Replica Theory of Spherical Boltzmann Machine Ensembles
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866913063861485568 |
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| author | Tulinski, Thomas Fernandez-De-Cossio-Diaz, Jorge Cocco, Simona Monasson, Rémi |
| author_facet | Tulinski, Thomas Fernandez-De-Cossio-Diaz, Jorge Cocco, Simona Monasson, Rémi |
| contents | Training in machine learning generally consists in finding one model, whose parameters minimize a data-dependent loss. Yet, empirical work shows that ensemble learning, an approach in which multiple models are sampled, can improve performance. Here, we provide an analytical framework to understand these observations in the case of Boltzmann machines, exploiting a duality between ensemble learning and large deviations of the free energy in spin-glass models. Replica calculations allow us to fully solve the case of spherical Boltzmann machine ensembles, and clarify when ensemble learning improves over standard loss minimization, in particular for nearly finite-dimensional data. Our framework can also be applied to complex data distributions, in agreement with numerical simulations on deep networks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_17936 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Replica Theory of Spherical Boltzmann Machine Ensembles Tulinski, Thomas Fernandez-De-Cossio-Diaz, Jorge Cocco, Simona Monasson, Rémi Disordered Systems and Neural Networks Statistical Mechanics Training in machine learning generally consists in finding one model, whose parameters minimize a data-dependent loss. Yet, empirical work shows that ensemble learning, an approach in which multiple models are sampled, can improve performance. Here, we provide an analytical framework to understand these observations in the case of Boltzmann machines, exploiting a duality between ensemble learning and large deviations of the free energy in spin-glass models. Replica calculations allow us to fully solve the case of spherical Boltzmann machine ensembles, and clarify when ensemble learning improves over standard loss minimization, in particular for nearly finite-dimensional data. Our framework can also be applied to complex data distributions, in agreement with numerical simulations on deep networks. |
| title | Replica Theory of Spherical Boltzmann Machine Ensembles |
| topic | Disordered Systems and Neural Networks Statistical Mechanics |
| url | https://arxiv.org/abs/2604.17936 |