Pith Number

pith:4TPXDFK2

pith:2024:4TPXDFK2UTJKJOVVGNJYWQSWA7

not attested not anchored not stored refs pending

Neural Collapse versus Low-rank Bias: Is Deep Neural Collapse Really Optimal?

Christoph Lampert, Marco Mondelli, Peter S\'uken\'ik

arxiv:2405.14468 v2 · 2024-05-23 · 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{4TPXDFK2UTJKJOVVGNJYWQSWA7}

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

The Implicit Bias of Depth: From Neural Collapse to Softmax Codes

Receipt and verification

First computed	2026-07-05T09:23:06.028266Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e4df71955aa4d2a4bab533538b425607dae089caab66e695cffc8983cdc72629

Aliases

arxiv: 2405.14468 · arxiv_version: 2405.14468v2 · doi: 10.48550/arxiv.2405.14468 · pith_short_12: 4TPXDFK2UTJK · pith_short_16: 4TPXDFK2UTJKJOVV · pith_short_8: 4TPXDFK2

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/4TPXDFK2UTJKJOVVGNJYWQSWA7 \
  | 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: e4df71955aa4d2a4bab533538b425607dae089caab66e695cffc8983cdc72629

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ef9245dd5ee18e879c8aca7414fa263e41327f91380bdd67c59f6583eabe36f4",
    "cross_cats_sorted": [
      "math.OC",
      "stat.ML"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2024-05-23T11:55:49Z",
    "title_canon_sha256": "33544e8b7fa8a5a5c69ae54c2aeee65e4d515f0e1f7c55829c47607d0b170283"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2405.14468",
    "kind": "arxiv",
    "version": 2
  }
}