aiqbench analysis
SoftServe introduces a novel Quasi-Newton optimization family that addresses the non-convexity and scale limitations hindering these methods in deep learning. By leveraging stable coupled Newton-Schulz iterations, it replaces expensive matrix decompositions with GPU-friendly multiplications to handle massive parameter counts effectively. This approach demonstrates superior performance on ill-conditioned tasks like physics-informed diffusion models compared to standard baselines such as Adam and Muon.
SoftServe: A Scalable Quasi-Newton Method for Deep Learning
arXiv:2610.02182v1 Announce Type: cross Abstract: Quasi-Newton (QN) methods have long been among the most effective methods for large-scale unconstrained convex optimization. Two obstacles have limited their use in deep learning: non-convexity and enormous parameter sizes. We introduce SoftServe, a family of QN methods designed to overcome these obstacles without line searches or ad hoc curvature corrections. SoftServe derives positivedefinite curvature estimates from the variational objective of Berglund et al. (2025), even in the presence of negative curvature. We develop diagonal and Kroneckerfactored variants that preserve positive definiteness by construction and scale to massive neural networks. Finally, SoftServe relies on the stable coupled Newton-Schulz iteration for the required matrix operations, replacing costly matrix decompositions with GPU-friendly matrix multiplications. SoftServe excels on problems that are severely ill-conditioned, including tasks such as recurrent networks, deep autoencoders, physics-informed neural networks, and a 136M-parameter physics-informed diffusion model, often achieving lower losses than established baselines including Adam, Muon, and SOAP.
Abstract:Quasi-Newton (QN) methods have long been among the most effective methods for large-scale unconstrained convex optimization. Two obstacles have limited their use in deep learning: non-convexity and enormous parameter sizes. We introduce SoftServe, a family of QN methods designed to overcome these obstacles without line searches or ad hoc curvature corrections. SoftServe derives positivedefinite curvature estimates from the variational objective of Berglund et al. (2025), even in the presence of negative curvature. We develop diagonal and Kroneckerfactored variants that preserve positive definiteness by construction and scale to massive neural networks. Finally, SoftServe relies on the stable coupled Newton-Schulz iteration for the required matrix operations, replacing costly matrix decompositions with GPU-friendly matrix multiplications. SoftServe excels on problems that are severely ill-conditioned, including tasks such as recurrent networks, deep autoencoders, physics-informed neural networks, and a 136M-parameter physics-informed diffusion model, often achieving lower losses than established baselines including Adam, Muon, and SOAP.
Machine Learning (cs.LG); Artificial Intelligence (cs.AI)
arXiv:2610.02182 [cs.LG]
(or arXiv:2610.02182v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2610.02182 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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Full text under the publisher's open licence · 246 words
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