Normalizing flows are exact-likelihood generative neural networks which
approximately transform samples from a simple prior distribution to samples of
the probability distribution of interest. Recent work showed that such
generative models can be utilized in statistical mechanics to sample
equilibrium states of many-body systems in physics and chemistry. To scale and
generalize these results, it is essential that the natural symmetries in the
probability density - in physics defined by the invariances of the target
potential - are built into the flow. We provide a theoretical sufficient
criterion showing that the distribution generated by equivariant normalizing
flows is invariant with respect to these symmetries by design. Furthermore, we
propose building blocks for flows which preserve symmetries which are usually
found in physical/chemical many-body particle systems. Using benchmark systems
motivated from molecular physics, we demonstrate that those symmetry preserving
flows can provide better generalization capabilities and sampling efficiency.
Description
[2006.02425] Equivariant Flows: exact likelihood generative learning for symmetric densities
%0 Journal Article
%1 kohler2020equivariant
%A Köhler, Jonas
%A Klein, Leon
%A Noé, Frank
%D 2020
%K equivariance flows generative-models readings symmetry
%T Equivariant Flows: exact likelihood generative learning for symmetric
densities
%U http://arxiv.org/abs/2006.02425
%X Normalizing flows are exact-likelihood generative neural networks which
approximately transform samples from a simple prior distribution to samples of
the probability distribution of interest. Recent work showed that such
generative models can be utilized in statistical mechanics to sample
equilibrium states of many-body systems in physics and chemistry. To scale and
generalize these results, it is essential that the natural symmetries in the
probability density - in physics defined by the invariances of the target
potential - are built into the flow. We provide a theoretical sufficient
criterion showing that the distribution generated by equivariant normalizing
flows is invariant with respect to these symmetries by design. Furthermore, we
propose building blocks for flows which preserve symmetries which are usually
found in physical/chemical many-body particle systems. Using benchmark systems
motivated from molecular physics, we demonstrate that those symmetry preserving
flows can provide better generalization capabilities and sampling efficiency.
@article{kohler2020equivariant,
abstract = {Normalizing flows are exact-likelihood generative neural networks which
approximately transform samples from a simple prior distribution to samples of
the probability distribution of interest. Recent work showed that such
generative models can be utilized in statistical mechanics to sample
equilibrium states of many-body systems in physics and chemistry. To scale and
generalize these results, it is essential that the natural symmetries in the
probability density - in physics defined by the invariances of the target
potential - are built into the flow. We provide a theoretical sufficient
criterion showing that the distribution generated by equivariant normalizing
flows is invariant with respect to these symmetries by design. Furthermore, we
propose building blocks for flows which preserve symmetries which are usually
found in physical/chemical many-body particle systems. Using benchmark systems
motivated from molecular physics, we demonstrate that those symmetry preserving
flows can provide better generalization capabilities and sampling efficiency.},
added-at = {2020-06-04T21:38:07.000+0200},
author = {Köhler, Jonas and Klein, Leon and Noé, Frank},
biburl = {https://www.bibsonomy.org/bibtex/2432031c56c93705e7d51eaf0210cc163/kirk86},
description = {[2006.02425] Equivariant Flows: exact likelihood generative learning for symmetric densities},
interhash = {c8e54ca06614561e5643e0239bff396a},
intrahash = {432031c56c93705e7d51eaf0210cc163},
keywords = {equivariance flows generative-models readings symmetry},
note = {cite arxiv:2006.02425},
timestamp = {2020-06-04T21:38:07.000+0200},
title = {Equivariant Flows: exact likelihood generative learning for symmetric
densities},
url = {http://arxiv.org/abs/2006.02425},
year = 2020
}