aiqbench analysis
This research introduces SESaMo, a novel technique for normalizing flows that integrates symmetry constraints via stochastic modulation to improve sampling from complex distributions in physics and chemistry. By effectively learning both exact and broken symmetries, the method enhances generative model flexibility without relying on standard equivariant architectures alone. The approach demonstrates significant potential for accelerating simulations of strongly correlated electron systems and field theories where prior knowledge is critical.
SESaMo: Symmetry-Enforcing Stochastic Modulation for Normalizing Flows
arXiv:2505.19619v3 Announce Type: replace 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.
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.
Machine Learning (cs.LG); Strongly Correlated Electrons (cond-mat.str-el); High Energy Physics - Lattice (hep-lat); Computational Physics (physics.comp-ph)
arXiv:2505.19619 [cs.LG]
(or arXiv:2505.19619v3 [cs.LG] for this version)
Full text under the publisher's open licence · 188 words
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