DP-Muon: Differentially Private Optimization via Matrix-Orthogonalized Momentum
Updated 5 h ago · first seen 11 Sept 2026
paper_01M294FS6RVG5VQ97294BQ5WB8
- Published
- 11 Sept 2026
- T1 · 5 h ago
- arXiv
- 2605.12994
- T1 · 5 h ago
- Category
- cs.LG
- T1 · 5 h ago
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 global clipping, retain finite-step orthogonalization error explicitly, and give an exact criterion for improvement of the resulting upper bound. A separate inequality exposes the effect of auxiliary Adam updates. GPT-2 experiments on E2E at four privacy targets favor the reported Muon configurations over Adam baselines in test NLL.
Authors 2
Jihwan Kim, Chenglin Fan
Specification
- Official page
Source:arXiv (Atom API + RSS)T1observed 5 h agohigh
- Arxiv announce type
- replace
Source:arXiv (Atom API + RSS)T1observed 5 h agohigh
- arXiv id
- 2605.12994
Source:arXiv (Atom API + RSS)T1observed 5 h agohigh
- Categories
- cs.LG
Source:arXiv (Atom API + RSS)T1observed 5 h agohigh
Source:arXiv (Atom API + RSS)T1observed 5 h agohigh
- Primary category
- cs.LG
Source:arXiv (Atom API + RSS)T1observed 5 h agohigh
- Published
- 11 Sept 2026
Source:arXiv (Atom API + RSS)T1observed 5 h agohigh
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5 h ago
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- Authors
- Jihwan Kim, Chenglin Fan
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Claim history · Abstract
Abstractabstract1
| Value | Valid from → to | Status | Source | Confidence | Extractor |
|---|---|---|---|---|---|
| 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 global clipping, retain finite-step orthogonalization error explicitly, and give an exact criterion for improvement of the resulting upper bound. A separate inequality exposes the effect of auxiliary Adam updates. GPT-2 experiments on E2E at four privacy targets favor the reported Muon configurations over Adam baselines in test NLL. | → current | current | arXiv (Atom API + RSS)T1 | high | deterministic |
Claims are temporal and append-only: a new observation closes the previous claim (valid_to) instead of overwriting it. Conflicting claims from different sources are kept side by side and flagged — never averaged. Methodology →
New paper: DP-Muon: Differentially Private Optimization via Matrix-Orthogonalized Momentum
arxiv
| Source | Document | Type | Tier | Last observed | Snapshots |
|---|---|---|---|---|---|
| arXiv (Atom API + RSS) | rss.arxiv.org/rss/cs.LG | feed | T1· Official | 4 h ago | 1 |
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