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It seems that there should be a way to algebraically simplify neural nets.

Trivially a node that has a zero weight can be removed as can any links to / from that node.

It should also be possible to eliminate nodes that have a full-value (aka '1' on the 0-1 scale)

I have also seen work where the matrix multiplies during training can have columns "collapsed".

The ultimate question might be applying an "algebraic simplification" of the final network to simplify a post-trained network used for inference.

The idea is to take a path through a network, constructing the equation for that path, reducing it to a shorter path by conbining nodes and weights.

It is certain that a node participates in several (hundred?) paths. In this case it might be useful to "copy" the node so it can be part of a path reduction without affecting other paths.

I believe that in theory some neural networks can be reduced to a single hidden layer[1]. The game would be to algebraically reduce network depth.

[1] Lee, et al. "On the ability of neural nets to express distributions" https://arxiv.org/pdf/1702.07028.pdf (2021)

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Article URL: https://github.com/HardhatChad/ore

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Article URL: https://apnews.com/article/citizen-scientist-snow-rocky-mountains-drought-water-3a4e053d7db9be3eb22aa6809eab57c0

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