Calculus & Optimization

Derivatives, gradients, the chain rule, and gradient descent built by hand before autograd does it for you.

Module 01.2 · Beginner
Free

12h · 9 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: you differentiate scalar functions, then vector functions, then a two-layer network on paper, and only then write the autograd engine that does it for you.

The optimization half covers why gradient descent works, why it stalls, and what momentum, RMSProp and Adam each fix — so that when a loss curve goes flat you have a hypothesis rather than a shrug.

After this module you can

9 lessons

Lesson 1
Derivatives, and what a gradient points at
Kind
Concept
Length
45 min
Lesson 2
Partial derivatives, Jacobians and Hessians
Kind
Concept
Length
55 min
Lesson 3
The chain rule as a graph
Kind
Concept
Length
50 min
Lesson 4
Backprop by Hand: differentiate the network
Kind
Interactive
Length
35 min
Lesson 5
Build a tiny autograd engine
Kind
Lab
Length
100 min
Lesson 6
Gradient descent, learning rates and convergence
Kind
Concept
Length
50 min
Lesson 7
Momentum, RMSProp, Adam: what each one fixes
Kind
Concept
Length
55 min
Lesson 8
Convexity, saddle points and local minima
Kind
Concept
Length
40 min
Lesson 9
Checkpoint: read the loss curve
Kind
Checkpoint
Length
25 min

The challenge: Backprop by Hand

A network is drawn as a graph. Propagate the gradient node by node against the clock; your answer is checked against autograd to four decimal places.

Worth 450 XP.

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