The goal of this chapter is to introduce the basic principles of deep learning. If you already have lots of experience with deep learning, you should feel free to skim this chapter and then go on to the next. If you have less experience, you should study this chapter carefully as the material it covers will be essential to understanding the rest of the book.
In most of the problems we will discuss, our task will be to create a mathematical function:
Notice that $\mathbf{x}$ and $\mathbf{y}$ are written in bold. This indicates they are vectors. The function might take many numbers as input, perhaps thousands or even millions, and it might produce many numbers as outputs. Here are some examples of functions you might want to create:
$\mathbf{x}$ contains the colors of all the pixels in an image. $f\left(\mathbf{x}\right)$ should equal 1 if the image contains a cat and 0 if it does not.
The same as above, except $f\left(\mathbf{x}\right)$ should be a vector of numbers. The first element indicates whether the image contains a cat, the second whether it contains a dog, the third whether it contains an airplane, and so on for thousands of types of objects.
$\mathbf{x}$ contains the DNA sequence for a chromosome. $\mathbf{y}$ should be a vector whose length equals the number of bases in the chromosome. Each element should equal 1 if that base is part of a region that codes for a protein, or 0 if not.
$\mathbf{x}$ describes the structure of a molecule. (We will discuss various ways of representing molecules in later chapters.) ...
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