Pith Number

pith:M3YWY4QQ

pith:2020:M3YWY4QQRWWEX6BGPARH7T3M63

not attested not anchored not stored refs pending

Optimization Theory for ReLU Neural Networks Trained with Normalization Layers

Guido Mont\'ufar, Quanquan Gu, Yonatan Dukler

arxiv:2006.06878 v1 · 2020-06-11 · cs.LG · math.OC · 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{M3YWY4QQRWWEX6BGPARH7T3M63}

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	2026-07-05T01:09:47.798369Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

66f16c72108dac4bf82678227fcf6cf6fc308315d0340685513ef694b31e2039

Aliases

arxiv: 2006.06878 · arxiv_version: 2006.06878v1 · doi: 10.48550/arxiv.2006.06878 · pith_short_12: M3YWY4QQRWWE · pith_short_16: M3YWY4QQRWWEX6BG · pith_short_8: M3YWY4QQ

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/M3YWY4QQRWWEX6BGPARH7T3M63 \
  | 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: 66f16c72108dac4bf82678227fcf6cf6fc308315d0340685513ef694b31e2039

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cf66613bdd7a758e553df4a3ba70d166387a2351cbb5bb7418f0efd4796b01ff",
    "cross_cats_sorted": [
      "math.OC",
      "stat.ML"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2020-06-11T23:55:54Z",
    "title_canon_sha256": "ec98980e5347881b71a26d90e1c5303a82bd227474bfd352cfa7411f82afe9bc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2006.06878",
    "kind": "arxiv",
    "version": 1
  }
}