{"ID":2921167,"CreatedAt":"2026-06-02T02:42:49.606572591Z","UpdatedAt":"2026-06-04T05:31:30.864274012Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2606.01720","arxiv_id":"2606.01720","title":"A Note on Stability for Orthogonalized Matrix Momentum with Client Sampling","abstract":"We study finite-sample generalization for a client-sampled distributed optimization scheme with matrix-valued parameters and orthogonalized momentum updates. The central quantity is the gap between the population and empirical objectives at the returned model when only a subset of clients participates in each round. Under independent heterogeneous client data, unequal local sample counts, and fixed aggregation weights, we derive a finite-round upper-tail guarantee from a coupled-neighbor stability recursion and a weighted concentration step. The bound keeps the client-selection counts through the amplification factor \\(Y_i(\\mathcal C)\\); in the uniform full-participation full-batch regime, it yields \\(\\widetilde{\\mathcal O}(n^{-1}+n^{-1/2})\\) scaling whenever the horizon-dependent amplification terms are controlled. The matrix-orthogonalization rule is required to be Lipschitz along paired trajectories, a condition satisfied by regularized polar-type maps and normalized finite-step Newton--Schulz orthogonalizers. For the unregularized matrix sign, the same argument requires coupled spectral separation, whereas Gaussian smoothing gives a finite-round smoothed variant. A one-dimensional counterexample shows why a gap, smoothing, or regularity condition is necessary.","short_abstract":"We study finite-sample generalization for a client-sampled distributed optimization scheme with matrix-valued parameters and orthogonalized momentum updates. The central quantity is the gap between the population and empirical objectives at the returned model when only a subset of clients participates in each round. Un...","url_abs":"https://arxiv.org/abs/2606.01720","url_pdf":"https://arxiv.org/pdf/2606.01720v1","authors":"[\"Da Chang\",\"Qiankun Shi\",\"Lvgang Zhang\",\"Yu Li\",\"Ruijie Zhang\"]","published":"2026-06-01T05:36:26Z","proceeding":"cs.LG","tasks":"[\"cs.LG\"]","methods":"[]","has_code":false}