Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2507.13543 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866911215772499968 |
|---|---|
| author | Kolpakov, Alexander |
| author_facet | Kolpakov, Alexander |
| contents | We develop a framework for dualizing the Kolmogorov structure function $h_x(α)$, which then allows using computable complexity proxies. We establish a mathematical analogy between information-theoretic constructs and statistical mechanics, introducing a suitable partition function and free energy functional. We explicitly prove the Legendre-Fenchel duality between the structure function and free energy, showing detailed balance of the Metropolis kernel, and interpret acceptance probabilities as information-theoretic scattering amplitudes. A susceptibility-like variance of model complexity is shown to peak precisely at loss-complexity trade-offs interpreted as phase transitions. Practical experiments with linear and tree-based regression models verify these theoretical predictions, explicitly demonstrating the interplay between the model complexity, generalization, and overfitting threshold. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_13543 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Loss-Complexity Landscape and Model Structure Functions Kolpakov, Alexander Information Theory Artificial Intelligence Machine Learning Mathematical Physics I.2.2; I.2.6 We develop a framework for dualizing the Kolmogorov structure function $h_x(α)$, which then allows using computable complexity proxies. We establish a mathematical analogy between information-theoretic constructs and statistical mechanics, introducing a suitable partition function and free energy functional. We explicitly prove the Legendre-Fenchel duality between the structure function and free energy, showing detailed balance of the Metropolis kernel, and interpret acceptance probabilities as information-theoretic scattering amplitudes. A susceptibility-like variance of model complexity is shown to peak precisely at loss-complexity trade-offs interpreted as phase transitions. Practical experiments with linear and tree-based regression models verify these theoretical predictions, explicitly demonstrating the interplay between the model complexity, generalization, and overfitting threshold. |
| title | Loss-Complexity Landscape and Model Structure Functions |
| topic | Information Theory Artificial Intelligence Machine Learning Mathematical Physics I.2.2; I.2.6 |
| url | https://arxiv.org/abs/2507.13543 |