Chapter 1: Introduction to Neural Networks

Welcome to the first chapter of our journey! In this chapter, we will introduce you to the fascinating world of neural networks. We will start with a brief overview of what neural networks are and how they work. We will then discuss why it's beneficial to build a neural network from scratch, and introduce the simple neural network that we will be building throughout this book. Finally, we will give you an overview of Python in Google Colab, the platform we will be using for our programming.

1.1: Brief Introduction to Neural Networks

Neural networks are a type of machine learning model that are designed to mimic the human brain. Just as our brain consists of interconnected neurons that work together to process information and make decisions, a neural network consists of artificial neurons, or "nodes", that are connected together and work in unison to process input data and make predictions.
Let's consider an analogy to understand this better. Imagine you're at a party and you're trying to identify a song that's playing. You might start by listening to the melody, then the lyrics, and finally the voice of the singer. Each of these steps can be thought of as a node in a neural network. The melody node takes the song as input and outputs a guess about what the song could be. This guess is then passed to the lyrics node, which refines the guess based on the lyrics of the song. Finally, the singer's voice node takes this refined guess and makes a final prediction about what the song is. This is essentially how a neural network processes input data to make a prediction.

1.2: Why Build a Neural Network from Scratch?

You might be wondering, "Why should I build a neural network from scratch when there are so many tools and libraries available that can do it for me?" Well, the answer is simple: understanding. By building a neural network from scratch, you will gain a deep, fundamental understanding of how neural networks work. This understanding is crucial if you want to be able to design, implement, and troubleshoot your own neural networks in the future.
Think of it like learning to drive. You could learn to drive by simply memorizing which pedals to press and when to turn the steering wheel. But if you understand how the car works, how the engine powers the wheels, how the brakes slow the car down, and how the steering system controls the direction of the car, you'll be a much better, more confident driver. The same principle applies to neural networks.

1.3: A Simple Neural Network: Key Elements and Design

The neural network that we're going to build in this book is a simple linear model. It consists of an input layer, a single node (or "neuron"), and an output layer. The input layer takes in data, the node processes the data, and the output layer produces a prediction.
Let's go back to our party analogy. This time, you're trying to guess the age of a person based on their height. The height of the person is the input data. Your brain processes this data and makes a guess about the person's age. This guess is the output, or prediction, of the neural network.
The key elements of our neural network are the input data, the weights, and the output. The weights are like the brain's knowledge or experience. They determine how the input data is processed to make a prediction. We'll start with random weights, and then adjust them based on how accurate our predictions are. This process of adjusting the weights is known as "learning".

1.4: Python in Google Colab: An Overview

For our programming, we'll be using Python in Google Colab. Python is a popular programming language for machine learning due to its simplicity and the availability of robust libraries for scientific computing, such as NumPy, which we'll be using extensively.
Google Colab is a free, online platform that allows you to write and execute Python code right in your browser. It's like having a powerful computer at your disposal, no matter where you are or what device you're using. Plus, it comes with most of the popular Python libraries pre-installed, so you can start coding without any setup or installation.
In the next chapter, we'll dive into the basics of Python and NumPy. We'll cover Python syntax, variables, and data types, and we'll introduce you to the NumPy library and show you how to create and manipulate arrays of data. So, let's get started on this exciting journey into the world of neural networks and Python programming!