Minimal-Dissipation Learning for Energy-Based Models
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866911740231417856 |
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| author | Hnybida, Jeff Verret, Simon |
| author_facet | Hnybida, Jeff Verret, Simon |
| contents | We show that the bias of the approximate maximum-likelihood estimation (MLE) objective of a persistent chain energy-based model (EBM) is precisely equal to the thermodynamic excess work of an overdamped Langevin dynamical system. We then answer the question of whether such a model can be trained with minimal excess work, that is, energy dissipation, in a finite amount of time. We find that a Gaussian energy function with constant variance can be trained with minimal excess work by controlling only the learning rate. This proves that it is possible to train a persistent chain EBM in a finite amount of time with minimal dissipation and also provides a lower bound on the energy required for the computation. We refer to such a learning process that minimizes the excess work as minimal-dissipation learning. We then provide a generalization of the optimal learning rate schedule to general potentials and find that it induces a natural gradient flow on the MLE objective, a well-known second-order optimization method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_03137 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Minimal-Dissipation Learning for Energy-Based Models Hnybida, Jeff Verret, Simon Statistical Mechanics Adaptation and Self-Organizing Systems We show that the bias of the approximate maximum-likelihood estimation (MLE) objective of a persistent chain energy-based model (EBM) is precisely equal to the thermodynamic excess work of an overdamped Langevin dynamical system. We then answer the question of whether such a model can be trained with minimal excess work, that is, energy dissipation, in a finite amount of time. We find that a Gaussian energy function with constant variance can be trained with minimal excess work by controlling only the learning rate. This proves that it is possible to train a persistent chain EBM in a finite amount of time with minimal dissipation and also provides a lower bound on the energy required for the computation. We refer to such a learning process that minimizes the excess work as minimal-dissipation learning. We then provide a generalization of the optimal learning rate schedule to general potentials and find that it induces a natural gradient flow on the MLE objective, a well-known second-order optimization method. |
| title | Minimal-Dissipation Learning for Energy-Based Models |
| topic | Statistical Mechanics Adaptation and Self-Organizing Systems |
| url | https://arxiv.org/abs/2510.03137 |