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Discrete Ricci curvature estimation (Ollivier/Forman)

Techniqueadvanced

Builds a k-NN/r-neighborhood graph from a layer's activations and computes a graph-theoretic discretization of Ricci curvature at each edge — Ollivier-Ricci (via Wasserstein-1 optimal transport between neighbor distributions) or augmented Forman-Ricci (a combinatorial degree/triangle-count formula) — tracking how this intrinsic, graph-based curvature evolves across depth or training.

Used in (1 observation)

structure: Curvature profile of the representation manifold · models: Custom feedforward MLP (binary image classification, Hehl et al. 2025) · paper: Neural Feature Geometry Evolves as Discrete Ricci Flow