Pith Number

pith:LYRIAA3Q

pith:2021:LYRIAA3QCFK67ZLW6K3MIPOFJR

not attested not anchored not stored refs pending

A proof of convergence for the gradient descent optimization method with random initializations in the training of neural networks with ReLU activation for piecewise linear target functions

Adrian Riekert, Arnulf Jentzen

arxiv:2108.04620 v1 · 2021-08-10 · math.OC · cs.LG · cs.NA · math.NA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LYRIAA3QCFK67ZLW6K3MIPOFJR}

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.

Cited by

1 paper in Pith

On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations

Receipt and verification

First computed	2026-07-05T05:28:42.157893Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5e228003701155efe576f2b6c43dc54c7057cd1763da1a6cdc8ca59a3314866c

Aliases

arxiv: 2108.04620 · arxiv_version: 2108.04620v1 · doi: 10.48550/arxiv.2108.04620 · pith_short_12: LYRIAA3QCFK6 · pith_short_16: LYRIAA3QCFK67ZLW · pith_short_8: LYRIAA3Q

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/LYRIAA3QCFK67ZLW6K3MIPOFJR \
  | 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: 5e228003701155efe576f2b6c43dc54c7057cd1763da1a6cdc8ca59a3314866c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "199c1428ac208284d1b973c99c018cd18e9bdb8eeba7f66389cc1840476770ab",
    "cross_cats_sorted": [
      "cs.LG",
      "cs.NA",
      "math.NA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2021-08-10T12:01:37Z",
    "title_canon_sha256": "14742a7c8251bfb3986cae67cd9eaf289b4b4dd3810a18e0808f2fe11476a867"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2108.04620",
    "kind": "arxiv",
    "version": 1
  }
}