Hello everyone, I want to share here my small research github repository I like experimenting with neural network architectures and I’m a self-taught mathematician
I wrote here earlier about my other experiment, if you are interested, you can visit my profile and see that post there
Simply put, this work is a more rigorous mathematical model in the context of sheaf theory, with some minor innovations.
One problem: the result is negative;
But I wasn’t afraid to post it, and frankly, I’m not that concerned about the result.
If I were to describe what this architecture is, I’d say this:
The novelty here is not “a sheaf on a square” — cellular sheaf neural networks already handle arbitrary small graphs.
The narrower contribution is
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(1) hard functional enforcement via torch.linalg.solve instead of a soft consistency penalty, and
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(2) adding the pullback-preservation axiom F(A) ≅ F(B) ×_{F(D)} F(C) on top of the standard sheaf condition for the cover of D.
Both are enforced together by the four-term L_glue.
The empirical result suggests this combined constraint actively prevents the kind of factor independence one might have hoped to gain from it.
Here the repository: GitHub - kaifczxc-lab/CASNN: Small experimental sheaf neural network architecture · GitHub
The work may be raw, I won’t deny that, the code is LLM-assisted and may be rough in places, but the math part is correct