Equivariant Hamiltonian Flows

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.

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Cited by in corpus (22)

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• Equivariant Flows: Exact Likelihood Generative Learning for Symmetric Densities
• CaSPR: Learning Canonical Spatiotemporal Point Cloud Representations
• Neural Canonical Transformation with Symplectic Flows
• Independent SE(3)-Equivariant Models for End-to-End Rigid Protein Docking
• Deep Hamiltonian networks based on symplectic integrators
• Introduction to Normalizing Flows for Lattice Field Theory
• Learning Physical Constraints with Neural Projections
• E(n) Equivariant Normalizing Flows
• Temperature-steerable flows
• Learning Equivariant Energy Based Models with Equivariant Stein Variational Gradient Descent
• On Computational Poisson Geometry II: Numerical Methods
• The Convolution Exponential and Generalized Sylvester Flows
• SyMetric: Measuring the Quality of Learnt Hamiltonian Dynamics Inferred from Vision
• Embedded-model flows: Combining the inductive biases of model-free deep learning and explicit probabilistic modeling
• Training Invertible Linear Layers through Rank-One Perturbations
• Optimal Design of Experiments for Simulation-Based Inference of Mechanistic Acyclic Biological Networks
• Implicit Riemannian Concave Potential Maps
• Equivariant Manifold Flows
• Fixed-kinetic Neural Hamiltonian Flows for enhanced interpretability and reduced complexity