AI News, A primer on universal function approximation with deep learning (in Torch and R)

A primer on universal function approximation with deep learning (in Torch and R)

Clarke famously stated that “any sufficiently advanced technology is indistinguishable from magic.” No current technology embodies this statement more than neural networks and deep learning.

This primer sheds some light on how neural networks work, hopefully adding to the wonder while reducing the fear.

Recall that given enough terms, a Taylor series can approximate any function to a certain level of precision about a given point, while a Fourier series can approximate any periodic function.

For sake of argument, let’s attempt to approximate this function with a network anyway.

In its most basic form, a one layer neural network with $latex $n input nodes and one output node is described by , where is the input, is the bias and is the weight matrix.

In Torch, this network can be described by After training, we can apply the training set to the model to see what the neural network thinks looks like.

Before you lose faith in artificial neural networks, let’s understand what’s happening.

In the output layer we have a new weight matrix and bias term applied to .

The choice for ranges from the sigmoid to tanh to the default rectified linear unit (ReLU).

(I don’t include these parameters as this is related to an exercise for my students.) To render the plots, I evaluate the trained model against the complete training set and write out a CSV.

One of the key lessons with neural networks is that you cannot blindly create networks and expect them to yield something useful.

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