Kolmogorov--Arnold stability
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866908760723685376 |
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| author | Dzhenzher, Sviatoslav V. Freedman, Michael H. |
| author_facet | Dzhenzher, Sviatoslav V. Freedman, Michael H. |
| contents | Regarding the representation theorem of Kolmogorov and Arnold (KA) as an algorithm for representing or <<expressing>> functions, we test its robustness by analyzing its stability to withstand re-parameterizations of the hidden space. One may think of such re-parameterizations as the work of an adversary attempting to foil the construction of the KA outer function. We find KA to be stable under countable collections of continuous re-parameterizations, but unearth a question about the equi-continuity of the outer functions that, so far, obstructs taking limits and defeating continuous groups of re-parameterizations. This question on the regularity of the outer functions is relevant to the debate over the applicability of KA to the general theory of NNs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_05255 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Kolmogorov--Arnold stability Dzhenzher, Sviatoslav V. Freedman, Michael H. Machine Learning Artificial Intelligence Functional Analysis Regarding the representation theorem of Kolmogorov and Arnold (KA) as an algorithm for representing or <<expressing>> functions, we test its robustness by analyzing its stability to withstand re-parameterizations of the hidden space. One may think of such re-parameterizations as the work of an adversary attempting to foil the construction of the KA outer function. We find KA to be stable under countable collections of continuous re-parameterizations, but unearth a question about the equi-continuity of the outer functions that, so far, obstructs taking limits and defeating continuous groups of re-parameterizations. This question on the regularity of the outer functions is relevant to the debate over the applicability of KA to the general theory of NNs. |
| title | Kolmogorov--Arnold stability |
| topic | Machine Learning Artificial Intelligence Functional Analysis |
| url | https://arxiv.org/abs/2504.05255 |