arXiv Machine Learning
A Theory of Speciation in Generative Diffusion Models on Compact Riemannian Manifolds
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arXiv Machine Learning
2d ago
RW-Flow: One-Step Generation on Compact Manifolds via Wasserstein Gradient Flows
RW-Flow presents a new one‑step generative framework for data on compact manifolds, leveraging Wasserstein gradient flows. The authors derive a necessary and sufficient identifiability condition for velocity fields on compact, connected Riemannian manifolds, showing that a symmetric, Lipschitz‑continuous cost function yields identifiability iff its Gibbs kernel is nondegenerate. Experiments on geospatial events, protein and RNA torsion angles, and discretized manifolds demonstrate that RW‑Flow surpasses existing one‑step methods across most benchmark settings.
arXiv Machine Learning
Jul 8
EntroPath: Maximum Entropy Path Ensemble Embedding for Manifold Learning
arXiv:2607. 06497v1 Announce Type: new Abstract: We introduce EntroPath, a manifold learning method that recovers geodesic geometry from data graphs through ensembles of diffusion paths.
arXiv Machine Learning
Jul 14
Riemannian Denoising Diffusion Probabilistic Models
arXiv:2505. 04338v3 Announce Type: replace Abstract: We propose Riemannian Denoising Diffusion Probabilistic Models (RDDPMs) for learning distributions on submanifolds of Euclidean space that are level sets of functions, including most of the manifolds relevant to applications.
arXiv Machine Learning
Sep 21
Riemannian Neural Hamiltonian Flows: Geodesic Symplectic Transport and Interpretability
The paper introduces Riemannian Neural Hamiltonian Flows, a generative model that extends Hamiltonian normalizing flows to Riemannian manifolds by combining a fixed kinetic energy, a learned scalar potential, and a geodesic leapfrog integrator. It provides an analysis showing how the learned Hamiltonian can be interpreted through an implicit profile and a matched potential, with special cases such as isotropic Gaussian and local harmonic analysis around modes. Experiments on Euclidean, hyperbolic, and spherical spaces demonstrate competitive sample quality and computational efficiency compared to a Riemannian continuous normalizing flow, while confirming the interpretability of the learned potential.
arXiv Machine Learning
Jul 7
Statistically Meaningful Geometry (SMG) Beyond the Euclidean Paradigm, with Application to Generative AI
arXiv:2607. 03329v1 Announce Type: new Abstract: Conventional uniform convergence bounds and empirical risk minimization break down in massive over-parameterized models, such as large language transformers and biological sequence networks.
arXiv Computer Vision
Sep 22
Ananke: Contractive Torus Attractor Networks
arXiv:2609.24737v1 Announce Type: new Abstract: We introduce Ananke, a representation-learning framework that scaffolds latent representations onto a structured product-torus prior, and its flagship...