Introduction

Deep learning begins with a simple habit: always know what each array means and what shape it has.

A neural network does not receive ideas directly. It receives numbers arranged into arrays. A row may describe one house, one token, one image patch, or one training example. A column may describe one feature. A later axis may describe time, height, width, channels, heads, or hidden units.

The names change from problem to problem. The discipline is the same.

In this chapter, we will use small arrays and visible arithmetic. The goal is to make these questions routine:

• What does one entry mean?
• Which axis counts examples?
• Which axis stores features?
• Which shapes can multiply?
• Which shape should come out?

That may sound modest. It is not. Many deep learning errors begin as shape errors.

By the end of the chapter, tensors should feel like organized data, not a special object that only libraries understand.