Pith Number

pith:NPBCEGLP

pith:2025:NPBCEGLPKQRS43OIY2VC2TEJZO

not attested not anchored not stored refs pending

Exact Dynamics of Multi-class Stochastic Gradient Descent

Elizabeth Collins-Woodfin, Inbar Seroussi

arxiv:2510.14074 v2 · 2025-10-15 · stat.ML · cs.LG · math.OC · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NPBCEGLPKQRS43OIY2VC2TEJZO}

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

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

Receipt and verification

First computed	2026-07-14T02:22:28.769242Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6bc222196f54232e6dc8c6aa2d4c89cb898979f3cc35b49ac213db252726eb81

Aliases

arxiv: 2510.14074 · arxiv_version: 2510.14074v2 · doi: 10.48550/arxiv.2510.14074 · pith_short_12: NPBCEGLPKQRS · pith_short_16: NPBCEGLPKQRS43OI · pith_short_8: NPBCEGLP

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/NPBCEGLPKQRS43OIY2VC2TEJZO \
  | 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: 6bc222196f54232e6dc8c6aa2d4c89cb898979f3cc35b49ac213db252726eb81

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f1aebc68546bc436e1fd64af6f7be43da599445ea6b30fee8ed6af69dd3f19cc",
    "cross_cats_sorted": [
      "cs.LG",
      "math.OC",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "stat.ML",
    "submitted_at": "2025-10-15T20:31:49Z",
    "title_canon_sha256": "503be394e3954e222a4d35032a54900b44896f5aa4b2d82a6754b7b6ccde85f0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2510.14074",
    "kind": "arxiv",
    "version": 2
  }
}