# Sheaf Cohomology of Linear Predictive Coding Networks

arXiv: https://arxiv.org/abs/2511.11092 · HTML: https://mlsanity.com/paper/2511.11092/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Nov 2025.

## Built on by (most cited first, 4 of 4)

- [Neural Networks as Local-to-Global Computations](https://mlsanity.com/paper/2603.14831/) (2026)
- [Augmented Lagrangian Predictive Coding](https://mlsanity.com/paper/2605.31022/) (2026)
- [A Study of Hidden-State Optimization Order in Predictive Coding Networks](https://mlsanity.com/paper/2609.00686/) (2026)
- [Gluing Local Contexts into Global Meaning: A Sheaf-Theoretic Decomposition of Transformer Representations](https://mlsanity.com/paper/2610.17117/) (2026)

## Abstract (arXiv)

Predictive coding (PC) replaces global backpropagation with local optimization over weights and activations. We show that linear PC networks admit a natural formulation as cellular sheaves: the sheaf coboundary maps activations to edge-wise prediction errors, and PC inference is diffusion under the sheaf Laplacian. Sheaf cohomology then characterizes irreducible error patterns that inference cannot remove. We analyze recurrent topologies where feedback loops create internal contradictions, introducing prediction errors unrelated to supervision. Using a Hodge decomposition, we determine when these contradictions cause learning to stall. The sheaf formalism provides both diagnostic tools for identifying problematic network configurations and design principles for effective weight initialization for recurrent PC networks.