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Muon optimizer's momentum acts as spectral filter, study finds

By PulseAugur Editorial · [3 sources] ·

Researchers have published a paper detailing the theoretical underpinnings of the Muon optimizer, a technique used in large language model training. The study reveals that Muon's momentum acts as a spectral filter, effectively suppressing noise while preserving the core signal in gradients. This process enlarges the spectral gap, stabilizing the matrix updates and leading to more reliable results, particularly when momentum is applied before orthogonalization. AI

IMPACT Provides theoretical grounding for optimization techniques used in LLM training, potentially improving future model development.

RANK_REASON Academic paper published on arXiv detailing theoretical analysis of an optimization technique.

Read on arXiv cs.LG →

AI-generated summary · Google Gemini · from 3 sources. How we write summaries →

COVERAGE [3]

  1. arXiv cs.AI TIER_1 English(EN) · Gagik Magakyan, Pablo Parrilo, Asuman Ozdaglar ·

    Spectral Scaling Laws of Muon

    arXiv:2606.04058v1 Announce Type: cross Abstract: Orthonormalized update rules have rapidly become a leading choice of optimizer for training large language models, with recent open-source state-of-the-art models adopting Muon. To keep these updates tractable, Muon performs the o…

  2. arXiv cs.LG TIER_1 English(EN) · Xianliang Li, Zihan Zhang, Weiyang Liu, Han Bao ·

    Denoise First, Orthogonalize Later: Understanding Momentum in Muon via Spectral Filtering

    arXiv:2606.03899v1 Announce Type: new Abstract: Muon has recently demonstrated strong empirical performance in large language model training, but the theoretical role of momentum in Muon remains unclear. Existing analyses of Muon either remove momentum to study spectral updates i…

  3. arXiv cs.LG TIER_1 English(EN) · Han Bao ·

    Denoise First, Orthogonalize Later: Understanding Momentum in Muon via Spectral Filtering

    Muon has recently demonstrated strong empirical performance in large language model training, but the theoretical role of momentum in Muon remains unclear. Existing analyses of Muon either remove momentum to study spectral updates in isolation, or retain momentum without explaini…

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