Equivariant Flows: Exact Likelihood Generative Learning for Symmetric Densities
This work addresses the challenge of efficiently sampling symmetric probability densities in physics and chemistry, offering a method to enhance generative models for many-body systems, though it is incremental by building on existing normalizing flow techniques.
The paper tackled the problem of scaling and generalizing normalizing flows for sampling equilibrium states in many-body physical systems by incorporating natural symmetries into the model. It demonstrated that equivariant normalizing flows, which preserve these symmetries by design, lead to improved generalization capabilities and sampling efficiency in benchmark molecular physics systems.
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 \textit{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.