Pith Number

pith:UQ7R2ALZ

pith:2024:UQ7R2ALZ4B5DNWAVYAZFT4E7BR

not attested not anchored not stored refs pending

How Does Critical Batch Size Scale in Pre-training?

Dean Foster, Depen Morwani, Difan Zou, Hanlin Zhang, Jingfeng Wu, Nikhil Vyas, Sham Kakade, Udaya Ghai

arxiv:2410.21676 v4 · 2024-10-29 · cs.LG · cs.AI · math.OC · stat.ML

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{UQ7R2ALZ4B5DNWAVYAZFT4E7BR}

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

6 papers in Pith

Compute Efficiency and Serial Runtime Tradeoffs for Stochastic Momentum Methods

One-Step Gradient Delay is Not a Barrier for Large-Scale Asynchronous Pipeline Parallel LLM Pretraining

ReCoVer: Resilient LLM Pre-Training System via Fault-Tolerant Collective and Versatile Workload

ScheduleFree+: Scaling Learning-Rate-Free & Schedule-Free Learning to Large Language Models

ReCoVer: Resilient LLM Pre-Training System via Fault-Tolerant Collective and Versatile Workload

Receipt and verification

First computed	2026-07-05T10:51:27.587933Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a43f1d0179e07a36d815c03259f09f0c5ff4d6bcf804a757de6bda1b534edc2f

Aliases

arxiv: 2410.21676 · arxiv_version: 2410.21676v4 · doi: 10.48550/arxiv.2410.21676 · pith_short_12: UQ7R2ALZ4B5D · pith_short_16: UQ7R2ALZ4B5DNWAV · pith_short_8: UQ7R2ALZ

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/UQ7R2ALZ4B5DNWAVYAZFT4E7BR \
  | 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: a43f1d0179e07a36d815c03259f09f0c5ff4d6bcf804a757de6bda1b534edc2f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f98f13a2419d49928022d82e7680a148664675b0e09f57a37b306484a0c54dc1",
    "cross_cats_sorted": [
      "cs.AI",
      "math.OC",
      "stat.ML"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2024-10-29T02:54:06Z",
    "title_canon_sha256": "a6809947abd89815d1dc066c5b170cae4c4f73f5e5a6ef41c87a7486bbfa8139"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2410.21676",
    "kind": "arxiv",
    "version": 4
  }
}