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Retrospective Distillation Attribution via Normalized Response Similarity

Minwoo Jang, Jaechang Kim, Minhyeon Oh, Jeongyeon Hwang, Jungseul Ok

arXiv:2609.32749v1cs.AIcs.CLcs.CRcs.LGstat.ML

TL;DR

Attributing a distillation source after further training is challenging when existing methods rely on a pre-distillation checkpoint. SCOUT uses recurring syntactic patterns and candidate-pool calibration to attribute models from outputs alone. It selects the documented teacher for all evaluated descendants, while teacher-associated signatures emerge during distillation and persist through later training.

  • Problem

    Attribution must identify a teacher in descendants that undergo further training, while one existing approach compares student likelihoods with a pre-distillation checkpoint.

    Source: §1 · pp. 1–2

  • Method

    SCOUT builds candidate profiles from recurring syntactic patterns, filters low-contrast patterns, and calibrates student–candidate distances against the candidate pool.

    Source: §1 · p. 2, §7 · p. 9

  • Results

    SCOUT selects the documented teacher for all evaluated descendants, and teacher-associated signatures persist through preference optimization and reinforcement learning.

    Source: §1 · p. 2

  • Takeaways & Limitations

    SCOUT supports open-set attribution in controlled cohorts and closed-set retrospective attribution after subsequent training.

    Source: §7 · p. 9

    SCOUT depends on the supplied candidate pool, whose principled construction for third-party auditors remains open and whose composition bounds attribution resolution.

    Source: §7 · p. 10

Abstract

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Model distillation transfers capabilities through supervised fine-tuning (SFT) on teacher responses, often collected from commercial APIs, raising questions of model provenance. Existing distillation attribution methods have been largely evaluated on students immediately after the SFT step. However, a distilled model may undergo further SFT, preference optimization, or reinforcement learning before release, while an auditor may lack access to the pre-distillation checkpoint required by reference-based attribution. To close this gap, we propose SCOUT, an output-only method that aggregates recurring *syntactic patterns* into candidate profiles, filters low-contrast patterns, and calibrates student--candidate distances against inter-candidate distances. SCOUT supports attribution and abstention using only current texts, without model weights, token likelihoods, or historical checkpoints. Auditing publicly released descendants of distilled models spanning diverse post-training objectives, SCOUT consistently identifies the distillation source. Furthermore, tracing teacher-associated *syntactic signatures* along training trajectories reveals that they emerge during distillation and persist through subsequent preference optimization and reinforcement learning.

1 INTRODUCTION

Distillation attribution must address released models that may have undergone further training, often without access to the checkpoint needed by reference-based methods. SCOUT uses current outputs to identify candidate sources, and the reported evaluations find teacher-associated syntactic signatures after subsequent training.

Motivation

  • Distillation transfers capabilities through student SFT on teacher responses, and released artifacts alone do not reveal whether those data were used.The introduction notes provider prohibitions on using outputs to train competing models and reported attempts to collect outputs for that purpose.Source: §1 · p. 1
  • Retrospective attribution matters because released students may undergo further training, while auditors may lack a pre-distillation checkpoint and see only current outputs.Subsequent training may alter observable teacher-associated signatures, and using a post-distillation checkpoint can mask the distillation effect.Source: §1 · p. 2

Method

  • SCOUT aggregates recurring patterns across candidate responses, filters low-contrast patterns, and calibrates student–candidate distances against the candidate pool.It uses current student and teacher-candidate texts without a classifier, model weights, token likelihoods, or historical checkpoints.Source: §1 · pp. 1–2

Retrospective Evaluation

  • SCOUT selects the documented teacher for all evaluated descendants within the candidate pool using current outputs alone.The descendants underwent additional SFT, preference optimization, or reinforcement learning.Source: §1 · p. 2

Findings

  • Teacher-associated syntactic signatures emerge during SFT and remain readable through preference optimization and reinforcement learning across public training trajectories and released descendants.The reported signal also appears in a diffusion language model lineage.Source: §1 · p. 2

2 RELATED WORK

Prior attribution approaches use classifiers on syntactic patterns, likelihood shifts from earlier checkpoints, or verification requiring shadow distillation. SCOUT addresses post-training attribution using current texts, complementing proactive defenses that cannot address suspicions arising only after release.

