, 3, -5, -8, 3, 3, 3, 1, -8, -8, -4, 6, -6, 1, -1, -9, -5, -6, 9, -2, 4, 7, -1, 2, 1, 0, 0, 6, 2, 9, 2, 1, 0, 7, -1, -2, 2, -1, -2, -5, -12, 12, 1, -33, 1, -1, 4, -3, 3, 2, -3, 0, -1, -3, 14, 10, 1, 2, -5, 13, -8, 6, -1, 4, 3, 19, -7, 3, 3, -1, 2, 2, -3, -3, -5, 6, -2, -4, 11, -3, 6, 4, 1, 9, 13, 3, -2, 4, 3, 1, 0, -2, -5, 5, -4, -1, 0, 5, 2, 2, -7, -3, -5, 4, 2, 1, -3, 1], "explanation": ["The Model Y's impressive sales figures demonstrate its popularity and the growing demand for electric vehicles. Tesla's ability to continuously innovate and expand its production capabilities has contributed to its dominance in the electric vehicle market."], "whyItMatters": "Understanding the Model Y's success provides insights into consumer trends and the potential for future electric vehicle market growth.", "imageUrl": "https://upload.wikimedia.org/wikipedia/commons/thumb/e/e7/Tesla_Model_Y_Premium_%28Facelift%29_%E2%80%93_f_05052026.jpg/1280px-Tesla_Model_Y_Premium_%28Facelift%29_%E2%80%93_f_05052026.jpg"}, {"id": "3e95ffd82bf9", "title": "arithmetic intensity is", "slug": "arithmetic-intensity-is", "headline": "Arithmetic intensity = FLOPs / Bytes accessed", "summary": "What arithmetic intensity is \u2014 FLOPs per byte of memory accessed", "source": "What arithmetic intensity is \u2014 FLOPs per byte of memory accessed", "sourceUrl": "", "articleUrl": "", "publishedAt": "2026-06-12", "category": "learn", "cohortScore": 0.5, "embedding": [-11, -3, 2, 5, -3, 1, 4, -3, 16, -4, 8, -5, 4, 2, -2, 0, -5, -6, 3, 3, 16, -6, -3, -6, -5, 5, -2, -2, -2, -29, -2, 7, 0, -5, -2, -2, -6, 3, -5, 7, 2, 4, -9, -4, 0, -1, -6, 4, 2, 2, 1, 8, 6, 1, -3, 1, 11, 8, 7, -7, 6, 8, -13, 3, 6, 1, 5, -7, -2, 3, -3, -1, 1, 5, 4, -3, 4, 0, 4, -5, 0, -9, -5, -6, 4, -4, -5, 4, 9, 0, -4, 2, 1, 0, 8, 1, 9, 0, -2, 44, -1, -1, -3, 3, 8, -8, 4, 1, -7, -5, 4, -8, 0, 6, 9, -3, 2, -8, 2, 1, -7, 3, 3, 1, -6, -6, -10, 12, -3, -1, 2, -4, -4, -1, 3, -1, 3, -3, 0, 1, 0, -1, 8, 0, -2, 21, -7, 9, -1, -2, 3, -5, -1, -6, -2, 3, 0, 5, -1, -4, -6, 5, -2, 10, 2, -3, -1, 4, -4, -7, 4, 1, -7, 0, 4, 1, -2, -4, -3, 3, 4, -3, -3, 4, 3, -8, -3, 3, 2, 1, -10, -1, -15, 2, 2, 2, 3, 12, -6, -4, 10, 1, -2, 7, 3, -3, -5, -5, 2, 3, -8, -8, -1, 4, -12, -7, 2, 6, 1, -1, -3, -10, -6, -36, -4, 2, -11, 5, -9, 2, 0, 0, -1, -2, -11, 0, -8, -1, 2, -2, -2, 1, -1, -1, 5, -4, -6, 4, 0, 12, -6, 6, -4, -4, 1, -7, -4, 1, 0, -3, 7, 6, 2, -9, 4, -1, -6, -1, 4, 1, -7, 1, 10, -5, -4, 4, 6, 6, -6, -5, 3, 2, 7, 2, -7, -5, 0, -2, 1, -2, -6, 1, -1, 3, 9, -1, -6, 6, -5, 7, -6, -2, -5, 6, 4, -2, 2, 3, 0, 4, 10, -4, 1, -6, 3, 0, -8, -4, 4, -35, 2, -1, 3, 1, -3, 3, 3, -6, 6, -8, 3, 2, -7, 4, 2, 9, 2, 7, -7, 5, 3, 19, -3, -4, 5, 7, 14, 8, -2, 0, 2, 5, -1, 0, 7, 1, -2, 10, 1, 11, -6, -4, 8, 14, 2, 1, -10, 7, -3, -5, 5, 5, 6, 2, 5, -11, -1, 2, -1, 5, -2, 3, 2, 4], "imageUrl": "https://upload.wikimedia.org/wikipedia/commons/thumb/c/ca/Gabinete99.jpg/1280px-Gabinete99.jpg", "imageLicense": "CC BY-SA 4.0", "imageArtist": "Cancella"}, {"id": "5103314ae727", "title": "most transformer operations are memory-bound, not compute-bound", "slug": "most-transformer-operations-are-memory-bound-not-compute-bound", "headline": "Why do computers sometimes get tired?", "summary": "Why most transformer operations are memory-bound, not compute-bound", "source": "Why most transformer operations are memory-bound, not