Pith Number

pith:VEHMXFAH

pith:2026:VEHMXFAHMK5DCY6RGMIDNI4S4O

not attested not anchored not stored refs pending

Deep Neural Network Training as Random Effects: An Optimization-Inference Duality

Lin Liu, Minhao Yao, Ruoyu Wang, Xihong Lin, Zhonghua Liu

arxiv:2605.27991 v1 · 2026-05-27 · stat.ML · cs.LG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VEHMXFAHMK5DCY6RGMIDNI4S4O}

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	2026-05-28T01:04:55.422728Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a90ecb940762ba3163d1331036a392e382e5ec5bf8919ccc07536b4623362826

Aliases

arxiv: 2605.27991 · arxiv_version: 2605.27991v1 · doi: 10.48550/arxiv.2605.27991 · pith_short_12: VEHMXFAHMK5D · pith_short_16: VEHMXFAHMK5DCY6R · pith_short_8: VEHMXFAH

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/VEHMXFAHMK5DCY6RGMIDNI4S4O \
  | 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: a90ecb940762ba3163d1331036a392e382e5ec5bf8919ccc07536b4623362826

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a36b2a08c2bb3df86e52c61a8b89f1a460b59da57857cd5ed56c630e9d0f2265",
    "cross_cats_sorted": [
      "cs.LG"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "stat.ML",
    "submitted_at": "2026-05-27T05:32:24Z",
    "title_canon_sha256": "0855c97187bbd586933820a37dac95bf976751eec5e222d18a82ecd528e8e96d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.27991",
    "kind": "arxiv",
    "version": 1
  }
}