{"paper":{"title":"Row-Stochastic Matrices Can Provably Outperform Doubly Stochastic Matrices in Decentralized Learning","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Row-stochastic matrices can converge faster than doubly stochastic matrices in decentralized learning by avoiding extra consensus penalties in weighted geometry.","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Bing Liu, Boao Kong, Chengcheng Zhao, Kun Yuan, Limin Lu","submitted_at":"2025-11-24T02:58:38Z","abstract_excerpt":"Decentralized learning often involves a weighted global loss with heterogeneous node weights $\\lambda$. We revisit two natural strategies for incorporating these weights: (i) embedding them into the local losses to retain a uniform weight (and thus a doubly stochastic matrix), and (ii) keeping the original losses while employing a $\\lambda$-induced row-stochastic matrix. Although prior work shows that both strategies target the same $\\lambda$-weighted global loss, it remains unclear whether the Euclidean-space guarantees are tight and what fundamentally differentiates their behaviors. To clari"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"In this geometry, the row-stochastic matrix becomes self-adjoint whereas the doubly stochastic one does not, creating additional penalty terms that amplify consensus error, thereby slowing convergence. We then derive sufficient conditions under which the row-stochastic design converges faster even with a smaller spectral gap.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the weighted Hilbert-space framework L^2(λ; ℝ^d) is the appropriate geometry for revealing the true convergence behavior and that the identified penalty terms are the dominant differentiator rather than other unmodeled dynamics in the optimization process.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Row-stochastic matrices can provably outperform doubly stochastic matrices in convergence speed for weighted decentralized learning by becoming self-adjoint in a custom L^2(λ; ℝ^d) geometry, eliminating penalty terms that slow consensus.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Row-stochastic matrices can converge faster than doubly stochastic matrices in decentralized learning by avoiding extra consensus penalties in weighted geometry.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"1dfb0cf275064df2ab30bfd781d69d55e540cae2d9bb4c573f51e05e8840895d"},"source":{"id":"2511.19513","kind":"arxiv","version":3},"verdict":{"id":"37ff062d-beaa-4ee5-bcae-ccf9ad554c1a","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-17T05:34:41.572457Z","strongest_claim":"In this geometry, the row-stochastic matrix becomes self-adjoint whereas the doubly stochastic one does not, creating additional penalty terms that amplify consensus error, thereby slowing convergence. We then derive sufficient conditions under which the row-stochastic design converges faster even with a smaller spectral gap.","one_line_summary":"Row-stochastic matrices can provably outperform doubly stochastic matrices in convergence speed for weighted decentralized learning by becoming self-adjoint in a custom L^2(λ; ℝ^d) geometry, eliminating penalty terms that slow consensus.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the weighted Hilbert-space framework L^2(λ; ℝ^d) is the appropriate geometry for revealing the true convergence behavior and that the identified penalty terms are the dominant differentiator rather than other unmodeled dynamics in the optimization process.","pith_extraction_headline":"Row-stochastic matrices can converge faster than doubly stochastic matrices in decentralized learning by avoiding extra consensus penalties in weighted geometry."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2511.19513/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":1,"snapshot_sha256":"ee28d4fc6c1698e20b2b23c718c8e1ea1e342da67c506ee99f9bff3d92d31970"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}