A simple neural network

A simple neural net consists of a node which takes in an input or a list of inputs and performs a transformation. An example is shown in the following figure:

Mathematically, it takes the inputs x and applies a transformation W to get the output y:

The input x can be a vector or multi-dimensional array. Based on the transformation matrix W we get the output y to be a vector or multi-dimensional array. This structure is further modified by also including the non-linear transformation F:

Now, output y is not linearly ...

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