Non-Asymptotic Optimization and Generalization Bounds for Stochastic Gauss-Newton in Overparameterized Models

• URL: http://arxiv.org/abs/2511.03972v2
• Date: Thu, 13 Nov 2025 01:27:41 GMT
• Title: Non-Asymptotic Optimization and Generalization Bounds for Stochastic Gauss-Newton in Overparameterized Models
• Authors: Semih Cayci,
• Abstract summary: We analyze a matrix Gauss-Newton (SGN) method with Levenberg-Marquardt damping and mini-batch sampling.<n>Our theoretical results identify a favorable generalization regime for SGN in which a larger minimum eigenvalue of the Gauss-Newton along the optimization path yields tighter stability bounds.
• Score: 5.076419064097734
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: An important question in deep learning is how higher-order optimization methods affect generalization. In this work, we analyze a stochastic Gauss-Newton (SGN) method with Levenberg-Marquardt damping and mini-batch sampling for training overparameterized deep neural networks with smooth activations in a regression setting. Our theoretical contributions are twofold. First, we establish finite-time convergence bounds via a variable-metric analysis in parameter space, with explicit dependencies on the batch size, network width and depth. Second, we derive non-asymptotic generalization bounds for SGN using uniform stability in the overparameterized regime, characterizing the impact of curvature, batch size, and overparameterization on generalization performance. Our theoretical results identify a favorable generalization regime for SGN in which a larger minimum eigenvalue of the Gauss-Newton matrix along the optimization path yields tighter stability bounds.

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