arXiv:2605.22010v1 Announce Type: cross Abstract: We consider one-hidden layer neural networks trained in the feature-learning regime using gradient descent, and relate the output of the finite-width network $f_{\hat{\rho}_t^m}$ to its infinite-width counterpart $f_{\rho_t^{MF}}$, which evolves in the mean-field dynamics. While constant-time horizon bounds for $\|f_{\rho_t^{MF}} - f_{\hat{\rho}_t^m}\|$ may be obtained via standard Gr\"onwall estimates, the long-time behavior of the fluctuation is a more delicate matter. Uniform-in-time bounds often rely on (local) strong convexity in the lands
This is a theoretical paper in the field of machine learning, published as part of the ongoing academic research cycle.
For a strategic reader, this highly technical academic paper presents a very localized and theoretical advancement within AI research with no immediate practical implications.
No immediate or practical changes are brought about by this specific theoretical advancement for broader AI development or application.
This paper contributes to the academic body of knowledge regarding neural network dynamics.
Understanding the long-term behavior of neural networks could theoretically improve future training stability or predictability of specific models.
These theoretical insights might eventually inform the design of more robust or efficient AI systems, but such an impact is distant and indirect.
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