4 – Layers

Neural networks have a certain special architecture with layers. The first layer is called the input layer, which contains the inputs, in this case, x1 and x2. The next layer is called the hidden layer, which is a set of linear models created with this first input layer. And then the final layer is called the output layer, where the linear models get combined to obtain a nonlinear model. You can have different architectures. For example, here’s one with a larger hidden layer. Now we’re combining three linear models to obtain the triangular boundary in the output layer. Now what happens if the input layer has more nodes? For example, this neural network has three nodes in its input layer. Well, that just means we’re not living in two-dimensional space anymore. We’re living in three-dimensional space, and now our hidden layer, the one with the linear models, just gives us a bunch of planes in three space, and the output layer bounds a nonlinear region in three space. In general, if we have n nodes in our input layer, then we’re thinking of data living in n-dimensional space. Now what if our output layer has more nodes? Then we just have more outputs. In that case, we just have a multiclass classification model. So if our model is telling us if an image is a cat or dog or a bird, then we simply have each node in the output layer output a score for each one of the classes: one for the cat, one for the dog, and one for the bird. And finally, and here’s where things get pretty cool, what if we have more layers? Then we have what’s called a deep neural network. Now what happens here is our linear models combine to create nonlinear models and then these combine to create even more nonlinear models. In general, we can do this many times and obtain highly complex models with lots of hidden layers. This is where the magic of neural networks happens. Many of the models in real life, for self-driving cars or for game-playing agents, have many, many hidden layers. That neural network will just split the n-dimensional space with a highly nonlinear boundary, such as maybe the one on the right.

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