Second-order methods converge faster due to quadratic convergence but are expensive due to O(n³) per iteration
Image: Hans Hillewaert, CC BY-SA 4.0, via Wikimedia Commons
Second-order methods converge faster due to quadratic convergence but are expensive due to O(n³) per iteration
Linear multistep method
Why does skipping steps save time but lose accuracy?
approximation algorithms guarantee: solution within factor α of optimal
Can we always find the best solution quickly?
Overlapping subproblems
Ever calculated a huge Fibonacci sequence by hand?
the momentum term does: v_t = βv_{t-1} + ∇L, accumulates gradient direction
Momentum term accelerates convergence in the gradient direction
ill-conditioned matrices cause numerical instability: small input changes → large output changes
Small changes can lead to huge errors in math
Strength reduction
Why do computers sometimes get tired of doing the same math over and over?
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