Monarch-Muon: Structure-Aware Muon for Fast and Memory-Efficient Pretraining
Training large language models is constrained by both wall-clock time and memory footprint, and recent matrix-aware optimizers sharpen this tradeoff: Muon can improve optimization but its dense polar update remains expensive. We propose Monarch-Muon, a structured matrix-aware optimizer for weights parameterized by Monarch factors. The resulting structure reduces weights, gradients, and optimizer state, and exposes small independent update subproblems in place of a single dense orthogonalization; we formalize this through a blockwise trust-region interpretation. In quality runs, Monarch-Muon improves over Monarch-AdamW at fixed structure: 3.06 vs. 3.09 in the dense 257M model and 2.68 vs. ...
| Authors | Alexander Miasnikov, Ruslan Kabirov, Gleb Molodtsov et al. |
|---|---|
| Primary category | cs.LG |
| Published | 12 October 2026 |
| Last updated at source | 12 October 2026 |
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