Pith Number

pith:QMCAWIL5

pith:2026:QMCAWIL5AXFP4Y6GTLMEHQUJT2

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Nexus: Same Pretraining Loss, Better Downstream Generalization via Common Minima

Huanran Chen, Huaqing Zhang, Jun Zhu, Ke Shen, Xiao Li, Yinpeng Dong

Converging to common minima across data sources during pretraining improves downstream generalization even at identical loss values.

arxiv:2604.09258 v2 · 2026-04-10 · cs.LG

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\pithnumber{QMCAWIL5AXFP4Y6GTLMEHQUJT2}

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3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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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.

Claims

C1strongest claim

Nexus significantly boosts downstream performance, despite achieving the same pretraining loss. Notably, on the 3B model, Nexus reduces the out-of-distribution loss by 0.012 and yields up to a 15.0% accuracy improvement on complex reasoning tasks (e.g., GSM8k).

C2weakest assumption

The geometric closeness of task-specific minima is intrinsically linked to downstream generalization, and that maximizing gradient similarity during optimization produces this closeness.

C3one line summary

Nexus optimizer improves LLM downstream performance by converging to common minima across data sources despite identical pretraining loss.

Formal links

2 machine-checked theorem links

Cited by

1 paper in Pith

TrajTok: Adaptive Spatial Tokenization for Trajectory Representation Learning

Receipt and verification

First computed	2026-05-28T01:04:39.854864Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

83040b217d05cafe63c69ad843c2899e9fff1b2b8c52e61e1b0ba5ea911e6b9a

Aliases

arxiv: 2604.09258 · arxiv_version: 2604.09258v2 · doi: 10.48550/arxiv.2604.09258 · pith_short_12: QMCAWIL5AXFP · pith_short_16: QMCAWIL5AXFP4Y6G · pith_short_8: QMCAWIL5

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/QMCAWIL5AXFP4Y6GTLMEHQUJT2 \
  | 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: 83040b217d05cafe63c69ad843c2899e9fff1b2b8c52e61e1b0ba5ea911e6b9a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "84a5948012050bc97e76c01cda4ff86e78a223497cc5590b26437950090b5b33",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-04-10T12:17:18Z",
    "title_canon_sha256": "f59b06e55ceb072b5bc53af46f96114d78f57fc9ea1d72a33a834856408e498c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.09258",
    "kind": "arxiv",
    "version": 2
  }
}