Distillation Attribution and Model Provenance

  • SCOUT targets teacher attribution after subsequent training using current student and candidate texts, and abstains when evidence distinguishes no candidate.Unlike parameter-ancestry studies, it concerns which teacher generated responses used for SFT.Source: §2 · p. 2
  • Figure 2 contrasts SCOUT’s profile aggregation, low-contrast filtering, and candidate-pool calibration with earlier syntactic attribution approaches.The caption describes the candidate profiles and inter-candidate distances used in calibration.Source: Figure 2 · p. 3

Proactive Model Protection

  • Proactive defenses may require monitoring, extra training, controlled decoding, or intervention, and cannot address suspicions arising only after a third-party model is released.SCOUT addresses this complementary post-hoc auditing need without modifying the audited or candidate models.Source: §2 · p. 3

3 PROBLEM FORMULATION

Retrospective attribution asks whether a released student’s current outputs support identifying the teacher used in its distillation step. The auditor compares outputs on shared prompts and may abstain when the candidate pool or available evidence cannot support exact attribution.

3 PROBLEM FORMULATION

  • The target is the teacher T⋆ whose outputs supplied distillation from pre-distillation checkpoint S(0) to S(1), even if the student later undergoes additional training.The released model is S(L), after downstream stages such as additional SFT, preference optimization, or reinforcement learning.Source: §3 · p. 3
  • The auditor queries the released student and each candidate on shared audit prompts using only text responses, without assuming access to weights, likelihoods, supervision data, or earlier checkpoints.The candidate pool may or may not contain the true teacher.Source: §3 · p. 3
  • Correctness requires selecting the true teacher when it is in the pool and abstaining when it is absent; exact recovery is limited by pool resolution and output similarity.Abstention means current evidence supports no candidate, not that no candidate supplied responses at an earlier training stage.Source: §3 · p. 3

4 PROPOSED METHOD

SCOUT represents candidate syntax through recurring PoS patterns, filters patterns that do not distinguish candidates, and calibrates similarity against inter-candidate distances. Its trajectory margins describe changes in teacher-relative separation without themselves determining attribution verdicts.

4 PROPOSED METHOD

  • SCOUT combines PoS n-gram candidate profiles, candidate-contrast filtering, and candidate-pool calibration for attribution with abstention.Figure 2 summarizes these components.Source: §4 · p. 3

4.1 RESPONSE REPRESENTATION AND CANDIDATE PROFILES

  • Responses are encoded as counts of contiguous PoS n-grams of lengths 3, 4, and 5, and candidate profiles average these patterns across prompts rather than fitting a classifier to individual responses.This captures recurring patterns across candidate responses while the audited model remains at the prompt level.Source: §4.1 · p. 4

4.2 CANDIDATE-CONTRAST FILTERING

  • The filtering mask retains features at or above a candidate-pool contrast quantile, removing more low-contrast features as the filtering fraction increases.The experiments fix λ = 0.15 and report sensitivity to λ in Appendix B.Source: §4.2 · p. 4

4.3 CANDIDATE-POOL CALIBRATION AND DECISION RULE

  • SCOUT standardizes student–candidate distances using prompt-specific null locations and candidate-level scales estimated from inter-candidate distances.Lower calibrated scores mean the student is closer to a candidate than the pool null predicts; open-set attribution accepts when the closest-alternative gap reaches threshold τ and otherwise abstains.Source: §4.3 · pp. 4–5

4.4 TRAJECTORY MARGINS

  • Trajectory margins measure teacher-relative separation against a common pool with profiles and empirical nulls fixed along each trajectory.Positive changes indicate stronger teacher-relative separation than at S(0), but these teacher-aware quantities do not determine attribution verdicts.Source: §4.4 · p. 5

5 EXPERIMENTS

The experiments test SCOUT against existing methods on released descendants after further training and controlled students immediately after SFT. They assess attribution, rejection after teacher removal, prompt efficiency, and inheritance of teacher-associated patterns.

