108 citations · 112 across the 8 of their papers we have counts for
9 papers
Replica Symmetry Breaking and Algorithmic Thresholds in Empirical Risk Minimization under Multi-Index Model
Andrea Montanari, Kangjie Zhou
Modern machine learning models are trained by optimizing high-dimensional non-convex empirical risk functions. Such cost functions can have a multitude of local optima and yet, gra…
Topological trivialization in non-convex empirical risk minimization
Andrea Montanari, Basil Saeed
Given data , with standard -dimensional Gaussian feature vectors, and response variables, we study t…
Dynamical Decoupling of Generalization and Overfitting in Large Two-Layer Networks
Andrea Montanari, Pierfrancesco Urbani
Understanding the inductive bias and generalization properties of large overparametrized machine learning models requires to characterize the dynamics of the training algorithm. We…
Local minima of the empirical risk in high dimension: General theorems and convex examples
Kiana Asgari, Andrea Montanari, Basil Saeed
We consider a general model for high-dimensional empirical risk minimization whereby the data are -dimensional Gaussian vectors, the model is parametrized by $\ma…
Scaling Training Data with Lossy Image Compression
Katherine L. Mentzer, Andrea Montanari
Empirically-determined scaling laws have been broadly successful in predicting the evolution of large machine learning models with training data and number of parameters. As a cons…
Which exceptional low-dimensional projections of a Gaussian point cloud can be found in polynomial time?
Andrea Montanari, Kangjie Zhou
Given -dimensional standard Gaussian vectors , we consider the set of all empirical distributions of its -dimensional projections, f…
On Smale's 17th problem over the reals
Andrea Montanari, Eliran Subag
We consider the problem of efficiently solving a system of non-linear equations in . Addressing Smale's 17th problem stated in 1998, we consider a setting whereb…
Universality of max-margin classifiers
Andrea Montanari, Feng Ruan, Basil Saeed +1
Maximum margin binary classification is one of the most fundamental algorithms in machine learning, yet the role of featurization maps and the high-dimensional asymptotics of the m…
Extremal Cuts of Sparse Random Graphs
Amir Dembo, Andrea Montanari, Subhabrata Sen
For Erdős-Rényi random graphs with average degree , and uniformly random -regular graph on vertices, we prove that with high probability the size of both the Max-Cut and…