Chapter 2. Before we begin: the mathematical building blocks of neural networks


This chapter covers

  • A first example of a neural network
  • Tensors and tensor operations
  • How neural networks learn via backpropagation and gradient descent

Understanding deep learning requires familiarity with many simple mathematical concepts: tensors, tensor operations, differentiation, gradient descent, and so on. Our goal in this chapter will be to build your intuition about these notions without getting overly technical. In particular, we’ll steer away from mathematical notation, which can be off-putting for those without any mathematics background and isn’t strictly necessary to explain things well.

To add some context for tensors and gradient descent, we’ll begin the chapter with a practical example of a neural network. Then we’ll go over every new concept that’s been introduced, point by point. Keep in mind that these concepts will be essential for you to understand the practical examples that will come in the following chapters!

After reading this chapter, you’ll have an intuitive understanding of how neural networks work, and you’ll be able to move on to practical applications—which will start with chapter 3.

2.1. A first look at a neural network

2.2. Data representations for neural networks

2.3. The gears of neural networks: tensor operations

2.4. The engine of neural networks: gradient-based optimization

2.5. Looking back at our first example