Topological Simplification in Predictive Coding Networks

What the math gives to ML

The paper provides a concrete layer-wise statistic for locating irreversible topological simplification in a representation hierarchy: a weighted Betti-number drop distribution and its center of mass (COM). The transferable asset is not the empirical predictive-coding finding itself, but a model-agnostic diagnostic that can expose whether a network destroys connected components or holes too early. A practical use is topology-guided architecture allocation: periodically measure COM on validation embeddings, then widen or deepen models whose representations simplify prematurely, rather than uniformly increasing parameter count. This is most credible as an architecture-search or adaptive-capacity signal before attempting a differentiable persistent-homology loss.