---
title: "Learning representations by back-propagating errors"
description: "Back-propagation asks how a hidden layer can learn useful features when a teacher specifies only the desired output. Read it to see how a forward pass stores activations, an output mismatch travels backward as chained derivatives, and each connection receives a local weight update that can organize hidden units around the task's structure."
canonical_url: "https://fanout.sh/daily/2026-09-07-backpropagation-hidden-representations"
md_url: "https://fanout.sh/daily/2026-09-07-backpropagation-hidden-representations.md"
last_updated: "2026-09-07"
access: "public"
---

# Learning representations by back-propagating errors

Back-propagation asks how a hidden layer can learn useful features when a teacher specifies only the desired output. Read it to see how a forward pass stores activations, an output mismatch travels backward as chained derivatives, and each connection receives a local weight update that can organize hidden units around the task's structure.

## Paper details

- Authors: David E. Rumelhart, Geoffrey E. Hinton, and Ronald J. Williams

- Venue: Nature 1986

- Track: AI Research

- Difficulty: Easy

- Reading time: 30 min

- Original paper: https://doi.org/10.1038/323533a0

## What you will learn

- Why hidden units create a credit-assignment problem: unlike output units, they have no teacher-provided target state.

- How the chain rule sends output-error derivatives backward through the same weighted connections and produces a gradient for every weight.

- What the mirror-symmetry and family-tree examples demonstrate, and why local minima, biological plausibility, historical priority, and missing reproduction details still limit the claim.

## Continue exploring

[Explore backpropagation in Fanout](https://fanout.sh/knowledge-graph?node=ai-research%3Aconcept%3Abackpropagation): Connect the paper's two-pass derivative procedure to Fanout's backpropagation node, chain rule, gradient descent, activation functions, and from-scratch neural-network path.

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