Veiga, RodrigoStephan, LudovicLoureiro, BrunoKrzakala, FlorentZdeborova, Lenka2024-02-192024-02-192024-02-192023-11-0110.1088/1742-5468/ad01b1https://infoscience.epfl.ch/handle/20.500.14299/204231WOS:001105470100001Despite the non-convex optimization landscape, over-parametrized shallow networks are able to achieve global convergence under gradient descent. The picture can be radically different for narrow networks, which tend to get stuck in badly-generalizing local minima. Here we investigate the cross-over between these two regimes in the high-dimensional setting, and in particular investigate the connection between the so-called mean-field/hydrodynamic regime and the seminal approach of Saad & Solla. Focusing on the case of Gaussian data, we study the interplay between the learning rate, the time scale, and the number of hidden units in the high-dimensional dynamics of stochastic gradient descent (SGD). Our work builds on a deterministic description of SGD in high-dimensions from statistical physics, which we extend and for which we provide rigorous convergence rates.TechnologyPhysical SciencesLearning TheoryMachine LearningPhase Diagramstext::journal::journal article::research article