compute-bound", "sourceUrl": "https://en.wikipedia.org/wiki/Memory_bandwidth", "articleUrl": "https://en.wikipedia.org/wiki/Memory_bandwidth", "publishedAt": "2026-07-03", "category": "learn", "cohortScore": 0.5, "embedding": [-9, 4, 5, -3, -8, -1, -2, -1, 8, -1, -2, 2, 7, 0, -1, 1, -7, -2, -2, -8, 9, -9, -3, -2, -5, 0, -2, -4, -3, -29, -11, -1, 1, 0, 1, 0, 0, 3, -8, 0, -3, 6, 0, -4, 2, -5, 0, -7, 4, 3, -5, 2, 4, 8, 2, 4, 4, 11, 10, -10, 3, 7, -10, 10, 5, -4, -4, -15, 1, 1, 0, 1, -1, 6, 3, 0, 2, 4, -3, 2, 5, -8, -1, 2, -8, 0, -8, 3, 5, -2, -6, 5, 3, 6, -3, 0, 8, 13, -9, 46, -5, 2, 0, -1, 1, -1, 0, 1, -15, -4, 1, -2, 3, -1, 9, 1, -2, 0, -2, -2, -12, 7, 3, 10, 5, -4, 0, 11, 1, 5, 2, 6, 0, 4, 6, 5, 2, -5, 4, -1, -3, 10, 4, 0, 1, 10, 2, 5, -3, 1, -4, 6, -2, -12, -4, 6, 1, 0, 0, -6, -6, 1, -5, 10, -1, 1, 3, -2, -3, -1, 3, -1, 2, -9, 3, 0, -7, -2, -6, 4, 5, 1, -2, -1, 4, -9, -3, 2, -1, 2, -6, -2, 0, -1, -6, -6, 2, 4, -4, -3, 1, 2, -2, 2, 1, -2, -7, -3, 3, 7, 0, -9, 6, 2, -10, 3, 4, 3, 5, 1, 1, -1, -1, -41, -5, -4, -5, 12, -10, 4, -1, 0, 0, 2, -5, -7, -8, -2, 1, 0, 2, -9, 1, -3, 1, 3, -11, -1, -1, 26, -18, 4, 2, 3, 5, -6, -1, 1, 4, 2, 0, 8, 4, -7, 1, -2, -6, -1, -2, -2, -7, 0, 6, 1, -6, 2, 0, 4, -8, -3, -2, 3, 9, -1, -8, -2, -2, 4, 1, 7, -5, 0, -1, -4, 14, -4, -1, 4, 2, 7, 4, 2, -1, 3, -4, 4, 2, 0, -3, 4, 10, 0, 5, -3, 5, -3, -3, 7, -4, -32, 0, 5, -1, 0, 2, 1, 3, -5, 6, -6, 10, -1, 3, 2, 4, 15, -5, 1, -10, -3, 5, 21, -7, 1, 4, 2, 5, -1, -6, -4, -6, 2, -7, -1, 6, -6, 7, 5, 3, 8, 6, -3, -3, 8, 4, -1, -2, 2, -3, -2, -3, 4, -2, 3, 4, -5, -3, -3, 1, 6, -3, 8, 4, 3], "imageUrl": "https://upload.wikimedia.org/wikipedia/commons/8/8f/The-Transformer-model-architecture.png", "imageLicense": "CC BY-SA 3.0", "imageArtist": "Yuening Jia", "explanation": ["Imagine you're playing a video game on your computer. Suddenly, it starts to lag, and your character moves slower than before.", "It's like your computer is running out of energy to think fast. It's not about doing more calculations; it's about remembering things quickly."], "example": "When you try to open many apps at once, your computer struggles because it can't remember where everything is.", "whyItMatters": "Most computer tasks are memory-bound, meaning they're limited by how fast the computer can remember information, not by how fast it can calculate."}, {"id": "5102e0583d5f", "title": "NVIDIA's A100 has: 80GB HBM2e, 2TB/s bandwidth, 312 TFLOPS FP16", "slug": "nvidia-s-a100-has-80gb-hbm2e-2tb-s-bandwidth-312-tflops-fp16", "headline": "NVIDIA's A100 features: 80GB HBM2e, 2TB/s bandwidth, 312 TFLOPS FP16", "summary": "What NVIDIA's A100 has: 80GB HBM2e, 2TB/s bandwidth, 312 TFLOPS FP16", "source": "What NVIDIA's A100 has: 80GB HBM2e, 2TB/s bandwidth, 312 TFLOPS FP16", "sourceUrl": "", "articleUrl": "", "publishedAt": "2026-06-12", "category": "learn", "cohortScore": 0.5, "embedding": [-4, -2, 0, -5, 1, 3, -2, 5, 1, 1, 2, -6, -7, -2, 1, 1, 7, -15, 0, -2, 2, -8, -2, -2, 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"https://upload.wikimedia.org/wikipedia/commons/thumb/1/10/Blausen_0657_MultipolarNeuron.png/1280px-Blausen_0657_MultipolarNeuron.png", "imageLicense": "CC BY 3.0", "imageArtist": "BruceBlaus"}, {"id": "3cefb45a09a2", "title": "paged attention (vLLM) improves serving throughput", "slug": "paged-attention-vllm-improves-serving-throughput", "headline": "Paged