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Outcome School · ML foundations and math15 min read

by Amit Shekhar · 6 April 2026

Math Behind Backpropagation

The math behind backpropagation in neural networks.

2,928 words#math#llm#ai#machine-learning4 recall cards

Math Behind Backpropagation
Read on Outcome School ↗then come back to lock it in
Before you read, guess

What mathematical concept must be understood before diving into backpropagation?

Ten seconds, a guess, then read — a wrong guess still makes the answer stick.

What this article covers

  1. What is Backpropagation?
  2. The Chain Rule of Calculus
  3. Forward Pass
  4. Loss Calculation
  5. Backward Pass (Backpropagation)
  6. Step-by-Step Numeric Example
  7. Weight Update Using Gradient Descent
  8. Backpropagation in Python

The article lives on outcomeschool.com. Read it there, then come back: the tutor in the margin has read it and will answer questions, and the questions below check what stayed.

Before you go

In one sentence, what was this chapter about?

From memory, without scrolling up. Writing it is what makes it yours; the grade is only to show you what you had.

How sure?