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arXiv · 2408.00796

Discrepancy Algorithms for the Binary Perceptron

Shuangping Li·Tselil Schramm·Kangjie Zhou
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Abstract

The binary perceptron problem asks us to find a sign vector in the intersection of independently chosen random halfspaces with intercept $-\kappa$. We analyze the performance of the canonical discrepancy minimization algorithms of Lovett-Meka and Rothvoss/Eldan-Singh for the asymmetric binary perceptron problem. We obtain new algorithmic results in the $\kappa = 0$ case and in the large-$|\kappa|$ case. In the $\kappa\to-\infty$ case, we additionally characterize the storage capacity and complement our algorithmic results with an almost-matching overlap-gap lower bound.

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Shuangping Li, Tselil Schramm, Kangjie Zhou. 2024-07-19. Discrepancy Algorithms for the Binary Perceptron. https://arxiv.org/abs/2408.00796

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