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Global Exponential Convergence Proven for Two-Layer Linear Networks

By PulseAugur Editorial · [1 sources] ·

Researchers have proven global exponential convergence for training wide two-layer linear networks using smooth Polyak-Lojasiewicz predictor losses. The study demonstrates that gradient flow in the factors can be precisely described by a finite-dimensional Bures flow, which is influenced by the neuron law covariance. This convergence rate is further supported by mean-field conservation laws that establish spectral lower bounds on the hidden preconditioning blocks, provided the initial covariance meets a spectral support gap condition. The findings extend to deep linear ResNets and are illustrated through numerical experiments comparing predicted and observed rates. AI

IMPACT Provides theoretical guarantees for training linear neural networks, potentially informing future optimization techniques.

RANK_REASON Academic paper detailing theoretical convergence properties of neural network training. [lever_c_demoted from research: ic=1 ai=1.0]

Read on arXiv cs.LG →

AI-generated summary · Google Gemini · from 1 sources. How we write summaries →

Global Exponential Convergence Proven for Two-Layer Linear Networks

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Academic paper detailing theoretical convergence properties of neural network training. [lever_c_demoted from research: ic=1 ai=1.0]
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COVERAGE [1]

  1. arXiv cs.LG TIER_1 English(EN) · Stephen Y Zhang, Gabriel Peyr\'e ·

    Global Exponential Convergence of Two-Layer Linear Network Training

    arXiv:2610.09356v1 Announce Type: new Abstract: 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 te…

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