attention (vLLM) improves serving throughput by reducing latency through non-contiguous KV-cache pages, enabling faster data retrieval", "summary": "Why paged attention (vLLM) improves serving throughput \u2014 non-contiguous KV-cache pages", "source": "Why paged attention (vLLM) improves serving throughput \u2014 non-contiguous KV-cache pages", "sourceUrl": "", "articleUrl": "", "publishedAt": "2026-06-12", "category": "learn", "cohortScore": 0.5, "embedding": [-9, -2, 6, 0, 3, 0, -2, 0, 5, -3, 5, 2, 8, 9, 3, 3, -1, -2, 0, -6, 8, -3, 3, -3, -7, 0, -4, -6, -6, -28, 2, -1, 8, -1, -4, -5, 3, 6, -2, 6, 4, 7, -10, 1, -2, -11, -1, -6, 1, 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-3, 11, 10, -4, 0, 0, 3, 4, 23, 1, 0, 2, 4, 4, 2, -3, 1, 3, 8, 5, -3, 7, 0, 2, 1, 4, 8, 4, -3, 2, 7, -2, 5, -10, 2, -2, 2, -5, 5, 12, 11, 2, -2, -2, 2, 4, 8, -5, 3, -3, 0], "imageUrl": "https://upload.wikimedia.org/wikipedia/commons/thumb/9/93/Vision_Transformer.png/1280px-Vision_Transformer.png", "imageLicense": "CC BY 4.0", "imageArtist": "Daniel Voigt Godoy"}, {"id": "d5e49f2c1a71", "title": "continuous batching does", "slug": "continuous-batching-does", "headline": "How can you mix a cocktail perfectly every time without stirring?", "summary": "What continuous batching does \u2014 adds new requests to a running batch without waiting", "source": "What continuous batching does \u2014 adds new requests to a running batch without waiting", "sourceUrl": "https://en.wikipedia.org/wiki/Continuous_stirred-tank_reactor", "articleUrl": "https://en.wikipedia.org/wiki/Continuous_stirred-tank_reactor", "publishedAt": "2026-07-03", "category": "learn", "cohortScore": 0.5, "embedding": [-8, -3, -3, -2, 4, 0, 1, -7, -2, -1, 7, -1, -3, 4, -1, 4, -3, -2, -7, -4, -2, -6, -4, -4, -2, -1, -1, -5, -2, -30, 8, -4, -4, -5, -1, 2, 3, 4, 7, 6, 8, 8, -10, 0, -5, -5, 1, 6, 10, 1, 0, -6, 5, -6, 3, 5, 1, 0, 2, 1, 4, -4, -9, 6, 1, -5, -5, 5, -1, 19, -5, 9, -2, 17, 1, -8, 0, 5, -10, 14, -3, -6, 2, -7, -6, 1, 0, -1, 3, 5, -4, 0, -1, -1, -3, 0, 0, 3, 1, 45, -4, 2, -1, 2, 0, 1, -5, 4, -2, 3, 0, 4, 13, -10, -4, 8, -2, -5, 3, -1, 4, 7, 3, -5, 4, 2, -4, 7, -3, 2, 7, -2, -3, -1, 5, 0, 6, -7, 10, -6, -2, 4, 2, -14, 5, 14, 1, 3, -1, -7, -5, -1, -7, -7, 6, -2, 5, 3, 2, 1, -11, -2, -4, 8, -1, -13, -3, -1, -4, 4, 3, 2, -5, 0, 2, -8, -10, 1, 7, -3, 6, 1, 3, 9, 2, -8, 0, 0, 0, 2, -4, -4, 6, 3, 3, -4, 5, -3, 1, -6, -1, 8, -4, 0, 8, 4, 4, 0, 5, 7, -6, 4, -1, -4, -6, 5, 3, 0, 5, -1, 2, 3, 2, -38, 2, 5, -4, 4, -15, 2, -3, -2, 1, 6, -2, 1, -9, 3, 1, 6, 2, 0, 3, 1, 3, 3, -6, 0, -1, 17, 2, 1, -3, 0, 4, -9, -12, -4, 0, 6, -1, 4, 1, 0, 3, -5, -9, 0, -3, 1, -8, -4, -7, -3, 3, 2, -5, 3, -4, -1, -1, -6, -2, -1, 7, -1, 1, 5, 3, 3, -9, 7, 2, 3, 10, 2, 9, 8, 0, -5, -4, -9, 3, 1, -3, 11, 10, 8, 2, 5, 3, 3, 4, -4, 3, -8, 0, 6, 4, -30, 3, -2, 4, 2, 4, 1, -3, -3, 1, -7, 9, 0, 6, 3, 0, 3, -3, -2, -13, 6, -2, 18, 0, -3, 4, -4, 3, 0, -3, -9, 5, 13, -1, 4, -1, 1, 6, -1, -7, -9, -4, -4, -10, -1, -8, -1, -10, -7, 7, -2, -4, 4, 3, 0, 2, -6, 2, 1, 11, 6, -1, 8, 4, -12], "imageUrl": "https://upload.wikimedia.org/wikipedia/commons/8/89/Client-Server_Model.jpg", "imageLicense": "CC BY-SA 3.0", "imageArtist": "Bp2010.hprastiawan", "explanation": ["Imagine you're making a cocktail at a party and want to ensure every guest gets a perfectly mixed drink.", "Think of the drink as a