Convergence of stochastic gradient descent under a local Lojasiewicz condition for deep neural networks

• URL: http://arxiv.org/abs/2304.09221v2
• Date: Fri, 12 Jan 2024 23:41:44 GMT
• Title: Convergence of stochastic gradient descent under a local Lojasiewicz condition for deep neural networks
• Authors: Jing An and Jianfeng Lu
• Abstract summary: We establish the convergence of the local local convergence with positive gradient. We provide examples of neural networks with finite widths such that our assumptions hold.
• Score: 7.9626223030099545
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 \L{}ojasiewicz condition introduced by Chatterjee in \cite{chatterjee2022convergence} 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.

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