Storage capacity of perceptron with variable selection
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912740946214912 |
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| author | Xu, Yingying Ohzeki, Masayuki Kabashima, Yoshiyuki |
| author_facet | Xu, Yingying Ohzeki, Masayuki Kabashima, Yoshiyuki |
| contents | A central challenge in machine learning is to distinguish genuine structure from chance correlations in high-dimensional data. In this work, we address this issue for the perceptron, a foundational model of neural computation. Specifically, we investigate the relationship between the pattern load $α$ and the variable selection ratio $ρ$ for which a simple perceptron can perfectly classify $P = αN$ random patterns by optimally selecting $M = ρN$ variables out of $N$ variables. While the Cover--Gardner theory establishes that a random subset of $ρN$ dimensions can separate $αN$ random patterns if and only if $α< 2ρ$, we demonstrate that optimal variable selection can surpass this bound by developing a method, based on the replica method from statistical mechanics, for enumerating the combinations of variables that enable perfect pattern classification. This not only provides a quantitative criterion for distinguishing true structure in the data from spurious regularities, but also yields the storage capacity of associative memory models with sparse asymmetric couplings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_01861 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Storage capacity of perceptron with variable selection Xu, Yingying Ohzeki, Masayuki Kabashima, Yoshiyuki Information Theory Disordered Systems and Neural Networks Machine Learning A central challenge in machine learning is to distinguish genuine structure from chance correlations in high-dimensional data. In this work, we address this issue for the perceptron, a foundational model of neural computation. Specifically, we investigate the relationship between the pattern load $α$ and the variable selection ratio $ρ$ for which a simple perceptron can perfectly classify $P = αN$ random patterns by optimally selecting $M = ρN$ variables out of $N$ variables. While the Cover--Gardner theory establishes that a random subset of $ρN$ dimensions can separate $αN$ random patterns if and only if $α< 2ρ$, we demonstrate that optimal variable selection can surpass this bound by developing a method, based on the replica method from statistical mechanics, for enumerating the combinations of variables that enable perfect pattern classification. This not only provides a quantitative criterion for distinguishing true structure in the data from spurious regularities, but also yields the storage capacity of associative memory models with sparse asymmetric couplings. |
| title | Storage capacity of perceptron with variable selection |
| topic | Information Theory Disordered Systems and Neural Networks Machine Learning |
| url | https://arxiv.org/abs/2512.01861 |