--- title: "Neural network; back-propagation" subject: "Artificial Intelligence" chapter: 6 key: "semester_6/artificial_intelligence:neural-network-bp-algorithm" source: https://www.bctengineer.com/q/semester_6/artificial_intelligence/neural-network-bp-algorithm site: BCT Engineering --- # Neural network; back-propagation Artificial Intelligence · Chapter 6: Machine Learning - Asked in: 2070 Bhadra, 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/neural-network-bp-algorithm - Whole chapter: https://www.bctengineer.com/md/semester_6/artificial_intelligence/chapter-6 ## Question What is neural network? Explain back-propagation algorithm learning. ## Short answer A neural network is interconnected processing units with adjustable weights. Back-propagation is a supervised gradient-descent method that minimizes squared error by propagating output errors backward to update weights. For a 2-2-1 network, one update raised output from 0.7157 to 0.7267. ## Answer An **artificial neural network** is a network of simple, interconnected processing units (neurons) with adjustable weights. Each neuron computes the weighted sum of its inputs and applies an activation function. A network has an input layer, hidden layer(s) and an output layer. It learns from examples by changing weights. #### Back-propagation learning Back-propagation is a supervised learning method for multilayer feed-forward networks. It uses gradient descent to minimise the squared error E = ½ Σ (t − y)² between target and actual output. ```text input --> hidden --> output --> error = t - y ^ | +----- weights adjusted <-----------+ (error propagated backwards) ``` #### Steps 1. Initialise weights and biases to small random values; choose learning rate η. 2. **Feed-forward:** for an input pattern, compute hidden outputs h_j = f(Σ w_ij x_i + b_j), then output y_k = f(Σ v_jk h_j + b_k), with f(z) = 1/(1 + e^(−z)). 3. **Output error:** δ_k = (t_k − y_k) y_k (1 − y_k). 4. **Back-propagate to hidden layer:** δ_j = h_j (1 − h_j) Σ_k δ_k v_jk. 5. **Update weights:** v_jk ← v_jk + η δ_k h_j; w_ij ← w_ij + η δ_j x_i (biases similarly). 6. Repeat steps 2-5 for all patterns; stop when the total error is below a tolerance or after a set number of epochs. #### Small example (verified) 2-2-1 network, x = (1, 0), t = 1, η = 0.5, initial weights 0.5, 0.4, 0.3, 0.2 (input to hidden), biases 0.1, hidden-to-output 0.6, 0.7, output bias 0.1. Forward pass gives h = (0.6457, 0.6225), y = 0.7157; δ_output = 0.0579; δ_hidden = (0.0079, 0.0095). Updated output weights are 0.6187 and 0.7180; the new output for the same input is 0.7267, closer to the target 1. **Features:** handles non-linear problems such as XOR; **drawbacks:** local minima, slow training, needs a large labelled data set. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What does each neuron in a neural network compute? A. The weighted sum of its inputs plus bias passed through an activation function B. The maximum of its inputs C. The product of all weights D. Only the bias Answer: A. y = f(sum wi xi + b). (Key point: Neuron computation) 2. What does back-propagation minimise using gradient descent? A. The number of hidden layers B. The squared error E = 1/2 sum (t - y)^2 between target and output C. The learning rate D. The sum of the weights Answer: B. Weights are adjusted down the error gradient. (Key point: Cost minimized) 3. How does the error reach the hidden layer? A. delta_j = t - y copied directly B. delta_j = eta times x_i C. delta_j = h_j(1 - h_j) times sum of delta_k v_jk, i.e. output deltas propagated back through weights D. The hidden layer is not updated Answer: C. Errors are sent backwards weighted by v_jk. (Key point: Hidden delta) 4. Which is a drawback of back-propagation? A. It cannot solve XOR B. It needs no labelled data C. It works only with a single layer D. It may get stuck in local minima and train slowly Answer: D. BP does handle non-linear problems, but suffers local minima and slow training. (Key point: Drawbacks) ## Related in Artificial Intelligence - [Neural network, back-propagation, perceptron](https://www.bctengineer.com/question.md?key=semester_6%2Fartificial_intelligence%3Ann-bp-perceptron) — 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× - [Neural network; supervised vs unsupervised](https://www.bctengineer.com/question.md?key=semester_6%2Fartificial_intelligence%3Ann-supervised-unsupervised) — 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× ## Related in other subjects - [ANN and back propagation](https://www.bctengineer.com/question.md?key=semester_7%2Fdata_mining%3Aann-backpropagation) — Data Mining, chapter 3 - [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 - [Back-face detection algorithm](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_graphics%3Aback-face-detection-method) — Computer Graphics, chapter 7, asked 8×