Pith Number

pith:VDCTCJ3V

pith:2021:VDCTCJ3VOQ7DPDQJ7A53FH2VX7

not attested not anchored not stored refs pending

Analytic Insights into Structure and Rank of Neural Network Hessian Maps

Gregor Bachmann, Sidak Pal Singh, Thomas Hofmann

arxiv:2106.16225 v2 · 2021-06-30 · cs.LG · cs.NE · math.ST · stat.ML · stat.TH

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VDCTCJ3VOQ7DPDQJ7A53FH2VX7}

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

2 papers in Pith

Closed-Form Steepest Descent Direction toward Flat Minima: Reducing Upper Bounds on the Loss Hessian Eigenspectrum in Neural Networks

Wolkowicz-Styan Upper Bound on the Hessian Eigenspectrum for Cross-Entropy Loss in Nonlinear Smooth Neural Networks

Receipt and verification

First computed	2026-07-05T02:54:19.517857Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a8c5312775743e378e09f83bb29f55bfd34cafe5b547214bf52f7e2df87fa736

Aliases

arxiv: 2106.16225 · arxiv_version: 2106.16225v2 · doi: 10.48550/arxiv.2106.16225 · pith_short_12: VDCTCJ3VOQ7D · pith_short_16: VDCTCJ3VOQ7DPDQJ · pith_short_8: VDCTCJ3V

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/VDCTCJ3VOQ7DPDQJ7A53FH2VX7 \
  | 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: a8c5312775743e378e09f83bb29f55bfd34cafe5b547214bf52f7e2df87fa736

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f78213400ff09084df310c724435813686e67b18910d5a2d5948a3a8ee3db5b0",
    "cross_cats_sorted": [
      "cs.NE",
      "math.ST",
      "stat.ML",
      "stat.TH"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2021-06-30T17:29:58Z",
    "title_canon_sha256": "180cab23b20e8b5cb7a26e033bcd42d1d447acb8bab8c42703a0b76546bc111e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2106.16225",
    "kind": "arxiv",
    "version": 2
  }
}