Pith Number

pith:HPZ2TYLU

pith:2026:HPZ2TYLUIIQHXHRG4FXIOJQXM6

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Robust and Fast Training via Per-Sample Clipping

Davide Nobile, Philipp Grohs

Per-sample gradient clipping in SGD achieves optimal convergence rates for non-convex problems under heavy-tailed noise.

arxiv:2605.02701 v2 · 2026-05-04 · math.OC · cs.LG · stat.ML

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\pithnumber{HPZ2TYLUIIQHXHRG4FXIOJQXM6}

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3 Author claim open · sign in to claim

4 Citations open

5 Replications 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

We show that the resulting method, per-sample clipped SGD (PS-Clip-SGD), achieves optimal in-expectation convergence rates for non-convex optimization problems under heavy-tailed gradient noise. Moreover, we establish high-probability convergence guarantees that match the in-expectation rates up to polylogarithmic factors in the failure probability.

C2weakest assumption

The analysis requires that gradient noise follows a heavy-tailed distribution with specific moment bounds; if real gradients during training do not satisfy these tail conditions, the claimed optimal rates may not apply.

C3one line summary

Per-sample clipped SGD achieves optimal in-expectation and high-probability convergence rates for non-convex optimization under heavy-tailed gradient noise while outperforming standard SGD and batch clipping on CIFAR-100.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-06-24T01:15:03.316448Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3bf3a9e17442207b9e26e16e87261767bc066827e81d9a2eca60b588c355868c

Aliases

arxiv: 2605.02701 · arxiv_version: 2605.02701v2 · doi: 10.48550/arxiv.2605.02701 · pith_short_12: HPZ2TYLUIIQH · pith_short_16: HPZ2TYLUIIQHXHRG · pith_short_8: HPZ2TYLU

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/HPZ2TYLUIIQHXHRG4FXIOJQXM6 \
  | 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: 3bf3a9e17442207b9e26e16e87261767bc066827e81d9a2eca60b588c355868c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "81483593c864179e7b4f2c20037d60301afd256c002c88ce94643f81ab0195c7",
    "cross_cats_sorted": [
      "cs.LG",
      "stat.ML"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2026-05-04T15:11:36Z",
    "title_canon_sha256": "8d9580df019da6feb4704f296d90c73bb3b3f3d4ba7f32d36c8da0007da41cfc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.02701",
    "kind": "arxiv",
    "version": 2
  }
}