# Experimental Neural Network Architecture on unusual math: Categorical Square-Sheaf Neural Network

**URL:** <https://replit.discourse.group/t/experimental-neural-network-architecture-on-unusual-math-categorical-square-sheaf-neural-network/12034>\
**Category:** Showcase\
**Created:** [May 15, 2026, 4:41am UTC](https://replit.discourse.group/t/experimental-neural-network-architecture-on-unusual-math-categorical-square-sheaf-neural-network/12034 "2026-05-15T04:41:24Z")\
**Posts on this page:** 1\
**Page:** 1

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**Author:** ![siritoriyowai](https://yyz2.discourse-cdn.com/flex010/user_avatar/replit.discourse.group/siritoriyowai/32/2896_2.png) [@siritoriyowai](https://replit.discourse.group/u/siritoriyowai)\
**Post date:** [May 15, 2026, 4:41am UTC](https://replit.discourse.group/t/experimental-neural-network-architecture-on-unusual-math-categorical-square-sheaf-neural-network/12034/1 "2026-05-15T04:41:24Z")

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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

- (1) hard functional enforcement via torch.linalg.solve instead of a soft consistency penalty, and

- (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](https://github.com/kaifczxc-lab/CASNN)

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