A PAC-Bayesian approach to generalization for quantum models
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arXiv
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| Autori principali: | , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| author | Rodriguez-Grasa, Pablo Caro, Matthias C. Eisert, Jens Gil-Fuster, Elies Schreiber, Franz J. Bravo-Prieto, Carlos |
| author_facet | Rodriguez-Grasa, Pablo Caro, Matthias C. Eisert, Jens Gil-Fuster, Elies Schreiber, Franz J. Bravo-Prieto, Carlos |
| contents | Generalization is a central concept in machine learning theory, yet for quantum models, it is predominantly analyzed through uniform bounds that depend on a model's overall capacity rather than the specific function learned. These capacity-based uniform bounds are often too loose and entirely insensitive to the actual training and learning process. Previous theoretical guarantees have failed to provide non-uniform, data-dependent bounds that reflect the specific properties of the learned solution rather than the worst-case behavior of the entire hypothesis class. To address this limitation, we derive the first PAC-Bayesian generalization bounds for a broad class of quantum models by analyzing layered circuits composed of general quantum channels, which include dissipative operations such as mid-circuit measurements and feedforward. Through a channel perturbation analysis, we establish non-uniform bounds that depend on the norms of learned parameter matrices; we extend these results to symmetry-constrained equivariant quantum models; and we validate our theoretical framework with numerical experiments. This work provides actionable model design insights and establishes a foundational tool for a more nuanced understanding of generalization in quantum machine learning. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_22964 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A PAC-Bayesian approach to generalization for quantum models Rodriguez-Grasa, Pablo Caro, Matthias C. Eisert, Jens Gil-Fuster, Elies Schreiber, Franz J. Bravo-Prieto, Carlos Quantum Physics Quantum Gases Machine Learning Generalization is a central concept in machine learning theory, yet for quantum models, it is predominantly analyzed through uniform bounds that depend on a model's overall capacity rather than the specific function learned. These capacity-based uniform bounds are often too loose and entirely insensitive to the actual training and learning process. Previous theoretical guarantees have failed to provide non-uniform, data-dependent bounds that reflect the specific properties of the learned solution rather than the worst-case behavior of the entire hypothesis class. To address this limitation, we derive the first PAC-Bayesian generalization bounds for a broad class of quantum models by analyzing layered circuits composed of general quantum channels, which include dissipative operations such as mid-circuit measurements and feedforward. Through a channel perturbation analysis, we establish non-uniform bounds that depend on the norms of learned parameter matrices; we extend these results to symmetry-constrained equivariant quantum models; and we validate our theoretical framework with numerical experiments. This work provides actionable model design insights and establishes a foundational tool for a more nuanced understanding of generalization in quantum machine learning. |
| title | A PAC-Bayesian approach to generalization for quantum models |
| topic | Quantum Physics Quantum Gases Machine Learning |
| url | https://arxiv.org/abs/2603.22964 |