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Convergence of stochastic gradient descent under a local Lojasiewicz condition for deep neural networks
Jing An, Jianfeng Lu · 2023-04-19 · via stat.ML updates on arXiv.org

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 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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