{"ID":2834598,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.01861","arxiv_id":"2512.01861","title":"Storage capacity of perceptron with variable selection","abstract":"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 $α\u003c 2ρ$, 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.","short_abstract":"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 s...","url_abs":"https://arxiv.org/abs/2512.01861","url_pdf":"https://arxiv.org/pdf/2512.01861v1","authors":"[\"Yingying Xu\",\"Masayuki Ohzeki\",\"Yoshiyuki Kabashima\"]","published":"2025-12-01T16:44:57Z","proceeding":"cs.IT","tasks":"[\"cs.IT\",\"cond-mat.dis-nn\",\"stat.ML\"]","methods":"[]","has_code":false}