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On Single Index Models beyond Gaussian Data
Joan Bruna, Loucas Pillaud-Vivien, Aaron Zweig
Sparse high-dimensional functions have arisen as a rich framework to study the behavior of gradient-descent methods using shallow neural networks, showcasing their ability to perfo…
A Neural Collapse Perspective on Feature Evolution in Graph Neural Networks
Vignesh Kothapalli, Tom Tirer, Joan Bruna
Graph neural networks (GNNs) have become increasingly popular for classification tasks on graph-structured data. Yet, the interplay between graph topology and feature evolution in…
Learning Single-Index Models with Shallow Neural Networks
Alberto Bietti, Joan Bruna, Clayton Sanford +1
Single-index models are a class of functions given by an unknown univariate ``link'' function applied to an unknown one-dimensional projection of the input. These models are partic…
On Feature Learning in Neural Networks with Global Convergence Guarantees
Zhengdao Chen, Eric Vanden-Eijnden, Joan Bruna
We study the optimization of wide neural networks (NNs) via gradient flow (GF) in setups that allow feature learning while admitting non-asymptotic global convergence guarantees. F…
Simultaneous Transport Evolution for Minimax Equilibria on Measures
Carles Domingo-Enrich, Joan Bruna
Min-max optimization problems arise in several key machine learning setups, including adversarial learning and generative modeling. In their general form, in absence of convexity/c…
Lattice-Based Methods Surpass Sum-of-Squares in Clustering
Ilias Zadik, Min Jae Song, Alexander S. Wein +1
Clustering is a fundamental primitive in unsupervised learning which gives rise to a rich class of computationally-challenging inference tasks. In this work, we focus on the canoni…