Pith Number

pith:OKRWYSAY

pith:2026:OKRWYSAYOYQ2YBEQZU3DUSWYRC

not attested not anchored not stored refs resolved

Data Difficulty and the Generalization--Extrapolation Tradeoff in LLM Fine-Tuning

Jingzhao Zhang (IIIS, Shanghai Qi Zhi Institute), Siyuan Liu (IIIS, Tinghong Chen (College of AI, Tsinghua University, Tsinghua University), Xinghan Li (IIIS, Yifei Wang (Amazon AGI SF Lab)

For any fixed data budget in LLM fine-tuning, an optimal difficulty level exists and moves toward harder examples as the budget grows.

arxiv:2605.12906 v1 · 2026-05-13 · cs.LG · cs.AI

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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

For a fixed data budget, there exists an optimal data difficulty for SFT, and this optimal difficulty shifts toward harder data as the data budget increases.

C2weakest assumption

The controlled synthetic experiments and PAC-Bayesian analysis capture the dominant mechanism in real LLM fine-tuning on natural language data; the paper does not demonstrate that the generalization-extrapolation tradeoff observed synthetically transfers without additional confounding factors from tokenizer or pretraining distributions.

C3one line summary

For a fixed data budget in LLM supervised fine-tuning, optimal data difficulty shifts toward harder examples as the budget grows because of the tradeoff between in-distribution generalization gap and extrapolation gap.

References

34 extracted · 34 resolved · 5 Pith anchors

[1] Anchored Supervised Fine-Tuning , author=. 2025 , eprint= 2025

[2] On the Generalization of SFT: A Reinforcement Learning Perspective with Reward Rectification , author=. 2025 , eprint= 2025

[3] Proximal Supervised Fine-Tuning , author=. 2025 , eprint= 2025

[4] Beyond Log Likelihood: Probability-Based Objectives for Supervised Fine-Tuning across the Model Capability Continuum , author=. 2025 , eprint= 2025

[5] Physics of language models: Part 2.1, grade-school math and the hidden reasoning process

Receipt and verification

First computed	2026-05-18T03:09:10.608910Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

72a36c48187621ac0490cd363a4ad88884146fe1f1b0830a903a40cf97d88b92

Aliases

arxiv: 2605.12906 · arxiv_version: 2605.12906v1 · doi: 10.48550/arxiv.2605.12906 · pith_short_12: OKRWYSAYOYQ2 · pith_short_16: OKRWYSAYOYQ2YBEQ · pith_short_8: OKRWYSAY

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Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/OKRWYSAYOYQ2YBEQZU3DUSWYRC \
  | 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: 72a36c48187621ac0490cd363a4ad88884146fe1f1b0830a903a40cf97d88b92

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "32a654e265a252cac2761f4d005baa5ccc25c122046d518230ed6e059987a0a7",
    "cross_cats_sorted": [
      "cs.AI"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-05-13T02:33:04Z",
    "title_canon_sha256": "49a67c3de86fd4f54ab6de25c3887d95f423b20bec2870c56c07b57b806cceb0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.12906",
    "kind": "arxiv",
    "version": 1
  }
}