2025/12/01 by Yun Xu, Masayuki Ohzeki, Xu, Yingying +3
Computer Science · Neuroscience · #Advanced Statistical Modeling Techniques #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Computer and information sciences #FOS: Physical sciences #Information Theory (cs.IT) #Machine Learning (stat.ML) #Neural Networks and Applications #Neural dynamics and brain function
paper · pdf · doi:10.48550/arxiv.2512.01861
openalex publication_date 2025/12/01 · openalex created_date 2025/12/03 · openalex updated_date 2026/07/28
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.