Limit Theorems for Stochastic Gradient Descent in High-Dimensional Single-Layer Networks

A recent paper published on arXiv investigates the high-dimensional scaling limits of online stochastic gradient descent (SGD) applied to single-layer neural networks. Building on earlier work by Saad and Solla, the study focuses on the critical scaling regime of the step size in SGD and its impact on the effective dynamics of the learning process. The authors analyze how these dynamics are governed by ballistic limits, providing new insights into the behavior of SGD in high-dimensional settings. This research contributes to a deeper understanding of the theoretical properties of SGD, particularly in the context of single-layer networks. The findings align with ongoing efforts in the machine learning community to characterize optimization algorithms under various scaling conditions. By elucidating the role of step size scaling, the paper offers a refined perspective on the convergence and stability of SGD. These results may inform future developments in training algorithms for neural networks, especially those operating in high-dimensional parameter spaces.