Variational Bounds for Perceptron Learning from Structured Data
Francesco Camilli, Pierluigi Contucci, Federica Gerace, Emanuele Mingione
cs.LG, cond-mat.dis-nn, math-ph, stat.ML
Submitted: 2026-08-05
Comments: 51 pages, 10 figures
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Terminology
Sources
- High Dimensional Classification via Regularized and Unregularized Empirical Risk Minimization: Precise Error and Optimal Loss
- Universality laws for Gaussian mixtures in generalized linear models
- Characterizing Finite-Dimensional Posterior Marginals in High-Dimensional GLMs via Leave-One-Out
- Strong replica symmetry for high-dimensional disordered log-concave Gibbs measures
- The Gaussian min-max theorem in the Presence of Convexity
- Fundamental limits of overparametrized shallow neural networks for supervised learning
- A statistical mechanics framework for Bayesian deep neural networks beyond the infinite-width limit
- Implicit Self-Regularization in Deep Neural Networks: Evidence from Random Matrix Theory and Implications for Learning
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