part_foundation_learning.qmd

# Foundations of Learning {#sec-foundations-of-learning}

Learning is one of the key components of a computer vision system. In these chapters, we cover the foundations of machine learning from a general perspective but explore examples using vision problems.

## Outline

- **Chapter @sec-intro_to_learning** introduces the basic principles of machine learning.

- **Chapter @sec-gradient_descent** describes how to learn the parameters that fit a model to data.

- **Chapter @sec-problem_of_generalization** describes the difference between fitting to training data and generalizing to test data, and the new considerations that arise given this difference.

- **Chapter @sec-neural_nets** introduces neural networks, a general family of models common in both biological and artificial vision systems.

- **Chapter @sec-neural_nets_as_distribution_transformers** presents neural networks as functions that apply a series of geometric transformations to a data distribution.

- **Chapter @sec-backpropagation** describes the backpropagation algorithm for calculating the gradient of a neural network with respect to its parameters.

## Notation

- The algorithms we will see apply to many kinds of signals, not just images. Therefore, in this part we will use $\mathbf{x}$ to represent model inputs rather than ${\boldsymbol\ell}$. A model's final output will usually be represented by $\mathbf{y}$.
  
- Neural networks consist of a sequence of layers that perform a sequence of transformations $\mathbf{x}_0 \rightarrow \mathbf{x}_1 \rightarrow \ldots \rightarrow \mathbf{y}$. When we consider a single layer in isolation, we will generically refer to its input as ${\mathbf{x}_{\texttt{in}}}$ and its output as ${\mathbf{x}_{\texttt{out}}}$. We will also use the variables $\mathbf{h}$ and $\mathbf{z}$ to represent certain kinds of intermediate representations in neural nets, which will be defined when they are first used.