Pith Number

pith:BOPFA7EB

pith:2026:BOPFA7EB7LSEEDCY5CGPQ6F5SD

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Distributed Seeking for Fixed Points of Biased Stochastic Operators: A Communication-Efficient Approach

Fan Li, Guanghui Wen, Lei Xu, Tao Yang, Xinlei Yi, Yang Shi

A surrogate function proves convergence for distributed fixed-point seeking under biased stochastic operators with communication compression.

arxiv:2605.07633 v2 · 2026-05-08 · math.OC

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\pithnumber{BOPFA7EB7LSEEDCY5CGPQ6F5SD}

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Record completeness

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4 Citations open

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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

By introducing a surrogate function for general non-contractive and contractive operators, we establish convergence guarantees of the distributed fixed point iteration, achieving among the first theoretical unifications with distributed non-convex optimization algorithms.

C2weakest assumption

The relaxed growth bias and variance conditions on the stochastic operators, which generalize traditional unbiased and bounded additive variance assumptions.

C3one line summary

A communication-efficient distributed algorithm for fixed-point seeking of biased stochastic operators with convergence guarantees under relaxed conditions and unification to non-convex optimization.

Formal links

2 machine-checked theorem links

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1 paper in Pith

Distributed Seeking for Fixed Points of Biased Stochastic Operators: A Communication-Efficient Approach

Receipt and verification

First computed	2026-05-22T01:04:05.342809Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0b9e507c81fae4420c58e88cf878bd90e3d94c52004ab05ea37c2f98770719c7

Aliases

arxiv: 2605.07633 · arxiv_version: 2605.07633v2 · doi: 10.48550/arxiv.2605.07633 · pith_short_12: BOPFA7EB7LSE · pith_short_16: BOPFA7EB7LSEEDCY · pith_short_8: BOPFA7EB

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/BOPFA7EB7LSEEDCY5CGPQ6F5SD \
  | 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: 0b9e507c81fae4420c58e88cf878bd90e3d94c52004ab05ea37c2f98770719c7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "820c12ca8799f44b09f18e8d1b26b62069081999f11ab2e07e9957aee7d5d588",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2026-05-08T12:00:59Z",
    "title_canon_sha256": "a09e53ed4bf23a9383af394fec536a5a20f7fa6b02ac906134842056b2ae8080"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.07633",
    "kind": "arxiv",
    "version": 2
  }
}