@Article{JML-4-2,
author = {Jing, An and Lu, Jianfeng},
title = {Convergence of Stochastic Gradient Descent under a Local Łojasiewicz Condition for Deep Neural Networks},
journal = {Journal of Machine Learning},
year = {2025},
volume = {4},
number = {2},
pages = {89--107},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {2790-2048},
doi = {https://doi.org/10.4208/jml.240724},
url = {https://global-sci.com/article/91924/convergence-of-stochastic-gradient-descent-under-a-local-lojasiewicz-condition-for-deep-neural-networks}
}