Meet PyTorch & tensors

Step 1

Start with a real Python environment

Use Open in Colab above for the ready-to-run notebook. Sign in if prompted, connect to a runtime, and run the code cells from top to bottom with Shift + Enter. The default CPU is enough; no paid GPU or API key is needed for these examples. Colab availability and usage limits are controlled by Google. Save a copy to keep your changes.

Prefer your own computer? Follow the linked PyTorch installation guide for your operating system, using a virtual environment and the CPU option where offered. Download this lesson's Python file and run it with that environment's Python. In an existing notebook where import torch fails, run %pip install torch in a separate code cell, restart the kernel if asked, and run the lesson again.

Room310's standard Python cells do not include PyTorch. Do not paste these examples into the ordinary assignment runner. The complete lesson notebook includes all previous steps; it does not depend on another lesson's kernel state.

import torch

torch.manual_seed(7)
print("PyTorch:", torch.__version__)
print("A tensor on:", torch.tensor([1.0]).device)

Step 2

A tensor is an array with a shape

A tensor stores numbers with a shape. A scalar has no axes; a vector has one; a matrix has two. For our course, rows represent examples and columns represent features.

Here we have three examples, each with two features, so X.shape is [3, 2]. The single target for each example is stored as [3, 1]. Keep the column dimension: mixing predictions of shape [3, 1] with targets of shape [3] can accidentally broadcast into a [3, 3] calculation.

Use floating-point tensors for these inputs and targets. Not every task uses float targets—multiclass classification with CrossEntropyLoss usually uses integer class indices—but our binary examples will use floats.

X = torch.tensor([[1.0, 2.0], [3.0, 4.0], [5.0, 6.0]])
y = torch.tensor([[0.0], [1.0], [1.0]])

print("Input shape:", X.shape)
print("Target shape:", y.shape)
print("Input dtype:", X.dtype)
print("First example:", X[0])

Step 3

Run the same neuron on a whole batch

The @ operator is matrix multiplication, not element-by-element multiplication. [3, 2] @ [2, 1] produces [3, 1]: three predictions. The inner dimensions must match. This calculation replaces a Python loop over neurons and examples.

The scalar bias is broadcast across the three predictions. Broadcasting is convenient when intentional, but always inspect your shapes before relying on it.

weights = torch.tensor([[0.5], [1.0]])
bias = torch.tensor(0.25)
predictions = X @ weights + bias

print("Predictions:", predictions)
assert predictions.shape == y.shape
print("One prediction per target:", predictions.shape)