mixture that's perfectly mixed from the moment it enters the glass. This way, everyone gets the same taste. This is what continuous mixing in a CSTR does \u2014 it keeps adding new ingredients to the mix without stopping the process."], "example": "You pour fresh fruit juice into the glass continuously while stirring, ensuring the drink stays perfectly mixed throughout the party.", "whyItMatters": "Continuous mixing in a CSTR ensures a consistent and uniform mixture, just like your perfectly mixed cocktail."}, {"id": "adda7597c5ed", "title": "Masking (behavior)", "slug": "masking-behavior", "headline": "Can you not see what's right in front of you?", "summary": "What causal masking does \u2014 prevents attention to future tokens in the decoder", "source": "What causal masking does \u2014 prevents attention to future tokens in the decoder", "sourceUrl": "https://en.wikipedia.org/wiki/Masking_(behavior)", "articleUrl": "https://en.wikipedia.org/wiki/Masking_(behavior)", "publishedAt": "2026-07-03", "category": "learn", "cohortScore": 0.5, "embedding": [-4, 1, -4, 0, 0, -2, 8, -4, 2, -7, 8, -4, 2, 11, 3, 4, -6, 4, -3, -6, 5, -6, 6, -4, -9, 4, -3, -3, -2, -27, 3, -10, 6, -1, 1, -2, -7, 3, -3, 3, -2, 2, -7, -4, -3, -7, 0, -3, -3, -4, -3, -3, 2, 6, 2, 8, -1, 14, 4, 5, 2, 6, -9, 6, 8, 6, 0, -5, -3, 8, -2, 1, -3, 2, 7, 4, 5, 0, 5, -4, 4, 7, 0, 0, -3, -2, -1, -1, -2, -4, -9, -8, 4, 3, -7, 2, 5, 10, 2, 48, 1, 1, -3, -5, 6, -8, 2, 1, -4, 9, 4, -7, 3, 4, 4, 7, 8, 1, 2, -2, -1, 3, 1, -6, -1, -4, 0, 17, 0, -2, 5, -2, 0, 3, 4, -2, -2, -1, 2, -5, -2, 6, 2, 5, -10, 8, -4, -2, -3, -4, -5, 2, -3, -5, -1, 2, -2, -2, -4, 4, 1, -2, -10, 12, -3, -1, 0, -6, 1, -7, -3, -6, 4, -3, -6, 3, -15, 2, -7, -1, 0, -9, 2, 9, 2, -6, -3, 1, 2, -4, -3, -3, -10, 1, -7, -4, 6, 3, -13, -2, 1, 1, -2, 1, 4, 3, -3, -6, 13, 1, -5, 0, 3, -2, -1, 0, 1, 6, 1, 0, -2, 0, -5, -41, -2, -1, -3, -4, -7, 4, 6, 8, 7, -6, -2, -6, -2, 0, 6, -2, 4, -1, 4, 2, 4, 11, -10, -4, 7, 19, 5, 6, 3, -3, 3, -1, -6, 6, 0, 2, 4, 4, 2, -4, -7, 3, -7, -5, -3, -4, 1, 4, 5, 5, -1, 3, 7, 2, -6, 2, -10, -5, 6, 5, 2, -8, -5, 1, 8, -4, -3, 4, 2, -4, 15, 0, 1, 5, 3, 2, -6, -4, 2, 11, 3, 4, -3, 4, -2, 2, 1, 3, 1, -9, 7, -6, -6, 1, -3, -34, 2, 6, -3, 4, 4, 5, -5, -7, -5, -13, 3, 6, -2, -3, 5, 12, -7, 2, -4, -4, 3, 24, 3, -1, -6, 0, -1, 6, -1, 4, 2, 8, -3, -5, 4, 3, 1, 8, -3, 6, 5, 4, -9, 9, 5, -1, 3, -1, -7, -2, -2, -1, -8, 0, 4, -5, 1, -1, 5, 1, 0, 1, 0, -6], "imageUrl": "https://upload.wikimedia.org/wikipedia/commons/thumb/f/fe/Autism_Aspect_Masking_1.png/1280px-Autism_Aspect_Masking_1.png", "explanation": ["Imagine you're at a party, and someone you don't know well starts talking to you. You feel uncomfortable but don't want to be rude. So, you smile and nod, even though you're not interested.", "You're subconsciously hiding your true feelings to fit in, a process known as masking."], "example": "You smile and nod, even though you're feeling awkward and uninterested.", "whyItMatters": "Masking helps us hide our true emotions to fit into social situations."