Pith Number

pith:LBYHKZIF

pith:2025:LBYHKZIFBC3NFDMIJCWCR3OEE7

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Row-Stochastic Matrices Can Provably Outperform Doubly Stochastic Matrices in Decentralized Learning

Bing Liu, Boao Kong, Chengcheng Zhao, Kun Yuan, Limin Lu

Row-stochastic matrices can converge faster than doubly stochastic matrices in decentralized learning by avoiding extra consensus penalties in weighted geometry.

arxiv:2511.19513 v3 · 2025-11-24 · cs.LG

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Claims

C1strongest 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.

C2weakest 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.

C3one 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.

Formal links

1 machine-checked theorem link

Receipt and verification

First computed	2026-06-01T01:02:26.012014Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

587075650508b6d28d8848ac28edc427d22e74088bdea84fb06de791e033ab91

Aliases

arxiv: 2511.19513 · arxiv_version: 2511.19513v3 · doi: 10.48550/arxiv.2511.19513 · pith_short_12: LBYHKZIFBC3N · pith_short_16: LBYHKZIFBC3NFDMI · pith_short_8: LBYHKZIF

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/LBYHKZIFBC3NFDMIJCWCR3OEE7 \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 587075650508b6d28d8848ac28edc427d22e74088bdea84fb06de791e033ab91

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e954eb4601c01dbdbba7a830b24a85367764ce34a926bf558bab17547e27c15a",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2025-11-24T02:58:38Z",
    "title_canon_sha256": "7f36bbc78e23d25b3faf514c734e5938d7fc62e19cdf81b459838812fc9819ca"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2511.19513",
    "kind": "arxiv",
    "version": 3
  }
}