Better Convergence Guarantees for Sign-Based Momentum Methods

arXiv:2507.12091 · math.OC, cs.LG · Submitted 2025-07-16 · Read on arXiv

math.OC, cs.LG

Submitted: 2025-07-16

Updated: 2026-10-01

Code: https://github.com/OptimalScale/LMFlow

Terminology

• Convergence Guarantees — 1× in this paper · explained in 3 episodes

Sources

• Convergence Rate Analysis of LION
• Stochastic-Sign SGD for Federated Learning with Theoretical Guarantees
• Muon is Scalable for LLM Training
• MARS-M: When Variance Reduction Meets Matrices
• LLaMA: Open and Efficient Foundation Language Models
• Qwen3 Technical Report

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