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stat.ML2025
Learning quadratic neural networks in high dimensions: SGD dynamics and scaling laws
Gérard Ben Arous, Murat A. Erdogdu, Nuri Mert Vural +1
We study the optimization and sample complexity of gradient-based training of a two-layer neural network with quadratic activation function in the high-dimensional regime, where th…
stat.ML2025
Stochastic gradient descent in high dimensions for multi-spiked tensor PCA
Gérard Ben Arous, Cédric Gerbelot, Vanessa Piccolo
We study the high-dimensional dynamics of online stochastic gradient descent (SGD) for the multi-spiked tensor model. This multi-index model arises from the tensor principal compon…
stat.ML2024
Langevin dynamics for high-dimensional optimization: the case of multi-spiked tensor PCA
Gérard Ben Arous, Gérard Ben Arous, Cédric Gerbelot +2
We study nonconvex optimization in high dimensions through Langevin dynamics, focusing on the multi-spiked tensor PCA problem. In this tensor estimation model, the goal is to recov…