convolution (f * g)(t) = ∫f(τ)g(t-τ)dτ

How do different shapes combine to create new patterns?

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) = ∫f(τ)g(t-τ)dτ 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.

Remember this

Convolution helps us understand how combining different functions (like mixing paints) results in a new function (a new shade).

Text adapted from Wikipedia, licensed under CC BY-SA 4.0.

Related concepts

mixup does: trains on convex combinations of pairs: x̃=λx_i+(1-λ)x_j

Ever wondered how to blend two colors perfectly?

Cosine similarity

Cosine similarity formula: cos(θ) = (A · B) / (||A|| ||B||)

Matryoshka embeddings are: trained to be useful at multiple truncated dimensions

Ever wondered how a simple doll can teach us about nested complexities?

random projection to O(log n/ε²) dimensions preserves pairwise distances within 1±ε

Can you shrink a 3D object into 2D without losing its shape?

Write the multi-head attention formula: MultiHead(Q,K,V) = Concat(head_1,...,head_h)W^O

Ever wondered how machines understand the importance of words in a sentence?

to use a CNN: for data with spatial structure like images or time series

Why can't we just feed all data into one big neural net?

Swipe through 100 ML concepts daily

Open Pocket Polymath