Pith Number

pith:MBNTRUP4

pith:2018:MBNTRUP47YKM4NDRBGOSUJ3U64

not attested not anchored not stored refs pending

Exponential Convergence Time of Gradient Descent for One-Dimensional Deep Linear Neural Networks

Ohad Shamir

arxiv:1809.08587 v4 · 2018-09-23 · cs.LG · cs.NE · math.OC · stat.ML

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\usepackage{pith}
\pithnumber{MBNTRUP47YKM4NDRBGOSUJ3U64}

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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

1 paper in Pith

Hessian based analysis of SGD for Deep Nets: Dynamics and Generalization

Receipt and verification

First computed	2026-05-17T23:43:28.243609Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

605b38d1fcfe14ce3471099d2a2774f73170e5674477e044ce046762fdc2a4bc

Aliases

arxiv: 1809.08587 · arxiv_version: 1809.08587v4 · doi: 10.48550/arxiv.1809.08587 · pith_short_12: MBNTRUP47YKM · pith_short_16: MBNTRUP47YKM4NDR · pith_short_8: MBNTRUP4

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/MBNTRUP47YKM4NDRBGOSUJ3U64 \
  | 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: 605b38d1fcfe14ce3471099d2a2774f73170e5674477e044ce046762fdc2a4bc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7682a179b6c92b15f437f65dc528628bc78f9e07d0453c9d0c01c6bf609f3fcb",
    "cross_cats_sorted": [
      "cs.NE",
      "math.OC",
      "stat.ML"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2018-09-23T12:32:45Z",
    "title_canon_sha256": "4cea27c5e6772158e1df8f56770a6b94f6767822742538d045e9a4049e21783d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1809.08587",
    "kind": "arxiv",
    "version": 4
  }
}