5.1 COMPARED METHODS AND PROBE SETS

  • The evaluation compares SCOUT with DistillDetect, PoS Templates, and two training-free LLM judges across math and conversation probe sets.The probes are OpenMathInstruct and s1 for math, and OASST1 and Dolly for conversation.Source: §5.1 · p. 5

5.2 DISTILLATION ATTRIBUTION AFTER SUBSEQUENT TRAINING

  • SCOUT correctly assigns all 12 descendants and both distilled parents to R1, and identifies both pre-distillation bases as non-R1 on all four probes.Its output-only accuracy is highest on every probe under both distributional-separation and same-prompt comparisons.Source: §5.2 · p. 6, Table 1 · p. 6
  • With five prompts, SCOUT attributes 10.7/12 descendants on OMI and 11.7/12 on Dolly, reaching 12/12 with 100 and 50 prompts, respectively.On Dolly, the other output-only methods fall to 1/12 as the budget grows.Source: §5.2 · p. 6, Figure 3 · p. 7

5.3 DISTILLATION ATTRIBUTION BEFORE SUBSEQUENT TRAINING

  • Under fold-fitted thresholds, SCOUT detects 18/19 math and 15/19 conversation students while accepting none after teacher removal.The cohorts use disjoint SFT and audit examples, and threshold transfer is tested with student-backbone and teacher holdouts.Source: §5.3 · p. 7, Table 2 · p. 7
  • SCOUT detects 19/19 math and 17/19 conversation students at zero false positives, versus 13/19 and 12/19 for DistillDetect, which requires a pre-distillation reference checkpoint.Student-level AUCs are 1.000 for math and 0.970 for conversation.Source: §5.3 · p. 7, Figure 4 · p. 8
  • Figure 5’s block-diagonal structure shows that controlled students consistently inherit teacher-associated syntactic patterns across backbones and domains.The figure compares candidate models’ characteristic PoS n-grams with student responses grouped by true teacher.Source: §5.3 · p. 7, Figure 5 · p. 8
  • On one held-out Dolly prompt, raw gaps attribute 8/10 students and centered gaps 7/10; candidate-specific scaling moves all ten scaled gaps above zero.The full procedure aggregates 200 prompts per probe and requires agreement across probes.Source: §5.3 · p. 8, Figure 6 · p. 8

6 READING THE SIGNATURE ALONG A TRAINING TRAJECTORY

This section uses trajectory margin change to track when teacher-associated evidence appears and whether it persists through later training. Across public trajectories and descendants, signatures remain readable after varied post-training, including in a diffusion lineage.

6.1 TEACHER SIGNATURES EMERGE AND PERSIST ACROSS TRAINING TRAJECTORIES

  • On OMI, margins became positive immediately after distillation and stayed positive at every later checkpoint across all 13 trajectories; the same pattern held on s1.The trajectories span five teachers, dense and mixture-of-experts models, and roughly 1B active to 32B dense parameters.Source: §6.1 · p. 9, Figure 7 · p. 9
  • All 12 public descendants retained an R1 signature relative to the Qwen2.5-Math base, while margins exceeded their distilled parent’s for 7/12 on OMI and 3/12 on s1.The signature persists across descendants, but further strengthening varies.Source: §6.1 · p. 9

6.2 THE SIGNATURE EXTENDS BEYOND AUTOREGRESSIVE MODELS

  • In Dream-7B, margins toward both documented teachers increased after instruction tuning and stayed positive across four post-training branches on both probes.This diffusion-language-model result uses mixed-teacher instruction data.Source: §6.2 · p. 9

7 CONCLUSION

SCOUT attributes distillation from current outputs, with trajectory analyses finding teacher-associated signatures that emerge during distillation and persist through later training. The conclusion also identifies candidate-pool construction and attribution resolution as limitations.

7 CONCLUSION

  • SCOUT aggregates recurring syntactic patterns into candidate profiles, filters low-contrast patterns, and calibrates student–candidate distances against inter-candidate distances.The conclusion reports open-set attribution in controlled cohorts and closed-set retrospective attribution after subsequent training.Source: §7 · p. 9
  • Teacher-associated signatures emerge during distillation and persist through preference optimization and reinforcement learning; the signal also extends to a diffusion model under mixed-teacher supervision.The conclusion reports these findings across controlled students and public descendants.Source: §7 · p. 9
  • SCOUT depends on the supplied candidate pool, and principled pool construction for third-party auditors remains open.Pool composition bounds attribution resolution; sibling-enriched pools sharply reduce exact attribution from current outputs.Source: §7 · p. 10
  • Future work includes testing persistence for watermarks and fingerprints under matched post-training and response-rewriting interventions, and evaluating adversaries optimized to evade attribution.Source: §7 · p. 10

AI USE STATEMENT

The authors report using generative AI tools during manuscript preparation and experiments, while retaining responsibility for interpretation and scientific conclusions.

