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pith:LNW3CB62

pith:2026:LNW3CB62LK72KULJRMF3EGTANG

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Decoupling KL and Trajectories: A Unified Perspective for SFT, DAgger, Offline RL, and OPD in LLM Distillation

Anhao Zhao, Haoran Xin, Junlong Tong, Wenjie Li, Xiaoyu Shen, Yingqi Fan

Decoupling prefix source from token-level KL direction reveals four distinct LLM distillation objectives that unify SFT, DAgger, offline RL, and OPD.

arxiv:2605.16826 v1 · 2026-05-16 · cs.LG · cs.AI · cs.CL

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Claims

C1strongest claim

We show that the prevailing paradigms, off-policy distillation and on-policy distillation (OPD), implicitly couple two orthogonal choices: prefix source and token-level KL direction. This follows from decomposing sequence-level KL over autoregressive response distributions.

C2weakest assumption

The decomposition of sequence-level KL divergence into independent prefix-source and token-level KL-direction axes is valid and produces four distinct, usable objectives without hidden inconsistencies or additional constraints.

C3one line summary

Decoupling prefix source from token-level KL direction in autoregressive sequence KL yields four objectives unifying SFT, DAgger, offline RL and OPD, with KL mixing and entropy-gated curriculum improving math reasoning accuracy and shortening responses.

References

42 extracted · 42 resolved · 18 Pith anchors

[1] On-policy distillation of language models: Learning from self- generated mistakes 2024

[2] American mathematics competitions, 2023 2023

[3] Scheduled sampling for sequence prediction with recurrent neural networks 2015

[4] Retaining by doing: The role of on-policy data in mitigating forgetting, 2025 2025

[5] Unveiling the key factors for distilling chain-of-thought reasoning 2025 · doi:10.18653/v1/2025.findings-acl.782

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Receipt and verification

First computed	2026-05-20T00:03:24.706776Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5b6db107da5abfa551698b0bb21a60699a6df2ab510fa487f7178e53db0a9a6f

Aliases

arxiv: 2605.16826 · arxiv_version: 2605.16826v1 · doi: 10.48550/arxiv.2605.16826 · pith_short_12: LNW3CB62LK72 · pith_short_16: LNW3CB62LK72KULJ · pith_short_8: LNW3CB62

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/LNW3CB62LK72KULJRMF3EGTANG \
  | 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: 5b6db107da5abfa551698b0bb21a60699a6df2ab510fa487f7178e53db0a9a6f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bddc47ea4ea050c810668ed5f5a1583ffac6926fc75361a5137b37298f859e64",
    "cross_cats_sorted": [
      "cs.AI",
      "cs.CL"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-05-16T06:05:27Z",
    "title_canon_sha256": "79444aa24cbc3a1728b876a8be6a74b13f59c0c7333180e7eeef189d7db8c98b"
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  "source": {
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    "kind": "arxiv",
    "version": 1
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}