MARS-M: When Variance Reduction Meets Matrices

Code

• github.com/agi-arena/mars
  OfficialIn paper★ 717

Abstract

Matrix-based preconditioned optimizers, such as Muon, have recently been shown to be more efficient than scalar-based optimizers for training large-scale neural networks, including large language models (LLMs). Recent benchmark studies of LLM pretraining optimizers have demonstrated that variance-reduction techniques such as MARS can substantially speed up training compared with standard optimizers that do not employ variance reduction. In this paper, we introduce MARS-M, a new optimizer that integrates MARS-style variance reduction with Muon. Under standard regularity conditions, we prove that MARS-M converges to a first-order stationary point at a rate of O(T^-1/3), improving upon the O(T^-1/4) rate attained by Muon. Empirical results on language modeling and computer vision tasks demonstrate that MARS-M consistently yields lower losses and improved performance across various downstream benchmarks. The implementation of MARS-M is available at https://github.com/AGI-Arena/MARS/tree/main/MARS_M.

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