Equivariant Hamiltonian Flows

2019/09/30 by Danilo Jimenez Rezende, Sébastien Racanière, Rezende, Danilo Jimenez +6 · 6 citations
Computer Science · Mathematics · #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Machine Learning in Healthcare #Time Series Analysis and Forecasting #Topic Modeling #cs.LG #stat.ML

paper · pdf · doi:10.48550/arxiv.1909.13739

arxiv created 2019/09/30 · openalex publication_date 2019/09/30 · arxiv updated 2019/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper introduces equivariant hamiltonian flows, a method for learning expressive densities that are invariant with respect to a known Lie-algebra of local symmetry transformations while providing an equivariant representation of the data. We provide proof of principle demonstrations of how such flows can be learnt, as well as how the addition of symmetry invariance constraints can improve data efficiency and generalisation. Finally, we make connections to disentangled representation learning and show how this work relates to a recently proposed definition.

Citations

• Adam: A Method for Stochastic Optimization
• Stochastic Backpropagation and Approximate Inference in Deep Generative Models
• Backpropagation Applied to Handwritten Zip Code Recognition
• Representation Learning: A Review and New Perspectives
• Density estimation using Real NVP
• Normalizing Flows on Riemannian Manifolds
• Towards a Definition of Disentangled Representations

Cited by

• HollowFlow: Efficient Sample Likelihood Evaluation using Hollow Message Passing
• Hamiltonian Normalizing Flows as kinetic PDE solvers: application to the 1D Vlasov-Poisson Equations
• CaSPR: Learning Canonical Spatiotemporal Point Cloud Representations
• Space Group Equivariant Crystal Diffusion
• Geometric Causal Models
• Equivariant Flow-Based Sampling for Lattice Gauge Theory

Related

• Equivariant Manifold Flows
• Equivariant Flows: Exact Likelihood Generative Learning for Symmetric Densities
• Symmetry Preservation in Hamiltonian Systems: Simulation and Learning
• Equivariant Representation Learning via Class-Pose Decomposition
• Learning finite symmetry groups of dynamical systems via equivariance detection