---
title: "Neural network, back-propagation, perceptron"
subject: "Artificial Intelligence"
chapter: 6
key: "semester_6/artificial_intelligence:nn-bp-perceptron"
source: https://www.bctengineer.com/q/semester_6/artificial_intelligence/nn-bp-perceptron
site: BCT Engineering
---

# Neural network, back-propagation, perceptron

Artificial Intelligence · Chapter 6: Machine Learning

- Asked in: 2072 Asoj, 2+4+4 marks
- Video: [Backpropagation in Neural Networks | Back Propagation Algorithm with Examples | Simplilearn](https://www.youtube.com/watch?v=ayOOMlgb320) — Simplilearn
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/artificial_intelligence/nn-bp-perceptron
- Whole chapter: https://www.bctengineer.com/md/semester_6/artificial_intelligence/chapter-6

## Question

What is a neural network? Explain the back propagation algorithms and perceptron.

## Short answer

A neural network is interconnected neurons with weighted links. Back-propagation trains multilayer networks by gradient descent, computing output error and propagating backward. A perceptron is a single neuron with step activation; its rule converges for linearly separable problems like AND but not XOR.

## Answer

#### Neural network
An **artificial neural network** is a set of simple processing units (neurons) connected by weighted links, organised in an input layer, hidden layer(s) and an output layer. Each neuron computes y = f(Σ wᵢxᵢ + b). The network learns by adjusting weights from examples.

#### Back-propagation algorithm
Back-propagation is the supervised gradient-descent method used to train multilayer feed-forward networks.
1. Initialise weights with small random values; choose learning rate η.
2. Forward pass: compute hidden outputs h_j = f(Σ w_ij x_i + b_j) and output y_k = f(Σ v_jk h_j + b_k), f(z) = 1/(1 + e^(−z)).
3. Output error: δ_k = (t_k − y_k) y_k (1 − y_k).
4. Hidden error: δ_j = h_j (1 − h_j) Σ_k δ_k v_jk (error sent backwards).
5. Update: v_jk ← v_jk + η δ_k h_j; w_ij ← w_ij + η δ_j x_i (biases likewise).
6. Repeat for all training patterns (epochs) until the total error ½ Σ (t − y)² is small.

Example (verified): for a 2-2-1 network, input (1,0), target 1, η = 0.5, one update raises the output from 0.7157 to 0.7267.

#### Perceptron
A **perceptron** (Rosenblatt) is a single neuron with a step activation:
y = 1 if Σ wᵢxᵢ + b > 0, else 0.
```text
 x1 --w1-->\
 x2 --w2--->( Σ + b )--> step --> y
```
**Learning rule:** w_i ← w_i + η (t − y) x_i, b ← b + η (t − y). It converges for linearly separable problems (AND, OR) but cannot learn XOR, which needs a hidden layer trained by back-propagation.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. What does each neuron compute?
   A. y = f(sum w_i x_i + b)
   B. y = the largest input
   C. y = sum of weights only
   D. y = b times x
   Answer: A. Weighted sum plus bias through an activation. (Key point: Neuron output)

2. What is delta_k in back-propagation?
   A. (t_k + y_k)
   B. (t_k - y_k) y_k (1 - y_k)
   C. y_k only
   D. (t_k - y_k) h_j
   Answer: B. Error times the sigmoid derivative. (Key point: Output delta)

3. What is the perceptron learning rule?
   A. w_i <- w_i * eta
   B. w_i <- w_i - x_i
   C. w_i <- w_i + eta (t - y) x_i and b <- b + eta (t - y)
   D. Weights set by outer product once
   Answer: C. Updates are proportional to the error. (Key point: Perceptron rule)

4. Why can't a perceptron learn XOR?
   A. XOR needs more than two inputs
   B. The step function cannot output 1
   C. Learning rate is too small
   D. XOR is not linearly separable; a hidden layer trained by back-propagation is needed
   Answer: D. A single neuron draws one straight line. (Key point: Perceptron limit)

## Related in Artificial Intelligence

- [Neural network; back-propagation](https://www.bctengineer.com/question.md?key=semester_6%2Fartificial_intelligence%3Aneural-network-bp-algorithm) — Artificial Intelligence, chapter 6
- [Role of perceptron in neural network](https://www.bctengineer.com/question.md?key=semester_6%2Fartificial_intelligence%3Aperceptron-role) — Artificial Intelligence, chapter 6, asked 2×
- [Perceptron; neural network as OR gate](https://www.bctengineer.com/question.md?key=semester_6%2Fartificial_intelligence%3Aperceptron-or-gate) — Artificial Intelligence, chapter 6, asked 2×
- [Perceptron; neural network as XOR gate](https://www.bctengineer.com/question.md?key=semester_6%2Fartificial_intelligence%3Aperceptron-xor-gate) — Artificial Intelligence, chapter 6, asked 2×
- [Neural network; supervised vs unsupervised](https://www.bctengineer.com/question.md?key=semester_6%2Fartificial_intelligence%3Ann-supervised-unsupervised) — Artificial Intelligence, chapter 6
- [Back propagation algorithm](https://www.bctengineer.com/question.md?key=semester_6%2Fartificial_intelligence%3Aback-propagation-algorithm) — Artificial Intelligence, chapter 6, asked 3×

## Related in other subjects

- [Short note: Neural network, perceptron rule](https://www.bctengineer.com/question.md?key=semester_7%2Fdata_mining%3Aneural-network-perceptron-note) — Data Mining, chapter 3
- [ANN and back propagation](https://www.bctengineer.com/question.md?key=semester_7%2Fdata_mining%3Aann-backpropagation) — Data Mining, chapter 3