Theory of Intelligence
MATH FOR AI•Calculus•Multivariate Calculus•2.5 Useful Gradient Identities

Introduction

Gradients of linear and quadratic forms, trace and determinant identities, and the derivative of an inverse.

Introduction

Deriving every gradient entry by entry is slow. A small table of identities covers most of what appears in ML: linear models, quadratic losses, Gaussian likelihoods. Learn these and you can derive the normal equations, the Gaussian MLE, and many loss gradients in a few lines.

Convention below: gradients of a scalar with respect to a column vector x\mathbf{x} are written as columns (same shape as x\mathbf{x}), the convention most ML code uses.

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