Pith Number

pith:NFZGS7BD

pith:2024:NFZGS7BDFWNR2UBDYKPXZDGOM7

not attested not anchored not stored refs pending

Scaling Optimal LR Across Token Horizons

Alon Benhaim, Furu Wei, Johan Bjorck, Vishrav Chaudhary, Xia Song

arxiv:2409.19913 v3 · 2024-09-30 · cs.LG · cs.AI · cs.CL

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NFZGS7BDFWNR2UBDYKPXZDGOM7}

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

2 papers in Pith

How to Allocate Your Tokens? Scaling Laws with Training Steps and Batch Size

Theory of Optimal Learning Rate Schedules and Scaling Laws for a Random Feature Model

Receipt and verification

First computed	2026-07-05T10:18:42.086203Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6972697c232d9b1d5023c29f7c8cce67e803eafdd945f09277c80697cd0a201f

Aliases

arxiv: 2409.19913 · arxiv_version: 2409.19913v3 · doi: 10.48550/arxiv.2409.19913 · pith_short_12: NFZGS7BDFWNR · pith_short_16: NFZGS7BDFWNR2UBD · pith_short_8: NFZGS7BD

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/NFZGS7BDFWNR2UBDYKPXZDGOM7 \
  | 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: 6972697c232d9b1d5023c29f7c8cce67e803eafdd945f09277c80697cd0a201f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "40283f870db5d43f03bc5bc9c34d1cd4c38294eeff187af29bc7e24e02db7b4a",
    "cross_cats_sorted": [
      "cs.AI",
      "cs.CL"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2024-09-30T03:32:02Z",
    "title_canon_sha256": "3964b1083d4e42bc457b3c238c32b1e756bdec30479658ad126f7c9874fca040"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2409.19913",
    "kind": "arxiv",
    "version": 3
  }
}