4 of 4 written

Matrix Calculus & Autodiff

How gradients actually get computed for learning and differentiable simulation, through matrix calculus, forward vs reverse-mode AD, backprop, and differentiating a physics step.

Part 0

Matrix Calculus

Matrix Calculus: Gradients and Jacobians

Differentiating vector and matrix expressions cleanly, the algebra behind every gradient in learning and control.

matrix calculus

Part 1

Automatic Differentiation

Automatic Differentiation: Forward vs Reverse

The computational graph, and why reverse mode is cheap for scalar losses while forward mode is cheap for few inputs.

autodiff

Part 2

Backpropagation

Backpropagation, Step by Step

Reverse-mode AD on a small network, worked through with real numbers.

backpropagation

Part 3

Differentiable Simulation

Differentiating Through a Simulator

The adjoint method and the implicit function theorem, how you get gradients through a physics step.

adjoint