}, {"id": "a796738bd16c", "title": "Transformer (deep learning)", "slug": "transformer-deep-learning", "headline": "Transformers use multi-head attention for contextualizing tokens", "summary": "What the feed-forward network in a transformer does \u2014 2-layer MLP applied independently per token", "source": "What the feed-forward network in a transformer does \u2014 2-layer MLP applied independently per token", "sourceUrl": "https://en.wikipedia.org/wiki/Transformer_(deep_learning)", "articleUrl": "https://en.wikipedia.org/wiki/Transformer_(deep_learning)", "publishedAt": "2026-06-12", "category": "learn", "cohortScore": 0.5, "embedding": [-5, 1, 0, -10, -6, 2, 3, 6, 0, 1, -4, -4, 4, 3, 11, 3, -5, 0, -4, -7, 10, -6, -1, -3, -2, -2, 0, -3, -2, -22, 0, -5, 4, 3, -7, -3, -2, 1, 5, -2, 0, -2, -2, -7, -3, -10, 2, -1, -6, -8, 5, -5, 7, 9, 5, 7, 6, 8, 9, 0, -2, 12, -13, 6, 1, 7, -12, -1, -3, 4, 4, -4, 1, -1, 8, 4, 2, 1, -4, -2, 5, 2, -3, 2, 1, 3, -6, -5, -2, -6, -9, 2, -2, -1, -1, -5, 1, 4, -6, 45, 1, -5, 3, -4, 9, -1, 1, -3, -7, 7, -3, -8, -9, 2, 2, 2, 2, 5, 3, -5, 2, 5, -1, -1, 3, -9, 7, 12, -1, 5, 2, 8, -5, 2, 3, 4, 3, -8, -2, 7, 2, 9, 0, 2, -3, 11, 1, -1, -1, 4, -10, 6, 0, -2, 6, 1, 0, -3, -3, 0, 0, -3, -9, 11, -2, -11, 4, -8, -2, -6, 1, 2, 5, 1, -2, 5, -14, -7, -4, 4, 2, -7, 6, -1, -3, -2, 3, -6, -3, 4, -8, 6, -5, 1, 2, -5, 0, 6, -6, 2, -5, -3, 0, -5, -2, 3, -5, 3, 1, 3, -5, -5, 10, -3, -5, 0, 2, 11, 2, 2, -2, 4, -6, -40, -4, 5, -1, 5, -10, 2, 2, 5, 5, 5, 0, -11, 1, 2, 6, 1, 5, -5, 0, 3, 2, 16, -14, 1, 4, 22, -4, 0, 2, -2, 4, -6, -3, 3, -3, 12, -1, 6, 2, -13, -3, 0, -8, -2, -4, -4, 3, 0, 1, 3, -9, -2, -2, -1, -3, 1, -4, -4, 3, 3, -1, -4, -3, 4, 2, -1, 2, -3, 2, -6, 9, 7, 4, 2, -2, 4, -1, -4, 7, 7, -2, 4, -5, 9, 0, 0, -6, 9, 1, -8, 6, -1, -4, 1, -5, -37, 7, 8, 6, -3, 10, 4, -1, 3, -2, -12, 5, 11, 2, 0, 7, 9, -3, 1, -4, -2, 7, 21, -8, 1, -6, -4, -3, 6, -3, 2, 1, 8, -6, -2, 9, -2, 2, 6, 4, 4, 3, 1, -7, 2, 2, 0, -1, -1, 0, 4, -2, 1, 0, 4, 4, -2, -7, -5, 0, 2, -7, 4, 0, -6], "explanation": ["In transformers, each token is contextualized through a multi-head attention mechanism. This allows the model to focus on different parts of the input sequence simultaneously, enhancing the representation of each token by considering its context."], "example": "For a sentence like \"The cat sat on the mat,\" each word token (e.g., \"cat,\" \"sat,\" \"mat\") is contextualized by considering its relationship with other words in the sentence.", "whyItMatters": "Understanding this helps grasp how transformers achieve efficient and effective language modeling.", "imageUrl": "https://upload.wikimedia.org/wikipedia/commons/thumb/3/34/Transformer%2C_full_architecture.png/1280px-Transformer%2C_full_architecture.png"}, {"id": "77275062fd67", "title": "transformers use LayerNorm not BatchNorm", "slug": "transformers-use-layernorm-not-batchnorm", "headline": "LayerNorm normalizes across all features, accommodating variable-length sequences unlike BatchNorm, which relies on fixed-size batches", "summary": "Why transformers use LayerNorm not BatchNorm \u2014 LayerNorm works with variable-length sequences", "source": "Why transformers use LayerNorm not BatchNorm \u2014 LayerNorm works with variable-length sequences", "sourceUrl": "", "articleUrl": "", "publishedAt": "2026-06-12", "category": "learn", "cohortScore": 0.5, "embedding": [-8, -1, -2, 1, 0, 5, -5, 1, -3, 1, 1, -1, 6, 8, 1, 0, -1, 4, -3, -4, 10, 1, -2, 1, 1, -1, -2, -4, -2, -30, 3, -1, 7, 3, -5, 1, -10, -1, 4, 9, 4, 6, -2, -5, -1, -4, -1, -3, -1, -1, 4, -8, 0, 12, -2, 2, 0, 9, 11, -1, -3, 8, -12, 8, -1, 2, -9, -7, -3, 7, 2, 3, -7, 3, 2, 2, 3, 2, -6, 0, -4, -4, 5, -6, -1, 1, -5, -6, -4, -1, -4, 