Sign compression for Muon: SignMuon, MuonSign, and the Limits of Error Feedback
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. Signing the gradient before the Linear Minimization Oracle (LMO), rather than after, does not repair this: we construct a small explicit instance on which sign-before (MuonUSign) and sign-on-both-sides (MuonSign) ascend as well, so no placement of the sign around the oracle descends in general. Error feedback, the standard remedy for a biased compressor, does not rescue SignMuon: when applied to Muon's output, er...
| Authors | Maria Smirnova, Alexey Kravatskiy |
|---|---|
| Primary category | math.OC |
| Published | 31 July 2026 |
| Last updated at source | 31 July 2026 |
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