PreprintUNDER REVIEW
Neural Ricci Flow: Curvature-Constrained SSL Regularizer
AUTHOR // KUSHAGRA GOYAL·NISQ & SYSTEM LABS
INFORMATION
- TypeResearch Paper
- VenuePreprint
- Index StatusUNDER REVIEW
CONTRIBUTIONS
- Geometric formulation of manifold collapse in self-supervised representation learning.
- Sinkhorn optimal transport alignment driven by local manifold curvature.
- Extensive testing on ImageNet-1k downstream classification tasks showing state-of-the-art results on sparse labels.
ABSTRACT.
Introduces a novel self-supervised learning (SSL) regularizer inspired by Riemannian geometry and Ricci flow. By modeling the latent embedding manifold's local curvature and dynamically smoothing high-curvature bottlenecks using Sinkhorn Optimal Transport, the regularizer prevents representation collapse. We show that curvature regularization yields a +5.2% accuracy improvement on low-resource downstream tasks.
METHODOLOGY.
Computes local Ricci curvature tensors in mini-batch latent spaces. Smooths bottlenecks through curvature-driven flow equations, preventing collapse of distinct clusters into a single dimension.