DP-Muon: Differentially Private Optimization via Matrix-Orthogonalized Momentum

תקציר מקורי באנגליתarXiv:2605.12994v2 Announce Type: replace Abstract: We study differentially private optimization with matrix-orthogonalized momentum. DP-Muon uses conventional global per-example clipping and one Gaussian gradient release per step; matrix updates and auxiliary updates are post-processing. Our main contribution concerns the additional mean distortion created when fresh Gaussian noise passes through a nonlinear matrix map. Conditioning on the actual adaptive history immediately before the current noise yields an exact Gaussian heat identity. For a smooth Newton-Schulz map, first-order DP-MuonBC reduces this conditional output bias from second to fourth order in the fresh noise scale, and an arbitrary-order extension has bias of order $2K+2$. We prove matrix-block stationarity bounds under gl