Chapter 18. Neural Networks

I like nonsense; it wakes up the brain cells.

Dr. Seuss

An artificial neural network (or neural network for short) is a predictive model motivated by the way the brain operates. Think of the brain as a collection of neurons wired together. Each neuron looks at the outputs of the other neurons that feed into it, does a calculation, and then either fires (if the calculation exceeds some threshhold) or doesn’t (if it doesn’t).

Accordingly, artificial neural networks consist of artificial neurons, which perform similar calculations over their inputs. Neural networks can solve a wide variety of problems like handwriting recognition and face detection, and they are used heavily in deep learning, one of the trendiest subfields of data science. However, most neural networks are “black boxes”—inspecting their details doesn’t give you much understanding of how they’re solving a problem. And large neural networks can be difficult to train. For most problems you’ll encounter as a budding data scientist, they’re probably not the right choice. Someday, when you’re trying to build an artificial intelligence to bring about the Singularity, they very well might be.

Perceptrons

Pretty much the simplest neural network is the perceptron, which approximates a single neuron with n binary inputs. It computes a weighted sum of its inputs and “fires” if that weighted sum is zero or greater:

def step_function(x):
    return 1 if x >= 0 else 0

def perceptron_output(weights, 

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