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Convergence of Stochastic Gradient Descent under a Local Łojasiewicz Condition for Deep Neural Networks

Year:    2025

Author:    Jing An, Jianfeng Lu

Journal of Machine Learning, Vol. 4 (2025), Iss. 2 : pp. 89–107

Abstract

We study the convergence of stochastic gradient descent (SGD) for non-convex objective functions. We establish the local convergence with positive probability under the local Łojasiewicz condition introduced by Chatterjee [arXiv:2203.16462, 2022] and an additional local structural assumption of the loss function landscape. A key component of our proof is to ensure that the whole trajectories of SGD stay inside the local region with a positive probability. We also provide examples of neural networks with finite widths such that our assumptions hold.

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jml.240724

Journal of Machine Learning, Vol. 4 (2025), Iss. 2 : pp. 89–107

Published online:    2025-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    19

Keywords:    Non-convex optimization Stochastic gradient descent Convergence analysis.

Author Details

Jing An

Jianfeng Lu