4, -5, 7, -2, -5, 2, 4, -4, 47, -7, -2, -6, 0, 2, 6, -8, -3, -7, 8, -3, 1, -3, -1, 1, -1, 2, 1, -2, -4, -6, 1, -3, -2, 3, -1, 6, 8, 5, 5, -1, 5, -10, 4, 4, 5, 13, -7, -11, -5, -1, 10, 4, 2, 0, 12, -9, 2, -4, 1, -2, 2, -4, -7, 4, -1, 0, -4, -7, -2, -6, -3, 0, 6, -3, -12, -2, -2, -1, -6, 2, -3, 2, -6, -1, 0, -10, -13, -2, 4, -3, 2, 7, -2, 1, 0, -1, -1, -1, -2, -1, -5, -2, 1, 6, -2, 2, 3, 0, 1, 0, 4, 8, -5, -11, 2, 0, -5, 3, 8, -6, -10, -2, 0, -2, 2, 1, 13, 6, 2, -3, 1, 0, -43, -1, 3, -2, 4, -4, 2, 1, -4, -2, 4, -3, -7, -8, 3, 10, 2, 1, 0, 2, -5, -1, 4, -12, 9, 3, 18, -7, 5, 6, 3, -4, -4, -2, 7, 1, 9, -1, 3, -3, -13, 0, 4, -13, -4, 3, -8, -2, 0, 0, -2, 1, 11, -4, 6, -2, -5, -10, -4, 2, 0, -9, -1, -11, 0, 0, 4, 1, 1, 3, -3, 14, 4, 1, 2, 2, 1, 3, -2, 2, 8, 1, 8, 5, 4, 1, 5, 8, 1, 5, -2, 1, 3, -5, 5, 2, -31, 4, 7, 10, 2, 1, 0, -5, 6, 0, -3, 5, 4, 3, 2, 3, 11, -7, 7, -1, 4, 6, 20, -10, -6, -1, 0, 2, 3, 1, 0, 6, 7, 7, 3, 5, 3, 4, 3, 1, -1, 1, -7, -2, 5, -6, 1, 1, -4, 3, -4, -4, -2, -1, 12, 3, -8, -9, -2, 3, 8, -10, 3, 2, -6], "imageUrl": "https://upload.wikimedia.org/wikipedia/commons/0/0b/Feature_Learning_Diagram.png", "imageLicense": "CC BY-SA 4.0", "imageArtist": "Fgpacini"}, {"id": "6ce231df8f02", "title": "Pre-LN", "slug": "pre-ln", "headline": "Why is normalizing data like tuning instruments before a concert?", "summary": "What Pre-LN vs Post-LN means \u2014 where LayerNorm is placed relative to attention", "source": "What Pre-LN vs Post-LN means \u2014 where LayerNorm is placed relative to attention", "sourceUrl": "https://en.wikipedia.org/wiki/Normalization_(machine_learning)", "articleUrl": "https://en.wikipedia.org/wiki/Normalization_(machine_learning)", "publishedAt": "2026-07-03", "category": "learn", "cohortScore": 0.5, "embedding": [-1, 0, 2, -4, 5, 6, 6, -3, 10, -5, 2, 6, 5, 7, 3, 3, 4, -5, -3, 0, 3, 1, 2, -2, 6, 1, -8, -1, -7, -27, -1, -6, 9, -2, -6, -1, -3, 1, -1, 6, 3, 5, -2, -4, 1, -5, 2, -4, -5, -3, 2, -11, 1, 6, 0, 6, 2, 4, 3, 13, 0, -1, -18, 6, 0, 7, -6, -9, -7, 8, -1, 1, 1, 0, 8, 1, 1, -1, 1, -3, 7, 4, -1, -7, 8, 2, -4, -3, -3, -6, -9, -3, -7, 3, 3, -1, 4, 6, -2, 47, -5, 3, -1, 8, 4, -6, 2, 4, 0, 7, 5, -10, -1, -2, 1, 5, 4, 6, 8, -6, -3, -2, -2, -3, 7, -6, 2, 9, 0, 4, 4, 1, -9, -1, -3, -3, 6, -10, -2, -1, 1, 3, 1, -2, -12, 15, -7, -4, -4, 0, -7, 0, -4, -4, 2, 5, -4, 0, -2, 0, -4, -7, -6, 12, -10, -2, 0, -3, -5, -2, -3, -4, 0, -1, 5, 7, -7, -5, -4, -3, 7, -3, 2, -3, 0, 0, -3, 2, 2, 5, -10, -2, -1, -1, -3, 0, -1, 2, 1, -1, 0, 5, 0, -2, -8, 8, 1, -3, 9, 7, -7, -3, 0, 0, -2, -2, -4, 8, 2, 5, -4, 1, -5, -41, 6, 5, -2, 3, 3, 2, 2, 5, 3, 4, 3, -8, -3, 2, 6, 2, -5, 1, 1, -3, 4, -3, -11, 2, 1, 19, -7, 1, -2, -3, -1, -6, -4, 2, 0, 14, 7, -7, -5, -8, -1, 6, -10, -8, 5, -7, -3, -3, -5, 1, -4, 0, 1, 2, -4, -11, -6, -10, 3, 6, -4, -2, -12, 0, 4, -4, 4, 7, -2, -6, 8, -1, 2, 2, 1, -2, 0, -1, 13, 9, 5, 2, 2, -1, 3, 9, 1, 3, 5, -7, 6, -2, -11, 0, 1, -35, 5, 7, 4, 4, 7, -5, -3, -5, 2, -3, 4, 7, -4, -8, 2, 11, 0, 2, -1, -2, 3, 21, 0, -2, 0, 4, 4, 5, 1, 5, 11, 6, 1, 0, 4, -3, 1, 8, -5, -1, -3, -4, 3, 13, -1, 4, 1, -5, -3, -3, 0, -2, 1, 5, 1, 0, -3, 6, 2, 6, -5, 6, -3, -5], "imageUrl": "https://upload.wikimedia.org/wikipedia/commons/thumb/3/3a/Photograph-by-mikeCaiChen.jpg/1280px-Photograph-by-mikeCaiChen.jpg", "imageLicense": "CC0", "imageArtist": "Mike Cai Chen", "explanation": ["Imagine you're cooking