Pith Number

pith:XENUDN3E

pith:2021:XENUDN3EDV2TG7OGNQCOHVVCGA

not attested not anchored not stored refs pending

On the existence of global minima and convergence analyses for gradient descent methods in the training of deep neural networks

Adrian Riekert, Arnulf Jentzen

arxiv:2112.09684 v2 · 2021-12-17 · math.OC · cs.LG · cs.NA · math.NA · math.ST · stat.TH

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\usepackage{pith}
\pithnumber{XENUDN3EDV2TG7OGNQCOHVVCGA}

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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

Mathematical analysis of the gradients in deep learning

Receipt and verification

First computed	2026-07-05T04:40:00.888897Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b91b41b7641d75337dc66c04e3d6a23035e3bf5bfede5317cf3aebbc37988881

Aliases

arxiv: 2112.09684 · arxiv_version: 2112.09684v2 · doi: 10.48550/arxiv.2112.09684 · pith_short_12: XENUDN3EDV2T · pith_short_16: XENUDN3EDV2TG7OG · pith_short_8: XENUDN3E

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/XENUDN3EDV2TG7OGNQCOHVVCGA \
  | 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: b91b41b7641d75337dc66c04e3d6a23035e3bf5bfede5317cf3aebbc37988881

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d48f60e8aaca009464e7541df651ae6fb542781c20e1500cda2ce9924203067b",
    "cross_cats_sorted": [
      "cs.LG",
      "cs.NA",
      "math.NA",
      "math.ST",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2021-12-17T18:55:40Z",
    "title_canon_sha256": "2603087c5ac9a7900cb7b1ffc9925a9adf545336d54a9bf35f969d25becaf409"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2112.09684",
    "kind": "arxiv",
    "version": 2
  }
}