Concatenated context selected linear mappings

Sean O'Connor — Wed, 02 Sep 2026 10:40:53 +0000

Imagine a chain of linear mappings each selected by something.
If the same mapping was selected each time that would be boring. Matrices such as A and B can be collapsed together to a single matrix M by matrix multiply, M=AB.

And M is actually very different from its parents A and B.

If you select A from a pool of 10 and likewise B you have 100 different possible M's from 20 matrices. They are like rabbits aren't they?
If you have 10 of A and B and C you have 1000 different matrices from 30.

This is exponentiation of expressiveness with depth similar to a neural network.

The something that is doing the matrix selection at each layer you can call the context. And that can be liberal in meaning.

That's nice but what if you now apply pressure from backpropagation on the matrix chain?
For a data channel input x and the co-selected linear mapping (eg A₂B₇C₅...) backpropagation drifts each chosen linear mapping to be an expert for the slice of the training data it sees.
Concatenated Context Selected Linear Mappings
ReLU neural networks as CCSML

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Concatenated context selected linear mappings