The interactive film is in the book's Companion

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Taylor Expansion, One Term at a Time

Chapter 11 · Mathematics for AI and Machine Learning · Advanced · 1:32

An interactive live film: the Taylor sheet grows from a flat plane to order five, term by term, and the region where it fits grows with it; pick the order and the point yourself.

Narration

Here is the surface from this chapter's figure, f equals three x times e to the minus x squared minus y squared, and a point a on it.

Order zero keeps only the value f of a: a flat red plane. It matches the surface at a, and nowhere else.

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

More from Chapter 11

Interactive1:54Backpropagation, One VJP per LayerChapter 11Preview1:27Partial Derivatives Are Two SlicesChapter 11Preview1:34The Gradient Is the Steepest DirectionChapter 11Preview1:42Jacobian Matrix: Linearizing a MapChapter 11Preview1:43The Derivative of the Matrix InverseChapter 11Preview1:54Forward or Reverse: Filling the JacobianChapter 11Preview1:30Second-Order Taylor: Where the Quadratic Model Can Be TrustedChapter 11Preview1:38A Hessian-Vector Product from Two GradientsChapter 11Preview1:34The Gauss–Newton MatrixChapter 11Preview1:44Hessian Matrix: Bowls, Saddles and Curvature DirectionsChapter 11Preview1:37Why the Hessian Is SymmetricChapter 11Preview1:26The Newton Step: Jumping to the Taylor Bowl's BottomChapter 11Preview2:36Corners, Maxima and Steps in the Chain RuleChapter 11Preview1:59GPTQ: Rounding with the HessianChapter 11Preview2:12AWQ: Activation-Aware Weight QuantizationChapter 11Preview1:41The Implicit Function TheoremChapter 11