AI RESEARCH
Uniform-in-Time Weak Propagation-of-Chaos in Shallow Neural Networks
arXiv CS.LG
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ArXi:2605.22010v1 Announce Type: cross 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 delicate matter.