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Donate arxiv logo > cs > arXiv:2305.14342 [ ] Help | Advanced Search [All fields ] Search arXiv logo Cornell University Logo [ ] GO quick links * Login * Help Pages * About Computer Science > Machine Learning arXiv:2305.14342 (cs) [Submitted on 23 May 2023 (v1), last revised 5 Mar 2024 (this version, v4)] Title:Sophia: A Scalable Stochastic Second-order Optimizer for Language Model Pre-training Authors:Hong Liu, Zhiyuan Li, David Hall, Percy Liang, Tengyu Ma View a PDF of the paper titled Sophia: A Scalable Stochastic Second-order Optimizer for Language Model Pre-training, by Hong Liu and 4 other authors View PDF HTML (experimental) Abstract:Given the massive cost of language model pre-training, a non-trivial improvement of the optimization algorithm would lead to a material reduction on the time and cost of training. Adam and its variants have been state-of-the-art for years, and more sophisticated second-order (Hessian-based) optimizers often incur too much per-step overhead. In this paper, we propose Sophia, Second-order Clipped Stochastic Optimization, a simple scalable second-order optimizer that uses a light-weight estimate of the diagonal Hessian as the pre-conditioner. The update is the moving average of the gradients divided by the moving average of the estimated Hessian, followed by element-wise clipping. The clipping controls the worst-case update size and tames the negative impact of non-convexity and rapid change of Hessian along the trajectory. Sophia only estimates the diagonal Hessian every handful of iterations, which has negligible average per-step time and memory overhead. On language modeling with GPT models of sizes ranging from 125M to 1.5B, Sophia achieves a 2x speed-up compared to Adam in the number of steps, total compute, and wall-clock time, achieving the same perplexity with 50% fewer steps, less total compute, and reduced wall-clock time. Theoretically, we show that Sophia, in a much simplified setting, adapts to the heterogeneous curvatures in different parameter dimensions, and thus has a run-time bound that does not depend on the condition number of the loss. Subjects: Machine Learning (cs.LG); Computation and Language (cs.CL); Optimization and Control (math.OC) Cite as: arXiv:2305.14342 [cs.LG] (or arXiv:2305.14342v4 [cs.LG] for this version) https://doi.org/10.48550/arXiv.2305.14342 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Hong Liu [view email] [v1] Tue, 23 May 2023 17:59:21 UTC (2,993 KB) [v2] Mon, 9 Oct 2023 19:54:09 UTC (2,777 KB) [v3] Tue, 17 Oct 2023 07:44:16 UTC (2,777 KB) [v4] Tue, 5 Mar 2024 17:07:16 UTC (6,090 KB) Full-text links: Access Paper: View a PDF of the paper titled Sophia: A Scalable Stochastic Second-order Optimizer for Language Model Pre-training, by Hong Liu and 4 other authors * View PDF * HTML (experimental) * TeX Source * Other Formats license icon view license Current browse context: cs.LG < prev | next > new | recent | 2305 Change to browse by: cs cs.CL math math.OC References & Citations * NASA ADS * Google Scholar * Semantic Scholar a export BibTeX citation Loading... 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