Top Tweets for #HTMuon

about 1 month ago

Introducing #HTMuon, a simple spectral correction to Muon inspired by Heavy-Tailed Self-Regularization, improving performance across LLM pretraining and image classification while retaining strong theoretical guarantees. #Muon #Optimization

Tianyu Pang

@TianyuPang327

about 1 month ago

🎉 Excited to share our recent Findings of ACL 2026 paper, HTMuon! Muon has recently shown promising results in LLM training. But can we further improve its update rule? In our new work, we study Muon from the perspective of Heavy-Tailed Self-Regularization (HT-SR) theory and introduce HTMuon, a simple yet effective spectral correction for Muon. Our key contributions are: 1. Understanding a limitation of Muon. Muon’s orthogonalized update rule can over-emphasize noise-dominated directions and suppress the emergence of heavy-tailed eigenspectral distributions in the model’s weight matrices, potentially limiting performance under HT-SR theory. 2. Introducing HTMuon. While Muon uses the orthogonalized update UV^T, HTMuon considers the more general form U\Sigma^pV^T, introducing a spectral correction. This enables HTMuon to produce heavier-tailed updates while preserving Muon’s strength in capturing parameter interdependencies. Across LLM pretraining and image classification, HTMuon consistently improves over Muon and other strong optimizers. It can also be used as a plug-in correction for existing Muon variants. For example, HTMuon reduces perplexity by up to 0.98 over Muon in LLaMA pretraining on C4. We further develop accelerated implementations and demonstrate improvements over Muon on LLaMA-1B. 3. Providing a theoretical characterization. We show that HTMuon is equivalent to steepest descent under a Schatten-q norm constraint and provide a convergence analysis in smooth non-convex settings. The results show that HTMuon retains competitive convergence guarantees while improving practical training performance. 📄 Paper: https://t.co/7yqov5p3jP 💻 Code: https://t.co/iWVtOBspcS Many thanks to my collaborators Yujie Fang, @HenryLiu0820, @DengShenyang24, @twweeb , Shuhua Yu and @nsfzyzz !

$TianyuPang327's tweet photo. 🎉 Excited to share our recent Findings of ACL 2026 paper, HTMuon! Muon has recently shown promising results in LLM training. But can we further improve its update rule? In our new work, we study Muon from the perspective of Heavy-Tailed Self-Regularization (HT-SR) theory and introduce HTMuon, a simple yet effective spectral correction for Muon. Our key contributions are: 1. Understanding a limitation of Muon. Muon’s orthogonalized update rule can over-emphasize noise-dominated directions and suppress the emergence of heavy-tailed eigenspectral distributions in the model’s weight matrices, potentially limiting performance under HT-SR theory. 2. Introducing HTMuon. While Muon uses the orthogonalized update UV^T, HTMuon considers the more general form U\Sigma^pV^T, introducing a spectral correction. This enables HTMuon to produce heavier-tailed updates while preserving Muon’s strength in capturing parameter interdependencies. Across LLM pretraining and image classification, HTMuon consistently improves over Muon and other strong optimizers. It can also be used as a plug-in correction for existing Muon variants. For example, HTMuon reduces perplexity by up to 0.98 over Muon in LLaMA pretraining on C4. We further develop accelerated implementations and demonstrate improvements over Muon on LLaMA-1B. 3. Providing a theoretical characterization. We show that HTMuon is equivalent to steepest descent under a Schatten-q norm constraint and provide a convergence analysis in smooth non-convex settings. The results show that HTMuon retains competitive convergence guarantees while improving practical training performance. 📄 Paper: https://t.co/7yqov5p3jP 💻 Code: https://t.co/iWVtOBspcS Many thanks to my collaborators Yujie Fang, @HenryLiu0820, @DengShenyang24, @twweeb , Shuhua Yu and @nsfzyzz !$

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