with ingredients measured in different units, like cups and teaspoons. It would be chaotic trying to mix them without a common measuring system.", "Normalization in machine learning is like converting cups to teaspoons so all ingredients mix smoothly. It's about making sure data from different sources plays nicely together in a model."], "example": "A recipe calls for 2 cups of sugar and 1 teaspoon of salt. Converting cups to teaspoons (1 cup = 48 teaspoons), you get 96 teaspoons of sugar and 1 teaspoon of salt, making it easier to combine them.", "whyItMatters": "Normalization ensures different data features work together seamlessly in machine learning models."}, {"id": "c503c9956576", "title": "Pre-LN transformers are easier to train", "slug": "pre-ln-transformers-are-easier-to-train", "headline": "Pre-LN transformers use residual connections, allowing gradients to flow more smoothly during backpropagation", "summary": "Why Pre-LN transformers are easier to train \u2014 gradients flow more smoothly", "source": "Why Pre-LN transformers are easier to train \u2014 gradients flow more smoothly", "sourceUrl": "", "articleUrl": "", "publishedAt": "2026-06-12", "category": "learn", "cohortScore": 0.5, "embedding": [-6, -4, -1, 4, -1, 4, -3, 1, 8, -2, -4, -3, 3, 6, -2, 1, -1, 4, -7, -1, 4, -6, 3, -4, 7, -3, 2, -2, -1, -31, 1, 0, -2, 4, -3, 1, -3, 1, -7, 2, -3, 5, -2, -3, 4, -4, 1, -8, -1, -3, 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The arm needs to rotate smoothly to paint the circle perfectly.", "Think of the arm's movement as a point on a piece of paper. To rotate this point smoothly, we use a special math trick called a rotation matrix. This matrix helps us rotate the point by a certain angle, making the arm move in a circle."], "example": "If the arm's starting position is (1, 0) and it needs to rotate 90 degrees, the rotation matrix R(90\u00b0) = [ [0, -1], [1, 0] ] will transform the position to (0, 1).", "whyItMatters": "The rotation matrix R(\u03b8_i) rotates the robot arm's position smoothly, ensuring it paints a perfect circle."}, {"id": "0b63c7afc397", "title": "Her Alibi", "slug": "her-alibi", "headline": "Bruce Beresford directed Her Alibi", "summary": "What ALiBi does \u2014 adds linear bias to attention scores based on distance", "source": "What ALiBi does \u2014 adds linear bias to attention scores based on distance", "sourceUrl": "https://en.wikipedia.org/wiki/Her_Alibi", "articleUrl": "https://en.wikipedia.org/wiki/Her_Alibi", "publishedAt": "2026-06-12", "category": "learn", "cohortScore": 0.5, "embedding": [-7, -2, -2, 2, 2, 1, 9, -3, 8, 0, 3, 0, 5, 12, 5, 5, 6, 2, -5, 0, -2, -5, 8, -1, -4, 6, -6, -2, -10, -21, 1, 3, 12, 4, -4, -2, -7, 1, -2, 0, 2, 5, -2, -3, -7, -6, -6, -3, -6, -4, -3, -12, 2, 4, 5, 2, 1, 4, 0, 2, 6, 3, -12, 2, 9, 6, -9, -6, -5, -1, -8, 0, 7, 5, 0, 3, -1, -1, 1, -9, 2, 6, -6, -1, 9, 1, 3, 1, 6, -1, -5, -1, -5, -3, 0, -9, 4, -4, -7, 45, 1, -2, 1, -7, 7, -3, 8, -7, -2, 9, -1, -7, 6, 1, 3, 15, 3, 6, 7, -2, 0, 0, -3, -7, -1, -11, 3, 18, -1, -4, 4, -4, -7, 4, -2, 5, -1, 0, 8, -1, 0, 4, -1, 3, -5, 16, 5, 2, -5, -5, -3, -1, -6, -5, -5, 6, -3, 4, 0, 9, 1, 1, -9, 8, -1, -2, 3, -2, -3, 0, 2, -5, -2, 8, -2, -4, -3, 9, 0, 1, 2, -7, -5, 1, 1, -3, 2, -5, 1, 9, -7, 1, 0, -1, -2, -7, -1, 1, -10, 4, -2, 0, -12, -4, 7, 3, 2, -5, 12, 3, -6, -3, -4, 2, -11, -8, 1, 3, 