Activation-graph Ricci curvature contracts flow-like, reversing at overfitting onset

Hehl et al. build k-NN graphs from layer-wise activations of over 20,000 real feedforward MLPs (widths 15/25/50, depths 7/10/15) trained to >99% accuracy on binary MNIST/Fashion-MNIST/CIFAR-10 subsets [hehl-etal-2025-neural-feature-geometry-ricci-flow] They compute discrete Ollivier-Ricci and augmented Forman-Ricci curvature per point plus a local Ricci-evolution coefficient (curvature versus neighborhood-distance change across layers) [hehl-etal-2025-neural-feature-geometry-ricci-flow] Negative coefficients dominate (88.7-98.3% of vertices), indicating genuine Ricci-flow-like contraction in the feature geometry [hehl-etal-2025-neural-feature-geometry-ricci-flow] The coefficient's trend reverses at the depth and training point coinciding with overfitting onset and the depth that maximizes test accuracy; the study is purely observational [hehl-etal-2025-neural-feature-geometry-ricci-flow]