The interactive film is in the book's Companion

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Memory by Orthogonal Projection (HiPPO)

Chapter 20 · Mathematics for AI and Machine Learning · Advanced · 1:26

An interactive live film: a signal summarized by its Legendre coefficients, which follow the HiPPO linear ODE; raise the number of coefficients and the rebuilt history becomes exact.

Narration

The blue curve is an input arriving over time. A sequence model must summarize everything it has seen in a state of fixed size N.

The best polynomial summary of the history is its orthogonal projection onto the first N Legendre polynomials, stretched over the time seen so far. The orange curve is the history rebuilt from those N numbers.

The rest of the narration is in the book's Companion.

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