[2603.25440] The Symmetric Perceptron: a Teacher-Student Scenario

Condensed Matter > Disordered Systems and Neural Networks arXiv:2603.25440 (cond-mat) [Submitted on 26 Mar 2026] Title:The Symmetric Perceptron: a Teacher-Student Scenario Authors:Giovanni Catania, Aurélien Decelle, Suhanee Korpe View a PDF of the paper titled The Symmetric Perceptron: a Teacher-Student Scenario, by Giovanni Catania and 2 other authors View PDF HTML (experimental) Abstract:We introduce and solve a teacher-student formulation of the symmetric binary Perceptron, turning a traditionally storage-oriented model into a planted inference problem with a guaranteed solution at any sample density. We adapt the formulation of the symmetric Perceptron which traditionally considers either the u-shaped potential or the rectangular one, by including labels in both regions. With this formulation, we analyze both the Bayes-optimal regime at for noise-less examples and the effect of thermal noise under two different potential/classification rules. Using annealed and quenched free-entropy calculations in the high-dimensional limit, we map the phase diagram in the three control parameters, namely the sample density $\alpha$, the distance between the origin and one of the symmetric hyperplanes $\kappa$ and temperature $T$, and identify a robust scenario where learning is organized by a second-order instability that creates teacher-correlated suboptimal states, followed by a first-order transition to full alignment. We show how this structure depends on the choice of potential,...