SESaMo: Symmetry-Enforcing Stochastic Modulation for Normalizing Flows
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866908395834966016 |
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| author | Kreit, Janik Schuh, Dominic Nicoli, Kim A. Funcke, Lena |
| author_facet | Kreit, Janik Schuh, Dominic Nicoli, Kim A. Funcke, Lena |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_19619 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | SESaMo: Symmetry-Enforcing Stochastic Modulation for Normalizing Flows Kreit, Janik Schuh, Dominic Nicoli, Kim A. Funcke, Lena Machine Learning Strongly Correlated Electrons High Energy Physics - Lattice Computational Physics 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. |
| title | SESaMo: Symmetry-Enforcing Stochastic Modulation for Normalizing Flows |
| topic | Machine Learning Strongly Correlated Electrons High Energy Physics - Lattice Computational Physics |
| url | https://arxiv.org/abs/2505.19619 |