arXiv cs.AI· Sungyoon Kim, Kaan Ozkara, Youngsuk Park·· 9 天前AI 评分22
用链式 LMO 优化大语言模型：TensorChain 在 Qwen3 预训练中比 Muon 省 9.6% token
Optimizing Large Language Models with Chained LMOs
AI 导读
研究者提出链式线性最小化预言机（chained LMOs）框架，将 Muon 等由多种矩阵归一化组合而成的优化器统一为 LMO 的组合，并指出许多链式方法超出标准 LMO 框架、在光滑凸目标上可能发散。
正文 · 原文
Abstract:Muon has motivated a growing family of optimizers that compose multiple matrix normalizations, but these methods remain fragmented and lack a unified perspective. We introduce chained linear minimization oracles (chained LMOs), which cast these methods as compositions of LMOs. Despite their empirical success, many chains fall outside the standard LMO framework and can diverge on smooth convex objectives. To explain why composition can nevertheless help, we turn to linear associative memory and show that chaining can improve over Muon under anisotropic embeddings. Empirically, we propose TensorChain, a novel optimizer within the framework that stacks compatible weight matrices across different layers and normalizes the 3d tensor across its axes. In Qwen3 0.6B and 1.7B pretraining, TensorChain outperforms all chained baselines in average token efficiency, with average token savings of 9.6% over Muon at matched validation loss.
| Subjects: | Machine Learning (cs.LG); Artificial Intelligence (cs.AI) |
| Cite as: | arXiv:2610.10975 [cs.LG] |
| (or arXiv:2610.10975v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2610.10975 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Sungyoon Kim [view email]
[v1]
Wed, 7 Oct 2026 22:56:55 UTC (3,151 KB)
来源：arXiv cs.AI · arxiv.org