Pith Number

pith:BFUH5PBJ

pith:2022:BFUH5PBJJ4WMKESEBOH6JSQAKV

not attested not anchored not stored refs pending

Homogenization of SGD in high-dimensions: Exact dynamics and generalization properties

Ben Adlam, Courtney Paquette, Elliot Paquette, Jeffrey Pennington

arxiv:2205.07069 v1 · 2022-05-14 · math.ST · math.OC · math.PR · 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{BFUH5PBJJ4WMKESEBOH6JSQAKV}

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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

3 papers in Pith

Homogenization of $\ell_2$-Adversarial Training in High-Dimensions: Exact Dynamics under Stochastic Gradient Descent

The Role of Symmetry in Optimizing Overparameterized Networks

Receipt and verification

First computed	2026-07-05T04:23:11.748113Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

09687ebc294f2cc512440b8fe4ca005573a082fa31e1bb561389471bbd22eb16

Aliases

arxiv: 2205.07069 · arxiv_version: 2205.07069v1 · doi: 10.48550/arxiv.2205.07069 · pith_short_12: BFUH5PBJJ4WM · pith_short_16: BFUH5PBJJ4WMKESE · pith_short_8: BFUH5PBJ

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/BFUH5PBJJ4WMKESEBOH6JSQAKV \
  | 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: 09687ebc294f2cc512440b8fe4ca005573a082fa31e1bb561389471bbd22eb16

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fc56886c77d7caca8909f0296bb9b0cf7ed920436ff0db91d3dffe7d82229993",
    "cross_cats_sorted": [
      "math.OC",
      "math.PR",
      "stat.ML",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.ST",
    "submitted_at": "2022-05-14T14:10:08Z",
    "title_canon_sha256": "ad67d16efff827db85e7572c1186288069b5e0dadf17eeedddc479f41d4ac604"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2205.07069",
    "kind": "arxiv",
    "version": 1
  }
}