The Benefits of Reusing Batches for Gradient Descent in Two-Layer Networks: Breaking the Curse of Information and Leap Exponents

التفاصيل البيبلوغرافية
العنوان: The Benefits of Reusing Batches for Gradient Descent in Two-Layer Networks: Breaking the Curse of Information and Leap Exponents
المؤلفون: Dandi, Yatin, Troiani, Emanuele, Arnaboldi, Luca, Pesce, Luca, Zdeborová, Lenka, Krzakala, Florent
سنة النشر: 2024
المجموعة: Computer Science
Statistics
مصطلحات موضوعية: Statistics - Machine Learning, Computer Science - Machine Learning
الوصف: We investigate the training dynamics of two-layer neural networks when learning multi-index target functions. We focus on multi-pass gradient descent (GD) that reuses the batches multiple times and show that it significantly changes the conclusion about which functions are learnable compared to single-pass gradient descent. In particular, multi-pass GD with finite stepsize is found to overcome the limitations of gradient flow and single-pass GD given by the information exponent (Ben Arous et al., 2021) and leap exponent (Abbe et al., 2023) of the target function. We show that upon re-using batches, the network achieves in just two time steps an overlap with the target subspace even for functions not satisfying the staircase property (Abbe et al., 2021). We characterize the (broad) class of functions efficiently learned in finite time. The proof of our results is based on the analysis of the Dynamical Mean-Field Theory (DMFT). We further provide a closed-form description of the dynamical process of the low-dimensional projections of the weights, and numerical experiments illustrating the theory.
Comment: Accepted at the International Conference on Machine Learning (ICML), 2024
نوع الوثيقة: Working Paper
URL الوصول: http://arxiv.org/abs/2402.03220
رقم الأكسشن: edsarx.2402.03220
قاعدة البيانات: arXiv