Global Exponential Convergence of Two-Layer Linear Network Training
We prove global exponential (linear) convergence with an explicit rate in the rich scaling for wide two-layer linear networks trained with smooth Polyak-Lojasiewicz predictor losses. Gradient flow in the factors closes exactly in terms of a finite-dimensional Bures flow of the neuron law covariance, in which the predictor dynamics are preconditioned by hidden covariance blocks. Mean-field conservation laws provide uniform spectral lower bounds on the hidden preconditioning blocks when the initial covariance satisfies a spectral support gap condition. This condition encompasses positive definiteness while still allowing for singular initializations. For an initial covariance $Σ_0 = σ^2 \ma...
| Authors | Stephen Y Zhang, Gabriel Peyré |
|---|---|
| Primary category | cs.LG |
| Published | 7 October 2026 |
| Last updated at source | 7 October 2026 |
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