Sheaf Cohomology of Linear Predictive Coding Networks

The article discusses the concept of predictive coding (PC) in neural networks, which replaces global backpropagation with local optimization of weights and activations. It presents a formulation of linear PC networks as cellular sheaves, where sheaf coboundary maps relate activations to prediction errors. The study also highlights the role of recurrent topologies that introduce feedback loops, leading to internal contradictions and prediction errors. A Hodge decomposition is utilized to analyze when these contradictions hinder learning.