Pith Number

pith:3PI3ZB4K

pith:2021:3PI3ZB4K6Y7MGMJ4U2SQYJ3ABK

not attested not anchored not stored refs pending

Convergence proof for stochastic gradient descent in the training of deep neural networks with ReLU activation for constant target functions

Adrian Riekert, Arnulf Jentzen, Katharina Pohl, Luca Scarpa, Martin Hutzenthaler

arxiv:2112.07369 v2 · 2021-12-13 · cs.LG · cs.NA · math.NA · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3PI3ZB4K6Y7MGMJ4U2SQYJ3ABK}

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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	2026-07-05T06:23:53.177333Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dbd1bc878af63ec3313ca6a50c27600aa82212eb7045bea0fb720e58e6af06d3

Aliases

arxiv: 2112.07369 · arxiv_version: 2112.07369v2 · doi: 10.48550/arxiv.2112.07369 · pith_short_12: 3PI3ZB4K6Y7M · pith_short_16: 3PI3ZB4K6Y7MGMJ4 · pith_short_8: 3PI3ZB4K

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/3PI3ZB4K6Y7MGMJ4U2SQYJ3ABK \
  | 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: dbd1bc878af63ec3313ca6a50c27600aa82212eb7045bea0fb720e58e6af06d3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "42b9434fc573a1bcf8314dfc996343d186240a30e586d329d5318767adab728b",
    "cross_cats_sorted": [
      "cs.NA",
      "math.NA",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2021-12-13T11:45:36Z",
    "title_canon_sha256": "7d62b9024fb8c61b502952d95d301aaa1090fdf88060461353923ed749a9c4ab"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2112.07369",
    "kind": "arxiv",
    "version": 2
  }
}