2, -2, -5, 4, -4, -41, -2, 3, 0, 0, -7, 0, 2, 11, 14, -2, -5, -8, -2, 1, -2, -7, 5, -3, 3, 1, 4, 2, -3, -2, -2, 18, 1, -4, 2, -4, 4, 5, -6, 1, -4, 6, -4, -9, 4, -9, -3, 3, -7, -13, -1, 2, 6, 3, 6, 6, -8, 3, -4, -2, -5, -7, 2, -6, 7, -1, -8, 0, -2, 5, 0, 1, 0, 2, 2, -1, 8, -1, -2, 4, 0, 13, -1, -4, 2, 14, 7, -1, -4, 4, 2, 5, -6, 7, 3, 0, -3, -10, -8, -2, 1, -35, 0, 2, 6, 4, -1, 6, -4, 0, -1, -2, -1, 3, -8, -5, 2, 8, -2, 5, 0, -2, 7, 20, -6, 3, -6, 0, -8, 0, -2, 4, 5, 6, -2, -4, 6, -4, 7, 5, 0, 1, -1, -1, -3, 15, 8, 1, 0, -2, 0, -7, -1, 9, 3, 2, 5, 1, 8, -1, 0, -4, -1, 6, 7, 1], "explanation": ["Her Alibi is a film directed by Bruce Beresford. The movie was released in 1989 and is categorized as a romantic comedy. It features actors such as Tom Selleck and Paulina Porizkova in its cast."], "example": "Her Alibi, starring Tom Selleck and Paulina Porizkova, was directed by Bruce Beresford.", "whyItMatters": "Understanding who directed Her Alibi helps in identifying the film's creative vision and style.", "imageUrl": "https://upload.wikimedia.org/wikipedia/commons/d/d7/XFCE-4.10-Desktop.png", "imageLicense": "GPL", "imageArtist": "Xfce Development Team"}, {"id": "dc6ffc1546f6", "title": "ALiBi allows length extrapolation better than learned position embeddings", "slug": "alibi-allows-length-extrapolation-better-than-learned-position-embeddings", "headline": "ALiBi uses relative positional encoding, avoiding fixed-size embeddings, enabling better handling of variable-length sequences", "summary": "Why ALiBi allows length extrapolation better than learned position embeddings", "source": "Why ALiBi allows length extrapolation better than learned position embeddings", "sourceUrl": "", "articleUrl": "", "publishedAt": "2026-06-12", "category": "learn", "cohortScore": 0.5, "embedding": [-8, -3, -2, -3, -1, 8, -7, -2, 11, 1, -2, -10, 2, 10, 6, 0, -3, 13, -1, -3, 2, -8, 4, -8, -11, 4, -4, -5, -4, -28, 3, 5, 8, 2, -2, -1, -12, 4, -3, 3, 3, 9, -3, -7, -1, -7, -3, -3, -8, 6, 1, -3, -2, 11, 4, -1, 4, 6, -3, -1, 2, 2, -10, 6, 3, 7, -3, 3, 1, 2, -1, -6, -2, 9, 0, 4, 5, 2, -4, -7, 1, -5, 2, -3, 3, -8, -3, -3, -1, 3, -5, -2, -5, 5, -1, -4, 6, 5, -2, 47, 0, 4, 2, -5, 7, -4, -3, 2, -8, 3, -9, 3, -2, 3, 3, 8, 5, 2, -2, 1, -5, -1, -9, -1, 0, -13, -1, 11, 5, 7, 1, 6, -4, 5, -5, 6, -1, -2, 4, -2, -4, 1, 2, 3, -9, 13, -8, 1, -11, -4, -3, 5, 2, -4, 2, 9, 2, -2, -11, 0, -3, -2, -6, 9, -2, -11, 1, -5, 5, 2, 5, -5, 1, 3, -1, 3, -9, 1, 3, 9, -2, -10, 0, 3, 1, -1, 2, 0, 0, 3, -2, 4, -4, 2, -1, -9, 1, 5, -4, 0, 6, 4, -4, 1, -1, -5, 5, -2, 5, 8, -5, -7, -1, -3, -2, -4, 0, 7, 3, -6, -7, -1, 1, -40, 3, 0, 0, 2, -12, -1, 7, 6, 3, -3, -7, -8, -7, -5, 3, 6, 5, -2, 6, -5, 4, -3, -7, 9, -1, 22, 1, 5, 0, -4, 2, 1, -4, 7, -2, 6, -6, 3, -1, -5, -5, 3, -5, -2, -2, -9, 3, -1, 5, 4, -6, 8, -9, 1, -2, 1, -2, 0, 2, 1, -10, 0, -4, 5, 0, -1, -2, 1, 2, -5, 7, -1, 2, 6, -3, 5, 6, -5, -3, 11, 4, 10, 0, 7, 6, 7, 3, 2, 5, 1, 6, -11, -2, 5, -1, -33, 7, 8, 4, -3, 4, 5, -6, 1, 0, -9, 0, 7, -3, -3, 5, 10, -8, 7, -2, 0, 7, 20, -5, -2, -6, -5, -9, 1, -6, -2, 3, 4, 0, -4, 12, -3, 5, 1, 1, 6, -7, 2, 0, 7, 9, 3, 5, 0, -1, -1, -3, 4, 0, 6, 4, -3, -1, -7, -1, 5, -7, 2, 1, -2], "imageUrl": "https://upload.wikimedia.org/wikipedia/commons/thumb/8/82/Geoffrey_Hinton_in_2026.jpg/1280px-Geoffrey_Hinton_in_2026.jpg", "imageLicense": "CC BY-SA 4.0", "imageArtist": "Cmichel67"}]}