Coding Grandmaster · project 39 of 46 · premium, free for now

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.

Learn

A smarter way to train: start with a guess, then nudge the parameter in the direction that lowers the error. The gradient says which way is uphill: for the line y = m × x it is (2 ÷ n) × the sum of (m × x − y) × x. Move m a small step against it, scaled by a learning rate. Repeat, and the error slides down like a ball rolling into a valley. Too big a learning rate overshoots; too small crawls.

Your task

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.

Stretch challenge

Set lr = 0.2 and watch the error grow instead of shrink. Why?

← Training by searching The straight-line formula →

Python

Press Run to see what your program prints.

Keep going in Coding Grandmaster

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.

Start →38

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.

Start →40

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).

Start →42

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.

Start →

Practise the idea

🚀 Play Orbit Slingshot

Launch a probe through real gravity. Curve around planets, moons and black holes to reach the portal.

Play now

FAQ

Gradient descent: common questions

I am stuck. What can I do?

Press Hint for a nudge, read the message next to each goal, and compare your code with the lesson text. If you still need it, Show answer reveals a model solution. Try to type it yourself rather than copy it.

Does my work get saved?

Your ticks and XP are saved in this browser, and in your account if you log in. The code you type is not stored on a server.

Start a conversation

Enjoying coding? Meet a teacher.

Tell us the learner's age, country and what they would like to build, and we will suggest a class. A parent or guardian can make the enquiry.

Tell us the learner’s age or grade and goals
We’ll suggest a suitable class or learning path
We’ll confirm format, timing and fees with a parent or guardian

Play it, don't just read it

Write some code right now

Free games that need no sign-up. Pick one and play for five minutes.

All free games →

Pick a game

Today's maths challengeFive questions · the same for everyone today · keep your streak goingPlay