Sign compression for Muon: SignMuon, MuonSign, and the Limits of Error Feedback
By Maria Smirnova · Paper · math.OC
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 communication budget. It outperforms SignSGD in practice, yet it can ascend even on a linear function.