This chapter introduces deep learning concepts and their implementation using Julia's primary deep learning library, Flux.jl. Building upon your understanding of machine learning, we will now focus on neural networks, a class of models that have driven significant advancements in fields like image recognition and natural language processing.

You will learn to:

• Review the fundamental components of neural networks, such as layers, activation functions like the sigmoid $\sigma(x) = \frac{1}{1 + e^{-x}}$, and common architectures.
• Get started with Flux.jl, understanding its core data structures like tensors and how to define network layers.
• Construct feedforward neural networks.
• Define appropriate loss functions, for instance, the mean squared error $L = \frac{1}{N}\sum_{i=1}^{N}(y_i - \hat{y}_i)^2$, and select optimizers for training.
• Understand the training loop, including forward propagation, backpropagation, and weight updates.
• Learn about Zygote.jl for automatic differentiation, a key component enabling gradient-based optimization in Flux.jl.
• Work with gradients during the model training process.

By the end of this chapter, you will be prepared to build and train basic neural network models in Julia using Flux.jl.