Tensors, Batches, and Shapes

What this chapter does

Before a network can learn, data must have shape. This chapter teaches how to read tensors as organized numbers, distinguish batches from features, and predict basic layer output shapes.

Lessons

Read these in order.

Start with the chapter introduction, then move through the topic lessons. The order is chosen so each page can reuse ideas from the pages before it.

01
Introduction
Why shape reasoning belongs at the beginning of Deep Learning.
02
Scalars, Vectors, Matrices, and Tensors
Arrays as organized numbers, with shape as part of the meaning.
03
Batch and Feature Dimensions
How examples and features appear in the shapes used by neural layers.
04
Shape Notation and Axis Conventions
How to read tensor shapes by naming each axis before trusting the numbers.
05
Reshaping and Flattening
Changing array shape while preserving the number of entries.
06
Broadcasting
Reusing smaller arrays across compatible axes, especially for bias terms.
07
Parameters, Activations, and Outputs as Tensors
The tensor roles that appear inside a neural network computation.
08
Shape Debugging
Tracing expected and actual shapes to find the first mismatch.

Review and practice

Close the chapter deliberately.

Use the conclusion and revision notes before the chapter exercises. Hints and solutions are collected here, while lesson-level exercises reveal their own help inline.

Conclusion

What Chapter 1 established and how it prepares later neural layers.

Summary and Revision Notes

A compact review of tensors, batches, features, and shapes.

Exercises

Chapter-level practice for tensor and batch shape reasoning.

Hints

Low-spoiler nudges for the Chapter 1 exercises.

Solutions

Explained solutions for the Chapter 1 exercises.