Week 2 Part I · Foundations

Tensors & Data Representation

Tensor operations, shapes, broadcasting, devices; representing images, text, and tabular data as tensors.

Learning goals

Manipulate tensors fluently (reshape, permute, reduce, index).
Reason about shapes, broadcasting, and device placement.
Encode real data into correctly shaped tensors.

This is the weekly homework lab, completed independently after the lecture and the practice lesson. It follows the course's Build / Predict & probe / Explain & defend model: use an AI assistant freely for the Build; the graded learning is in Predict and Explain. See the AI-use policy and a fully worked sample submission.

⚙Exercise

Part A · AI assistant welcomeBuild

Implement a set of tensor manipulations (reshape, permute, broadcasting, reductions, indexing) with an AI assistant's help.
Encode a small dataset (a few images and a small table) into tensors with the right dtype and device.

Part B · student reasoningPredict & probe

Predict the output shape of the eight provided broadcasting and reshape expressions before running them.
Predict which operations return a view versus copy memory.

Part C · in plain languageExplain & defend

Explain the three expressions whose result shape is surprising, and why broadcasting produced it.
Fix a seeded shape-mismatch bug and explain its root cause.

✓Deliverables

A notebook with the operations and a predicted-versus-actual shape table.
The fixed bug with a one-paragraph explanation.

Hints.

Print .shape and .dtype often; broadcasting aligns dimensions from the trailing axis.
.view needs contiguous memory; .reshape may copy.

❓Self-check

Answer each before expanding it. If one is unclear, revisit the lab and the references.

State the broadcasting rule.

Shapes align from the trailing dimension; each pair of sizes must be equal or one of them 1.

What is the difference between .view and .reshape?

.view needs contiguous memory and shares storage; .reshape may copy.

What is the conventional shape of a batch of images in PyTorch?

(N, C, H, W): batch, channels, height, width.

How is a tensor moved to the GPU?

tensor.to(device), with device chosen from torch.cuda.is_available().

Why does a tensor's dtype matter?

Layers and losses expect specific types (e.g., float32 inputs, long class indices).

Instructor lesson plan (with references)