Great visualizations. Really enjoyed having a well-written example where mathematical proofs directly help with understanding a practical application.

I wonder what would happen with this analysis if a momentum term was added to the gradient descent. It seems that it would fix the specific failure modes in the examples, but I wonder if there's a corresponding mathematical way of categorizing what kinds of functions can(not) be quickly optimized with GD + momentum.

The animation is very good, making the article easy to understand

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