Spherical mean-field Langevin dynamics concentrate near hidden indices in Gaussian multi-index models with a sharp temperature transition at λ ≃ 1 and achieve d/N and Md/N rates in single-index models via Lévy-Milman concentration.
arXiv preprint arXiv:2505.04898 , year=
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Proves GD convergence to stationary point neighborhoods for general NN architectures beyond NTK via block-level analysis, analyticity, and local smoothness conditions.
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The Geometry of Statistical Feature Learning in Mean-Field Langevin Dynamics
Spherical mean-field Langevin dynamics concentrate near hidden indices in Gaussian multi-index models with a sharp temperature transition at λ ≃ 1 and achieve d/N and Md/N rates in single-index models via Lévy-Milman concentration.
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Convergence of Gradient Descent for General Neural Network Architectures Beyond the NTK Regime
Proves GD convergence to stationary point neighborhoods for general NN architectures beyond NTK via block-level analysis, analyticity, and local smoothness conditions.
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Statistical Inference on Gradient Flows
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