aiqbench analysis
This paper introduces Chained LMOs, a unified framework for optimizing large language models by composing matrix normalizations to improve training efficiency over standard methods like Muon. By leveraging linear associative memory theory, the authors demonstrate that their proposed TensorChain optimizer achieves significant token savings during pretraining on Qwen3 models. The work addresses fragmentation in current optimization techniques and offers a more robust approach for handling anisotropic embeddings in deep learning architectures.
Optimizing Large Language Models with Chained LMOs
arXiv:2610.10975v1 Announce Type: cross 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.
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.
Machine Learning (cs.LG); Artificial Intelligence (cs.AI)
arXiv:2610.10975 [cs.LG]
(or arXiv:2610.10975v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2610.10975 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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