Calculus & Optimization

Derivatives, integrals, gradients and the descent that uses them, ending at Newton's method.

Module 01.3 · Beginner
Free

9h · 11 lessons · 1 challenge

Before this: Linear Algebra for Machine Learning

About this module

Backpropagation is the chain rule applied to a graph, and nothing more. This module makes that literal: single-variable derivatives, then the chain rule, then integration, then the multivariable versions, then gradient descent, and only then the autograd engine that does it for you.

The second-order half comes last, as the source course orders it: curvature, the Hessian, convexity and Newton's method, which is what tells you why a loss curve goes flat.

After this module you can

11 lessons

Lesson 1
1Derivatives, and what a gradient points at
Kind
Concept
Length
45 min
Lesson 2
2The chain rule as a graph
Kind
Concept
Length
50 min
Lesson 3
3Integrals, the fundamental theorem and areas under curves
Kind
Concept
Length
50 min
Lesson 4
4Partial derivatives, gradients and the Jacobian
Kind
Concept
Length
50 min
Lesson 5
5Gradient descent, learning rates and convergence
Kind
Concept
Length
50 min
Lesson 6
6Backprop by Hand: differentiate the network
Kind
Interactive
Length
35 min
Lesson 7
7Build a tiny autograd engine
Kind
Lab
Length
100 min
Lesson 8
8Second derivatives, curvature and the Hessian
Kind
Concept
Length
45 min
Lesson 9
9Convexity, saddle points and local minima
Kind
Concept
Length
40 min
Lesson 10
10Newton's method and second-order optimization
Kind
Concept
Length
45 min
Lesson 11
11Checkpoint: read the loss curve
Kind
Checkpoint
Length
25 min

The challenge: Backprop by Hand

Differentiate a two-layer network on paper, node by node, then check yourself against autograd. Scored on how far you get before you need a hint.

Worth 400 XP.

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