The Potential of Second-Order Optimization for LLMs: A Study with Full Gauss-Newton

• URL: http://arxiv.org/abs/2510.09378v1
• Date: Fri, 10 Oct 2025 13:35:10 GMT
• Title: The Potential of Second-Order Optimization for LLMs: A Study with Full Gauss-Newton
• Authors: Natalie Abreu, Nikhil Vyas, Sham Kakade, Depen Morwani,
• Abstract summary: Gauss-Newton (GN) preconditioning is highly effective for preconditioning, implying higher-order loss terms may not be critical for convergence speed.<n>A precise layerwise GN preconditioner, which ignores cross-layer information, nearly matches the performance of the full GN method.
• Score: 12.469584848673845
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Recent efforts to accelerate LLM pretraining have focused on computationally-efficient approximations that exploit second-order structure. This raises a key question for large-scale training: how much performance is forfeited by these approximations? To probe this question, we establish a practical upper bound on iteration complexity by applying full Gauss-Newton (GN) preconditioning to transformer models of up to 150M parameters. Our experiments show that full GN updates yield substantial gains over existing optimizers, achieving a 5.4x reduction in training iterations compared to strong baselines like SOAP and Muon. Furthermore, we find that a precise layerwise GN preconditioner, which ignores cross-layer information, nearly matches the performance of the full GN method. Collectively, our results suggest: (1) the GN approximation is highly effective for preconditioning, implying higher-order loss terms may not be critical for convergence speed; (2) the layerwise Hessian structure contains sufficient information to achieve most of these potential gains; and (3) a significant performance gap exists between current approximate methods and an idealized layerwise oracle.

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