Pith Number

pith:MDJRXQ3V

pith:2025:MDJRXQ3VZX2YYDOUQKAZ5ZIR7E

not attested not anchored not stored refs pending

High-Probability Convergence Guarantees of Decentralized SGD

Aleksandar Armacki, Ali H. Sayed

Decentralized SGD converges in high probability under the same cost conditions as mean-squared error convergence.

arxiv:2510.06141 v6 · 2025-10-07 · cs.LG · cs.MA · math.OC

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\usepackage{pith}
\pithnumber{MDJRXQ3VZX2YYDOUQKAZ5ZIR7E}

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Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

We show that DSGD converges in HP under the same conditions on the cost as in the MSE sense, removing the restrictive assumptions used in prior works. Our sharp analysis yields order-optimal rates for both non-convex and strongly convex costs and establishes a linear speed-up in the number of users.

C2weakest assumption

The noise is light-tailed so that moment-generating functions exist and can be bounded, which is weaker than uniform gradient bounds but still requires a specific tail condition on the stochastic gradients that may not hold for arbitrary data distributions.

C3one line summary

Decentralized SGD achieves high-probability convergence with order-optimal rates and linear speedup in the number of users under standard smoothness and convexity conditions on the cost function.

Receipt and verification

First computed	2026-05-22T01:03:47.739841Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

60d31bc375cdf58c0dd482819ee511f92ce49bc55800c56ba74de8ebc9d5a9fd

Aliases

arxiv: 2510.06141 · arxiv_version: 2510.06141v6 · doi: 10.48550/arxiv.2510.06141 · pith_short_12: MDJRXQ3VZX2Y · pith_short_16: MDJRXQ3VZX2YYDOU · pith_short_8: MDJRXQ3V

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/MDJRXQ3VZX2YYDOUQKAZ5ZIR7E \
  | 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: 60d31bc375cdf58c0dd482819ee511f92ce49bc55800c56ba74de8ebc9d5a9fd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9c2cc01ab7754beaeabacc352b1b2e41035d22d5802b5e2556450524975ef797",
    "cross_cats_sorted": [
      "cs.MA",
      "math.OC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2025-10-07T17:15:08Z",
    "title_canon_sha256": "945ee39b323cbbb4c27d71fa1ad428692319b38fea223f88d125d5e8c8004e14"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2510.06141",
    "kind": "arxiv",
    "version": 6
  }
}