Pith Number

pith:TU52P7R4

pith:2018:TU52P7R42NZTF3JY6CSVAZGBCU

not attested not anchored not stored refs pending

On the Global Convergence of Gradient Descent for Over-parameterized Models using Optimal Transport

Francis Bach (SIERRA), Lenaic Chizat (SIERRA)

arxiv:1805.09545 v2 · 2018-05-24 · math.OC · cs.NE · stat.ML

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\usepackage{pith}
\pithnumber{TU52P7R42NZTF3JY6CSVAZGBCU}

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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

4 papers in Pith

Learning Dynamic Stability Landscapes in Synchronization Networks

Convergence rates for gradient descent in the training of overparameterized artificial neural networks with piecewise affine activation

Limit Theorems for Stochastic Gradient Descent in High-Dimensional Single-Layer Networks

Unlearning with Asymmetric Sources: Improved Unlearning-Utility Trade-off with Public Data

Receipt and verification

First computed	2026-05-18T00:02:09.906157Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9d3ba7fe3cd37332ed38f0a55064c1151eb306804bcf7ef4c948dda9b224f406

Aliases

arxiv: 1805.09545 · arxiv_version: 1805.09545v2 · doi: 10.48550/arxiv.1805.09545 · pith_short_12: TU52P7R42NZT · pith_short_16: TU52P7R42NZTF3JY · pith_short_8: TU52P7R4

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/TU52P7R42NZTF3JY6CSVAZGBCU \
  | 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: 9d3ba7fe3cd37332ed38f0a55064c1151eb306804bcf7ef4c948dda9b224f406

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "223463b3bffb175fa4a796cde52157138f2b8785fdbbc597092a6b5f37166f20",
    "cross_cats_sorted": [
      "cs.NE",
      "stat.ML"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2018-05-24T08:28:01Z",
    "title_canon_sha256": "d4084a0d4c4a02bb6765cae84fa81868ce507fab80998da80b6c5c7be53f9d32"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1805.09545",
    "kind": "arxiv",
    "version": 2
  }
}