Continuous Function

Domain

Calculus

Rates of change and how they combine: derivatives, the chain rule, Jacobians and Taylor approximation, and the reverse-mode differentiation that makes backpropagation efficient.

4 notebooks4 demos
Start with DerivativesSearch concepts
Preview the recommended route
First notebookDerivatives

Start here. Make one prediction, then note what carries over to the next notebook.

f(x)dxdf/dxlocal change
Open first notebook
QuestionWhat carries over from Derivatives into Computation Graphs?
PredictionBefore opening the first demo, predict which quantity changes first.
Demos4 interactive demos in this domain
Before moving onSay in one sentence how the idea works before going to the next notebook.
LearnerWhich notebook should I read first?

Read the first notebook, make one prediction in its demo, then go on to the next.

Open the first notebook

Recommended route

Read these in order: each notebook comes after the notebooks in this domain that it builds on, and the label beside it gives its level. A prerequisite with no page here yet is marked as outside reading. A notebook is left out of the route only when a prerequisite has neither a page here nor a named outside reading; the full list below marks it.

  1. 01
    Derivatives

    The derivative is an instantaneous rate of change: the slope you get when a secant line becomes a tangent line.

    Introductory14 mincodedemoafter Functions (outside reading)
  2. 02
    Computation Graphs

    A computation graph breaks a calculation into nodes so values flow forward and sensitivities flow backward.

    Introductory13 mincodedemoafter Derivatives, Chain Rule (outside reading)

    Computation Graphs builds directly on Derivatives.

  3. 03
    Reverse-Mode Automatic Differentiation

    Reverse-mode autodiff computes gradients by sending sensitivities (cotangents) backward through a computation graph, so one backward pass gives the gradient of a scalar loss.

    Intermediate14 mincodedemoafter Computation Graphs

    Reverse-Mode Automatic Differentiation builds directly on Computation Graphs.

  4. 04
    Backpropagation

    Backpropagation applies reverse-mode autodiff to neural networks so one scalar loss can train many parameters.

    Intermediate15 mincodedemoafter Reverse-Mode Automatic Differentiation

    Backpropagation builds directly on Reverse-Mode Automatic Differentiation.

All notebooks

Every published notebook in this domain.

Derivatives

The derivative is an instantaneous rate of change: the slope you get when a secant line becomes a tangent line.

Introductory14 mindemo

Computation Graphs

A computation graph breaks a calculation into nodes so values flow forward and sensitivities flow backward.

Introductory13 mindemo

Reverse-Mode Automatic Differentiation

Reverse-mode autodiff computes gradients by sending sensitivities (cotangents) backward through a computation graph, so one backward pass gives the gradient of a scalar loss.

Intermediate14 mindemo

Backpropagation

Backpropagation applies reverse-mode autodiff to neural networks so one scalar loss can train many parameters.

Intermediate15 mindemo