# Storage capacity of perceptron with variable selection

arXiv: https://arxiv.org/abs/2512.01861 · HTML: https://mlsanity.com/paper/2512.01861/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 0 of its 20 references that are in the map.
- First posted on arXiv 1 Dec 2025.

## Built on by (most cited first, 1 of 1)

- [Shortcomings and capacities of real-constrained neural networks in complex spaces](https://mlsanity.com/paper/2606.04390/) (2026)

## Abstract (arXiv)

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 = α N random patterns by optimally selecting M = ρ N variables out of N variables. While the Cover--Gardner theory establishes that a random subset of ρ N dimensions can separate α N 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.