From Muon to Gradient Clipping: Some Thoughts on QK Stability

This technical article explores instability issues with the Muon optimizer when applied to Query and Key matrices in Transformer models, analyzing the root cause through function-space optimization theory and proposing that Muon's spectral norm constraint creates geometric conflicts in bilinear attention mechanisms. For IT organizations deploying large language models, this research has direct implications for training stability, infrastructure reliability, and the selection of optimization strategies that balance theoretical elegance with practical robustness in production environments.