Pith Number

pith:2RWIEOJC

pith:2022:2RWIEOJCIU3NHICHM35RGGCSP5

not attested not anchored not stored refs pending

The merged-staircase property: a necessary and nearly sufficient condition for SGD learning of sparse functions on two-layer neural networks

Emmanuel Abbe, Enric Boix-Adsera, Theodor Misiakiewicz

arxiv:2202.08658 v2 · 2022-02-17 · cs.LG · cs.DS · stat.ML

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

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\usepackage{pith}
\pithnumber{2RWIEOJCIU3NHICHM35RGGCSP5}

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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

A Theory of Saddle Escape in Deep Nonlinear Networks

Receipt and verification

First computed	2026-07-05T08:59:21.857340Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d46c8239224536d3a04766fb1318527f647514268d87abfb484c3633af8accdf

Aliases

arxiv: 2202.08658 · arxiv_version: 2202.08658v2 · doi: 10.48550/arxiv.2202.08658 · pith_short_12: 2RWIEOJCIU3N · pith_short_16: 2RWIEOJCIU3NHICH · pith_short_8: 2RWIEOJC

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/2RWIEOJCIU3NHICHM35RGGCSP5 \
  | 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: d46c8239224536d3a04766fb1318527f647514268d87abfb484c3633af8accdf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "10738478d8fb04f5482612843fd0d7a01d90d95988d037bc57f57ef9e07c9159",
    "cross_cats_sorted": [
      "cs.DS",
      "stat.ML"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2022-02-17T13:43:06Z",
    "title_canon_sha256": "2fc5e83f72092494dd79b90e9d01d927d824d307d01c7da66f39702829d5f45b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2202.08658",
    "kind": "arxiv",
    "version": 2
  }
}