Pith Number

pith:3DHDKGLG

pith:2026:3DHDKGLGZEWAOAHJ7LLGS76POO

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Clipped Stochastic Gradient Tracking For Locally Smooth Functions

Junyu Zhang, Leilei Mei

A clipped stochastic gradient tracking method with staggered variance reduction converges using only local smoothness for RUC-regular distributed problems.

arxiv:2605.17027 v1 · 2026-05-16 · math.OC

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Claims

C1strongest claim

For RUC-regular distributed optimization problems with finite-sum structure, we derive a clipped gradient tracking method with staggered variance reduction, which only relies on the local smoothness of objective functions, and an O(∑_i n_i^{1.5} + n_i^{0.5} ε^{-1}) complexity has been established for our algorithm.

C2weakest assumption

The distributed optimization problems satisfy the Relative Uniform Continuity (RUC) regularity condition for the local smoothness constant as a function of sets, which the paper states covers most common growth functions ranging from constant and logarithmic to polynomial and exponential.

C3one line summary

The authors derive a clipped gradient tracking method with staggered variance reduction for RUC-regular finite-sum distributed optimization problems, establishing an O(∑ n_i^{1.5} + n_i^{0.5} ε^{-1}) complexity bound that relies only on local smoothness.

References

56 extracted · 56 resolved · 1 Pith anchors

[1] Stochastic gradient push for distributed deep learning 2019

[2] A descent lemma beyond lipschitz gradient continuity: first-order methods revisited and applications 2017

[3] One hundred years since the introduction of the set distance by dimitrie pompeiu 2005

[4] First order methods beyond convexity and lipschitz gradient continuity with applications to quadratic inverse problems 2018

[5] Phase retrieval via wirtinger flow: Theory and algorithms 1985

Formal links

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Receipt and verification

First computed	2026-05-20T00:03:36.629224Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d8ce351966c92c0700e9fad6697fcf739525bd708073cfa230b629a140cb3a65

Aliases

arxiv: 2605.17027 · arxiv_version: 2605.17027v1 · doi: 10.48550/arxiv.2605.17027 · pith_short_12: 3DHDKGLGZEWA · pith_short_16: 3DHDKGLGZEWAOAHJ · pith_short_8: 3DHDKGLG

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/3DHDKGLGZEWAOAHJ7LLGS76POO \
  | 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: d8ce351966c92c0700e9fad6697fcf739525bd708073cfa230b629a140cb3a65

Canonical record JSON

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    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2026-05-16T14:55:54Z",
    "title_canon_sha256": "5800bf1cd15a693b49bf57698e8828c02b06542be1b44991e862037f3a67a71a"
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    "kind": "arxiv",
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