Non-Asymptotic Generalization and Optimization Bounds for Stochastic Gauss-Newton in Deep Neural Networks

Semih Cayci
Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, PMLR 300:1549-1557, 2026.

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 optimization 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 algorithmic 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, together with smaller batch sizes, yields tighter stability bounds.

Cite this Paper

BibTeX
@InProceedings{pmlr-v300-cayci26a, title = { Non-Asymptotic Generalization and Optimization Bounds for Stochastic Gauss-Newton in Deep Neural Networks }, author = {Cayci, Semih}, booktitle = {Proceedings of The 29th International Conference on Artificial Intelligence and Statistics}, pages = {1549--1557}, year = {2026}, editor = {Khan, Emtiyaz and Li, Yingzhen and Solin, Arno and Ramdas, Aaditya}, volume = {300}, series = {Proceedings of Machine Learning Research}, month = {02--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v300/main/assets/cayci26a/cayci26a.pdf}, url = {https://proceedings.mlr.press/v300/cayci26a.html}, 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 optimization 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 algorithmic 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, together with smaller batch sizes, yields tighter stability bounds. } }
Endnote
%0 Conference Paper %T Non-Asymptotic Generalization and Optimization Bounds for Stochastic Gauss-Newton in Deep Neural Networks %A Semih Cayci %B Proceedings of The 29th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2026 %E Emtiyaz Khan %E Yingzhen Li %E Arno Solin %E Aaditya Ramdas %F pmlr-v300-cayci26a %I PMLR %P 1549--1557 %U https://proceedings.mlr.press/v300/cayci26a.html %V 300 %X 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 optimization 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 algorithmic 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, together with smaller batch sizes, yields tighter stability bounds.
APA
Cayci, S.. (2026). Non-Asymptotic Generalization and Optimization Bounds for Stochastic Gauss-Newton in Deep Neural Networks . Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 300:1549-1557 Available from https://proceedings.mlr.press/v300/cayci26a.html.

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