AI USE STATEMENT

  • Generative AI tools assisted manuscript preparation and were used experimentally for training and audit responses and judge baselines; authors reviewed AI-assisted manuscript content and take responsibility for the final claims.Source: AI USE STATEMENT · p. 10

ETHICS STATEMENT

The statement cautions that output-based attribution is not conclusive evidence of a model’s training history and recommends considering independent provenance evidence.

ETHICS STATEMENT

  • Output-based attribution should be assessed alongside independent provenance evidence because non-detection does not establish non-use.Close source relatives can reduce exact-teacher attribution, and subsequent SFT made an earlier source unrecoverable by evaluated methods under tested budgets and probe sets.Source: ETHICS STATEMENT · p. 10

REPRODUCIBILITY STATEMENT

This statement points readers to the response representation, calibration equations, appendices, and qualitative examples of recurring part-of-speech patterns distinguishing candidate models. It also summarizes analyses of syntactic signatures under markup removal, across response windows and training, including signature inheritance and candidate-contrast sensitivity, while noting limits on interpreting individual patterns.

REPRODUCIBILITY STATEMENT

  • The reproducibility statement points to response representation and candidate-pool calibration, with appendices covering preprocessing, filtering, robustness, finite-prompt analysis, and generation, training, and evaluation procedures.Source: REPRODUCIBILITY STATEMENT · p. 10

APPENDIX CONTENTS

A QUALITATIVE EXAMPLES OF THE POS n-GRAM SIGNAL

  • SCOUT signatures count 3–5-grams in the first 2,000 characters using Penn Treebank tags, retain markup, and keep patterns appearing in at least 20 of 200 responses.The appendix’s unfiltered top-ten lists are descriptive and do not enter SCOUT’s score.Source: A QUALITATIVE EXAMPLES OF THE POS… · pp. 18–19
  • Recurring patterns include step headings, first-person reasoning, omitted subjects and articles, inline-math definitions, and reasoning descriptions; Qwen3-235B-A22B-Thinking repeats an opening sentence in 126/200 OMI and 145/200 s1 responses.Llama-3-70B-Instruct uses “I hope it is correct” in 140/200 OMI and 117/200 s1 responses.Source: A QUALITATIVE EXAMPLES OF THE POS… · p. 20
  • Candidate pool and signature size affect pattern lists, and tagging errors can complicate interpretation; recurring forms alone do not establish attribution.For example, sentence-initial “Compute b” receives the tag sequence . NNP NN.Source: A QUALITATIVE EXAMPLES OF THE POS… · p. 28

B.1 MARKUP AND WINDOW CONTROLS

  • Removing markup changes tag sequences without necessarily erasing writing habits, while every controlled student has positive teacher-associated gain across all tested window conditions.Five or six GPT-OSS-120B patterns and nine Qwen-3-8B patterns remain unchanged; the first 500 canonicalized characters retain 78.8% of the gain under D and C and 91.5% under SCOUT relative to the first 2,000 raw characters.Source: §B.1 · pp. 29–30, Table 6 · p. 30

B.2 INHERITANCE OF TEACHER SIGNATURES

  • Controlled students preferentially reproduce teacher-associated syntactic patterns, and this inheritance persists after training-format markers are removed.Teacher signatures recur across probes and model scales; rankings remain stable around k = 10, while broader lists eventually include patterns shared across models.Source: §B.2 · pp. 30, 32, Figure 9 · p. 31, Table 7 · p. 32

B.3 CANDIDATE-CONTRAST SENSITIVITY

  • All twelve descendants are assigned to DeepSeek-R1 across the evaluated grid on both math probes; conversation probes reach 12/12 for OASST1 and Dolly at λ = 0.10 and 0.15.Both distilled parents are also assigned to DeepSeek-R1, while both pre-distillation bases are correctly rejected as non-R1; profile distance D does not recover the conversation descendants.Source: §B.3 · pp. 32–33
  • λ = 0.10 and 0.15 yield no false acceptances under either threshold-transfer protocol in every controlled cohort while retaining high detection.Performance is less consistent outside these values, particularly for conversation and λ = 0.25; the additional 7–8B cohort shows the same pattern, and primary experiments fix λ = 0.15.Source: §B.3 · p. 32, Table 8 · p. 33

B.4 DECODING AND RESPONSE-LENGTH CONTROLS

The decoding controls find source attribution stable under the tested teacher- and candidate-side decoding changes and total-response-length controls. The appendix characterizes candidate-pool calibration, prompt-subsampling stability, and limits on candidate-only correction and output-only history recovery.

