Tractability from overparametrization: the example of the negative perceptron

DOI10.1007/s00440-023-01248-yarXiv2110.15824WikidataQ129600093 ScholiaQ129600093MaRDI QIDQ6193766

No author found.

Publication date: 19 March 2024

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2110.15824

Mathematics Subject Classification ID

Artificial neural networks and deep learning (68T07) Linear programming (90C05) Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics (82B44)

Cites Work

• Unnamed Item
• Unnamed Item
• Approximating Mills ratio
• On quadratic transportation cost inequalities
• Large deviations techniques and applications.
• On the capabilities of multilayer perceptrons
• Some inequalities for Gaussian processes and applications
• Inner and outer \(j\)-radii of convex bodies in finite-dimensional normed spaces
• A geometric analysis of phase retrieval
• Rigorous solution of the Gardner problem
• Broken replica symmetry bounds in the mean field spin glass model
• The landscape of empirical risk for nonconvex losses
• Optimization of mean-field spin glasses
• On the robustness of minimum norm interpolators and regularized empirical risk minimizers
• Proof of the satisfiability conjecture for large \(k\)
• The phase transition for the existence of the maximum likelihood estimate in high-dimensional logistic regression
• Just interpolate: kernel ``ridgeless regression can generalize
• Phase Retrieval via Wirtinger Flow: Theory and Algorithms
• The simplest model of jamming
• Random k‐SAT: Two Moments Suffice to Cross a Sharp Threshold
• The threshold for random k-SAT is 2 ^k (ln 2 - O(k))
• Information, Physics, and Computation
• High-Dimensional Probability
• Precise Error Analysis of Regularized <inline-formula> <tex-math notation="LaTeX">$M$ </tex-math> </inline-formula>-Estimators in High Dimensions
• Storage capacity in symmetric binary perceptrons
• Optimization of the Sherrington--Kirkpatrick Hamiltonian
• Capacity lower bound for the Ising perceptron
• A modern maximum-likelihood theory for high-dimensional logistic regression
• Theory of Simple Glasses
• Walksat Stalls Well Below Satisfiability
• Matrix Completion From a Few Entries
• Out-of-equilibrium dynamical mean-field equations for the perceptron model
• Understanding Machine Learning
• Enumeration of Seven-Argument Threshold Functions
• An Inequality for Mill's Ratio
• Deep learning: a statistical viewpoint
• Fit without fear: remarkable mathematical phenomena of deep learning through the prism of interpolation
• The free energy in a multi-species Sherrington-Kirkpatrick model
• A theory of capacity and sparse neural encoding