A Function-Space Stability Boundary for Generalization in Interpolating Learning Systems
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866911439120236544 |
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| author | Katende, Ronald |
| author_facet | Katende, Ronald |
| contents | Modern learning systems often interpolate training data while still generalizing well, yet it remains unclear when algorithmic stability explains this behavior. We model training as a function-space trajectory and measure sensitivity to single-sample perturbations along this trajectory. We propose a contractive propagation condition and a stability certificate obtained by unrolling the resulting recursion. A small certificate implies stability-based generalization, while we also prove that there exist interpolating regimes with small risk where such contractive sensitivity cannot hold, showing that stability is not a universal explanation. Experiments confirm that certificate growth predicts generalization differences across optimizers, step sizes, and dataset perturbations. The framework therefore identifies regimes where stability explains generalization and where alternative mechanisms must account for success. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_03514 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Function-Space Stability Boundary for Generalization in Interpolating Learning Systems Katende, Ronald Machine Learning Optimization and Control 68Q32, 68T05, 62G05, 90C25 Modern learning systems often interpolate training data while still generalizing well, yet it remains unclear when algorithmic stability explains this behavior. We model training as a function-space trajectory and measure sensitivity to single-sample perturbations along this trajectory. We propose a contractive propagation condition and a stability certificate obtained by unrolling the resulting recursion. A small certificate implies stability-based generalization, while we also prove that there exist interpolating regimes with small risk where such contractive sensitivity cannot hold, showing that stability is not a universal explanation. Experiments confirm that certificate growth predicts generalization differences across optimizers, step sizes, and dataset perturbations. The framework therefore identifies regimes where stability explains generalization and where alternative mechanisms must account for success. |
| title | A Function-Space Stability Boundary for Generalization in Interpolating Learning Systems |
| topic | Machine Learning Optimization and Control 68Q32, 68T05, 62G05, 90C25 |
| url | https://arxiv.org/abs/2602.03514 |