SESaMo: Symmetry-Enforcing Stochastic Modulation for Normalizing Flows

Deep generative models have recently garnered significant attention across various fields, from physics to chemistry, where sampling from unnormalized Boltzmann-like distributions represents a fundamental challenge.

In particular, autoregressive models and normalizing flows have become prominent due to their appealing ability to yield closed-form probability densities.

Moreover, it is well-established that incorporating prior knowledge - such as symmetries - into deep neural networks can substantially improve training performances.

In this context, recent advances have focused on developing symmetry-equivariant generative models, achieving remarkable results.

Building upon these foundations, this paper introduces Symmetry-Enforcing Stochastic Modulation (SESaMo).

Similar to equivariant normalizing flows, SESaMo enables the incorporation of inductive biases (e.g., symmetries) into normalizing flows through a novel technique called stochastic modulation.

This approach enhances the flexibility of the generative model, allowing to effectively learn a variety of exact and broken symmetries.

Our numerical experiments benchmark SESaMo in different scenarios, including an 8-Gaussian mixture model and physically relevant field theories, such as the $\phi^4$ theory and the Hubbard model.