Topological Simplification in Predictive Coding Networks
We study the topology of learned representations in predictive coding networks (PCNs), a neuro-inspired bidirectional architecture, using a quantitative layer-wise persistent homology analysis. We train well-performing PCNs on a synthetic classification dataset ($\geq 99.9\%$ test accuracy) and on MNIST ($\geq 95\%$ test accuracy), and measure how topological features change across layers for different architectures and activation functions. We find that smaller PCNs collapse connected components across layers earlier than larger models (Spearman $\unicode{x1D70C} \in [0.72, 0.79]$ across activations), with model size measured as the sum of hidden-layer widths. We also observe a strong ne...
| Authors | Adam Shaw, Jiayu Li, Michael Sperling et al. |
|---|---|
| Primary category | cs.LG |
| Published | 3 August 2026 |
| Last updated at source | 3 August 2026 |
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