Valid way to represent mutation and similarity of outputs in an artificial neuron

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I am defining an activation function like below where F and w are vectors with an arbitrary dimension and φ is the activation function that squashes w x F to a smaller dimension:

R_c (F_c)= φ_c (w_c  x F_c)

I then want to represent the similarity between R and R', which is output of a mutation function applied to R:

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This does not look right at all though. I am thinking about defining each value in F and w as vectors themselves (So instead of say F being an average of different simultaneous inputs, it would be a set of vectors where each vector is a different simultaneous input) and represent φ as a dot product with another vector. Not sure if that is the right approach either though.

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