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Am I missing something or is this just a linear transformation?

It says here ( https://www.researchgate.net/publication/370980395_A_NEURAL_... ) that each layer can be represented as a matrix multiplication (equation 3): Ax = s

So concatenating multiple layers could just be reduced to a single matrix multiplication?

If there is no non-linearity I don't see how this could replace neural networks, or am I missing something?

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The attempt is not to replace a particular neural network which has already been trained by using Sigmoid or Rel functions. If one does this then one would necessarily have to use non-linear maps. The whole point is that such a non-linear technique is not necessary for classifications. It is not necessary to confine clusters by hyperplanes for solving a classification problem. Our focus is on individual points.

We believe the brain does not do nonlinear maps!

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