Equivariant Hamiltonian Flows

By Danilo Jimenez Rezende, Sébastien Racanière, Irina Higgins, Peter Toth. 2019

72 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Generative Models, Model Architectures, Signal Processing

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Max Welling
2. Danilo Jimenez Rezende
3. Stefano Ermon
4. J. Tomczak
5. Balaji Lakshminarayanan
6. Sergey Levine
7. George Papamakarios
8. Yoshua Bengio

In Generative Models

1. Max Welling
2. Danilo Jimenez Rezende
3. Stefano Ermon
4. Balaji Lakshminarayanan
5. Shakir Mohamed
6. George Papamakarios
7. J. Tomczak
8. Emiel Hoogeboom

In Model Architectures

1. Erik J. Bekkers
2. David W. Romero
3. Mark Hoogendoorn
4. J. Tomczak
5. Jonas Köhler
6. Emiel Hoogeboom
7. Victor Garcia Satorras
8. Frank No'e

In Signal Processing

1. Danilo Jimenez Rezende
2. Eric T. Nalisnick
3. Balaji Lakshminarayanan
4. George Papamakarios
5. Shakir Mohamed
6. Leon Klein
7. Frank No'e
8. Jonas Köhler

Citations in the corpus

• E(n) Equivariant Graph Neural Networks (2021, background): “Group equivariant neural networks have demonstrated their effectiveness in a wide variety of tasks (Cohen & Welling, 2016; 2017; Weiler & Cesa, 2019; Rezende et al., 2019; Romero & Cordonnier, 2021).”
• Equivariant Flows: exact likelihood generative learning for symmetric densities (2020, methodology): “A preliminary account of equivariant normalizing flows has been given in two recent workshop submissions (Rezende et al., 2019; Köhler et al., 2019).”
• Equivariant Flows: sampling configurations for multi-body systems with symmetric energies (2019, methodology): “A Hamiltonian flow framework for incorporating equivariances that can be seen as a special case of our equivariant flow construction was developed in parallel in [15].”
• Normalizing Flows for Probabilistic Modeling and Inference (2019, methodology): “The concept of equivariant flows was proposed concurrently by Köhler et al. (2019) and Rezende et al. (2019), who described methods for building equivariant transformations in the context of continuous-time flows.”
• Wavelet Networks: Scale Equivariant Learning From Raw Waveforms (2020, background): “Similar intuitions have recently propelled the development of several deep learning approaches to model physical systems [54, 30, 73, 20].”