SESaMo: Symmetry-Enforcing Stochastic Modulation for Normalizing Flows

• URL: http://arxiv.org/abs/2505.19619v2
• Date: Thu, 05 Jun 2025 15:24:20 GMT
• Title: SESaMo: Symmetry-Enforcing Stochastic Modulation for Normalizing Flows
• Authors: Janik Kreit, Dominic Schuh, Kim A. Nicoli, Lena Funcke,
• Abstract summary: This paper introduces Symmetry-Enforcing Modulation (SESaMo)<n>SESaMo enables the incorporation of biases (e.g., symmetries) into normalizing flows through a novel technique called inductive modulation.<n>Our numerical experiments benchmark SESaMo in different scenarios, including an 8-Gaussian mixture model and physically relevant field theories.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: 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.

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