Pith Number

pith:NVIJ27ZV

pith:2021:NVIJ27ZV75VREMTK4AB62RIHJK

not attested not anchored not stored refs pending

What Happens after SGD Reaches Zero Loss? --A Mathematical Framework

Sanjeev Arora, Tianhao Wang, Zhiyuan Li

arxiv:2110.06914 v4 · 2021-10-13 · cs.LG · 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{NVIJ27ZV75VREMTK4AB62RIHJK}

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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

Structure Before Collapse: Transient semantic geometry in next-token prediction

SGD at the Edge of Stability: Stochastic Stabilization with Large Learning Rates

There Will Be a Scientific Theory of Deep Learning

Learning reveals invisible structure in low-rank RNNs

Receipt and verification

First computed	2026-07-05T04:44:18.847323Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6d509d7f35ff6b12326ae003ed45074a8eba1c97babeb1b4be3b946f088827af

Aliases

arxiv: 2110.06914 · arxiv_version: 2110.06914v4 · doi: 10.48550/arxiv.2110.06914 · pith_short_12: NVIJ27ZV75VR · pith_short_16: NVIJ27ZV75VREMTK · pith_short_8: NVIJ27ZV

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/NVIJ27ZV75VREMTK4AB62RIHJK \
  | 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: 6d509d7f35ff6b12326ae003ed45074a8eba1c97babeb1b4be3b946f088827af

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e3e75d3f9a1449806b4c5ff2a04dcfbb99bbcfa941b408af989df92f12b1cfff",
    "cross_cats_sorted": [
      "stat.ML"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2021-10-13T17:50:46Z",
    "title_canon_sha256": "f68b6c6940d48e11481b93a640edc0c74fd21902a987d12d297233f4692643c9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2110.06914",
    "kind": "arxiv",
    "version": 4
  }
}