DAI developerLab· about 50 min· server sandbox

Lab: tensors, autograd and your first training loop

Compute gradients with autograd, compare with hand calculation, and train a linear model with a real loop.

Requires: Gradient descentMatrices and matrix multiplication

Theory

requires_grad=True tracks the tensor, .backward() fills .grad, gradients accumulate — zero them every step. torch.no_grad() turns off tracking when you update weights by hand.

Sub-tasks

gradient with autograd — grad_of(f, x0) returns df/dx at x0 using autograd, where f is a Python function on a tensor.
gd_steps — gd_steps(f, x0, lr, steps) does gradient descent on f with autograd and zeroes the gradient every step.
train_linear — train_linear(X, y, lr, steps) trains w, b (MSE) and returns (w, b).

Passes when: mse <= 0.05

The starter code

runs in an isolated sandbox on the server

import torch


def grad_of(f, x0):
    # TODO: x = torch.tensor(float(x0), requires_grad=True); y = f(x); y.backward(); return x.grad.item()
    ...


def gd_steps(f, x0, lr=0.1, steps=100):
    x = torch.tensor(float(x0), requires_grad=True)
    for _ in range(steps):
        # TODO: forward, backward, uppdatera under no_grad, nollställ grad
        ...
    return x.item()


def train_linear(X, y, lr=0.05, steps=500):
    w = torch.zeros(X.shape[1], requires_grad=True)
    b = torch.zeros(1, requires_grad=True)
    for _ in range(steps):
        # TODO: pred = X @ w + b; mse; backward; steg; nollställ
        ...
    return w.detach(), b.detach()

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Expected results

grad_of(lambda x: x**2 + 2*x, 3.0) = 8; gd_steps on (x−3)² reaches ≈3; a linear model on y = 2x + 1 + noise gives MSE < 0.05.

Common mistakes

Forgets zero_() → the gradient accumulates and the steps are wrong.
Updates weights without torch.no_grad() → autograd error.
.item() missing when a number should be returned.