arXiv Machine Learning By Robert Simon Fong, Gouhei Tanaka, Kazuyuki Aihara

Symplectic Representation of Legendre Dynamics

Read the original on arXiv Machine Learning →

arXiv:2512. 19409v2 Announce Type: replace Abstract: Modern learning systems act on internal representations of data, yet how these representations encode underlying physical or statistical structure is often left implicit.

Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv Machine Learning.

arXiv Machine Learning
Jun 26

Symplectic Neural Networks for learning Generalized Hamiltonians

arXiv:2606. 27029v1 Announce Type: new Abstract: Hamiltonian Neural Networks (HNNs) integrate physical priors into neural models by learning a system's Hamiltonian, improving generalization and sample efficiency.

By Harsh Choudhary, Vyacheslav Kungurtsev, Chandan Gupta, Melvin Leok, Georgios Korpas
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.

By Vincent Souveton