Pith Number

pith:W6STJ5E7

pith:2025:W6STJ5E7L4KYLP5VVB4PIQM454

not attested not anchored not stored refs pending

Averaged Adam accelerates stochastic optimization in the training of deep neural network approximations for partial differential equation and optimal control problems

Adrian Riekert, Arnulf Jentzen, Steffen Dereich

arxiv:2501.06081 v1 · 2025-01-10 · math.OC · cs.LG · cs.NA · math.NA

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\usepackage{pith}
\pithnumber{W6STJ5E7L4KYLP5VVB4PIQM454}

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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

Central limit theorem for the averaged Adam optimizer

Receipt and verification

First computed	2026-07-05T09:59:33.033227Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b7a534f49f5f1585bfb5a878f4419cef381c97b6cda43326bda8e5585805c1fa

Aliases

arxiv: 2501.06081 · arxiv_version: 2501.06081v1 · doi: 10.48550/arxiv.2501.06081 · pith_short_12: W6STJ5E7L4KY · pith_short_16: W6STJ5E7L4KYLP5V · pith_short_8: W6STJ5E7

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/W6STJ5E7L4KYLP5VVB4PIQM454 \
  | 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: b7a534f49f5f1585bfb5a878f4419cef381c97b6cda43326bda8e5585805c1fa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "611cb5aa39cf2b02542f355616aeaec80fc32de21baf36f1dd5bee76895711bf",
    "cross_cats_sorted": [
      "cs.LG",
      "cs.NA",
      "math.NA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2025-01-10T16:15:25Z",
    "title_canon_sha256": "78b76535d9be4244d48cd451dfa92de6451b433ca6a286355e64e2374d8e428f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2501.06081",
    "kind": "arxiv",
    "version": 1
  }
}