Pith Number

pith:UR3E4SHP

pith:2024:UR3E4SHPJNSAFCTBCAPGXNKOOC

not attested not anchored not stored refs pending

Non-convergence to global minimizers in data driven supervised deep learning: Adam and stochastic gradient descent optimization provably fail to converge to global minimizers in the training of deep neural networks with ReLU activation

Arnulf Jentzen, Sonja Hannibal, Thang Do

arxiv:2410.10533 v2 · 2024-10-14 · cs.LG · cs.NA · math.NA · math.OC · math.PR · 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{UR3E4SHPJNSAFCTBCAPGXNKOOC}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

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.

Receipt and verification

First computed	2026-07-05T10:14:46.601229Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a4764e48ef4b64028a61101e6bb54e70bf0944a244665aaa422ee6e597af01c7

Aliases

arxiv: 2410.10533 · arxiv_version: 2410.10533v2 · doi: 10.48550/arxiv.2410.10533 · pith_short_12: UR3E4SHPJNSA · pith_short_16: UR3E4SHPJNSAFCTB · pith_short_8: UR3E4SHP

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/UR3E4SHPJNSAFCTBCAPGXNKOOC \
  | 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: a4764e48ef4b64028a61101e6bb54e70bf0944a244665aaa422ee6e597af01c7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4366533a10fa23f219f803d1dcb4a22d0d9d3313039b87d87d6dab6dfc6e6219",
    "cross_cats_sorted": [
      "cs.NA",
      "math.NA",
      "math.OC",
      "math.PR",
      "stat.ML"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2024-10-14T14:11:37Z",
    "title_canon_sha256": "f591922d4c97e663bb73f67ffecc2100639703be8b4f3ef16097e2ee593fa597"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2410.10533",
    "kind": "arxiv",
    "version": 2
  }
}