Pith Number

pith:DXVZJI3I

pith:2024:DXVZJI3IRCVBLBJ6KUB53N5AOT

not attested not anchored not stored refs pending

Parameter Symmetry and Noise Equilibrium of Stochastic Gradient Descent

Hongchao Li, Lei Wu, Liu Ziyin, Mingze Wang

arxiv:2402.07193 v3 · 2024-02-11 · cs.LG · math.OC · stat.ML

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DXVZJI3IRCVBLBJ6KUB53N5AOT}

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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.

Cited by

1 paper in Pith

Beyond the Permutation Symmetry of Transformers: The Role of Rotation for Model Fusion

Receipt and verification

First computed	2026-07-05T09:32:05.600147Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1deb94a36888aa15853e5503ddb7a074c0e3054aa540384e74ba24ef428f7541

Aliases

arxiv: 2402.07193 · arxiv_version: 2402.07193v3 · doi: 10.48550/arxiv.2402.07193 · pith_short_12: DXVZJI3IRCVB · pith_short_16: DXVZJI3IRCVBLBJ6 · pith_short_8: DXVZJI3I

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/DXVZJI3IRCVBLBJ6KUB53N5AOT \
  | 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: 1deb94a36888aa15853e5503ddb7a074c0e3054aa540384e74ba24ef428f7541

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "26e9bd0f271060bb439a0c9bd221fcd7ef985bbe6ad7c93488663d5fd7ada37c",
    "cross_cats_sorted": [
      "math.OC",
      "stat.ML"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2024-02-11T13:00:04Z",
    "title_canon_sha256": "9fca538bae59dd3aba680d7c5cf440d1ea3bc4fda3a550bf42a0c17788455573"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2402.07193",
    "kind": "arxiv",
    "version": 3
  }
}