Coding Grandmaster · project 42 of 46 · premium, free for now

A perceptron learns AND

Train a perceptron on the AND truth table starting from zero weights, for the number of epochs, with each update using a learning rate of 1. Print the final weights and bias as w1 w2 b, then the four predictions.

Learn

The perceptron, from the 1950s, is the ancestor of neural networks. It multiplies each input by a weight, adds a bias, and outputs 1 if the total is above zero, otherwise 0. To learn, it checks each example: if it was wrong, it nudges each weight by the error × the input (error = target − output). Repeat over the examples a few times and, if a straight line can separate the answers, it finds the weights.

Your task

Stretch challenge

Change the data to the XOR table and watch it never settle. Why can't one perceptron learn XOR?

← Classifying by neighbours A single neuron →

Python

Press Run to see what your program prints.

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Predictions and error

Write predict(x, m, b) and mse(xs, ys, m, b). Print the prediction for each size and the mean squared error of the line with the given m and b, rounded to 2 decimal places.

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Training by searching

Try every m from 0 to 100 in steps of 5 and every b from 0 to 200 in steps of 10 with the same data. Print the best m, the best b and their error rounded to 2 decimal places.

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Gradient descent

Starting from m = 0, repeat steps times: compute the gradient, then do m = m - lr * gradient. Print the final m rounded to 4 decimal places and the final mean squared error rounded to 4.

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The straight-line formula

Compute the slope and intercept with these formulas, print them rounded to 3 decimal places, and print the prediction for new_x rounded to 2 places.

Start →41

Classifying by neighbours

Write classify(point, train, k): sort the training examples by distance to the point, take the k closest, and return the label that appears most among them (if tied, the label of the nearest one).

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Practise the idea

🔌 Play Logic Gate Challenge

Predict the output of AND, OR, XOR, NAND and NOR gates from their inputs.

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FAQ

A perceptron learns AND: common questions

I am stuck. What can I do?

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