Pith Number

pith:JAN5S2J6

pith:2018:JAN5S2J64DEGYNL2RKPLZYYSWQ

not attested not anchored not stored refs pending

Stochastic Modified Equations and Dynamics of Stochastic Gradient Algorithms I: Mathematical Foundations

Cheng Tai, Qianxiao Li, Weinan E

arxiv:1811.01558 v1 · 2018-11-05 · cs.LG · stat.ML

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\usepackage{pith}
\pithnumber{JAN5S2J64DEGYNL2RKPLZYYSWQ}

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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

4 papers in Pith

Homogenization of $\ell_2$-Adversarial Training in High-Dimensions: Exact Dynamics under Stochastic Gradient Descent

Thermodynamic Irreversibility of Training Algorithms

Limit Theorems for Stochastic Gradient Descent in High-Dimensional Single-Layer Networks

Deterministic Adam-Inspired Methods with Accelerated Convergence Rate

Receipt and verification

First computed	2026-05-18T00:01:33.967934Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

481bd9693ee0c86c357a8a9ebce312b41f5691d50724f2f75cd7d76316c998d8

Aliases

arxiv: 1811.01558 · arxiv_version: 1811.01558v1 · doi: 10.48550/arxiv.1811.01558 · pith_short_12: JAN5S2J64DEG · pith_short_16: JAN5S2J64DEGYNL2 · pith_short_8: JAN5S2J6

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/JAN5S2J64DEGYNL2RKPLZYYSWQ \
  | 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: 481bd9693ee0c86c357a8a9ebce312b41f5691d50724f2f75cd7d76316c998d8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0c53dbaa3e59cc00d5ba40a345dfc09db9cf9b94144a73b1ba225a4ffa652634",
    "cross_cats_sorted": [
      "stat.ML"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2018-11-05T09:00:29Z",
    "title_canon_sha256": "7f532141b04077215796766a4095506fe45ea1f9d718bec3659af87ed967dc17"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1811.01558",
    "kind": "arxiv",
    "version": 1
  }
}