SESaMo: Symmetry-Enforcing Stochastic Modulation for Normalizing Flows
This work addresses a fundamental problem in physics and chemistry for researchers needing efficient generative models, but it is incremental as it builds on existing symmetry-equivariant approaches.
The paper tackles the challenge of sampling from unnormalized Boltzmann-like distributions by introducing SESaMo, a method that incorporates symmetries into normalizing flows using stochastic modulation, achieving enhanced flexibility in learning exact and broken symmetries as demonstrated in benchmarks like an 8-Gaussian mixture model and field theories.
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 $φ^4$ theory and the Hubbard model.