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math.OC2026
Sign compression for Muon: SignMuon, MuonSign, and the Limits of Error Feedback
Maria Smirnova, Alexey Kravatskiy
SignMuon compresses the Muon update to one bit per parameter by taking its elementwise sign, providing the most direct way to run a matrix-aware optimizer under an extremely low co…
math.OC2025
Ky Fan Norms and Beyond: Dual Norms and Combinations for Matrix Optimization
Alexey Kravatskiy, Ivan Kozyrev, Nikolai Kozlov +3
In this article, we explore the use of various matrix norms for optimizing functions of weight matrices, a crucial problem in deep learning. Moving beyond the spectral norm that un…