Sophia: A Scalable Stochastic Second-order Optimizer for Language Model Pre-training

Published: 20 Jun 2023, Last Modified: 16 Jul 2023ES-FoMO 2023 PosterEveryoneRevisionsBibTeX
Keywords: large language models, language modeling, pre-training, second-order optimizers, adaptive optimzers
TL;DR: We design a stochastic second-order optimizer for language model pre-training which is 2x faster than Adam.
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-2 models of sizes ranging from 125M to 770M, Sophia achieves a 2x speed-up compared with Adam in the number of steps, total compute, and wall-clock time.
Submission Number: 38