B.4 DECODING AND RESPONSE-LENGTH CONTROLS

  • 19/19 students moved most toward their true source under common teacher decoding; among 17 eligible for exact inference, mean IT was 0.158 (p=6.4 × 10^-5).The 19-student cohort had mean IT 0.163 under common decoding, versus 0.167 under original teacher configurations.Source: Table 10 · p. 34, §B.4 · p. 34
  • Candidate-side decoding changes altered none of 39 verdicts, and SCOUT identified every source group while length-only readouts failed for some sources.The 2,000-character cap reduced the longest-to-shortest candidate-median ratio from 3.26 to 1.08; total length alone did not explain attribution, though sentence structure may still contribute.Source: §B.4 · pp. 35–36

C.1 CANDIDATE-RELATIVE CALIBRATION

  • Centering removes candidate-wide proximity, but the calibrated score indicates closeness only relative to the supplied pool, not distillation by itself.An unusually close pool member can make a candidate’s centered score less favorable; changing the pool can also alter the vocabulary and contrast mask.Source: §C.1 · p. 36

C.2 FINITE-PROMPT STABILITY

  • Prompt-subsampling stability is conditional on the true source already uniquely winning on the full prompt bank, and the bound does not cover sorted-score voting.The required budget depends on the hardest competitor, not average separation.Source: §C.2 · p. 37
  • On OMI, SCOUT reached the 0.95 success criterion at 50 prompts; on OASST1 and Dolly, centering separated SCOUT from every baseline.Across four probes, the score aggregations had the same first evaluated budget reaching 0.95 except on Dolly, where SCOUT moved from 10 prompts to 20 under mean-score attribution.Source: Table 13 · p. 38, §C.2 · p. 38, Table 14 · p. 39

C.3 LIMITS OF CANDIDATE-ONLY CALIBRATION

  • Candidate-only calibration can remove candidate-wide proximity but cannot generally remove affinity specific to one audited-model–candidate pair.Shared model lineage may induce such an interaction, but the result does not imply that every lineage effect is nonseparable or unresolvable with additional information.Source: §C.3 · p. 40

C.4 LIMITS OF OUTPUT-ONLY HISTORY RECOVERY

  • When two training histories induce identical current-output distributions, no output-only auditor can exceed chance-level balanced accuracy.Abstention means current outputs support no candidate; it does not show that a candidate was never used earlier in training.Source: §C.4 · p. 40

C.5 SOURCE SWITCHING UNDER LATER SFT

Later SFT can redirect the source signature expressed in current outputs, while the capability change depends on the relative strength of the replacement source. The appendix also reports supplementary attribution analyses.

C.5 SOURCE SWITCHING UNDER LATER SFT

  • After removing the second-round source, SCOUT recovers the earlier source in 18/18 arms at 1% and 2%, but only 6/18 at the endpoint.The replication crosses three base models and all six ordered source pairs; random selection would recover the earlier source in 6/18 arms.Source: §C.5 · p. 40
  • SCOUT selects the second-round source in every switch arm from 25% of training onward, while no same-source control switches.At 5%, 10%, and 15%, it selects the new source in 16/36, 29/36, and 33/36 arms, respectively.Source: §C.5 · p. 40, Figure 11 · p. 41
  • When the replacement source is stronger, median accuracy rises by 0.143 on both GSM8K and MATH-500; when weaker, it falls by 0.105 and 0.136, respectively.Source strength is defined by the median accuracy before the second round among students initially trained on that source.Source: §C.5 · p. 41
  • On the 18-arm replication, every output-only readout selects the second-round source in 18/18 arms at the endpoint, so redirection is not specific to SCOUT.Every method selects the new source in a majority of arms by 10%.Source: §C.5 · p. 41, Table 15 · p. 41

D ADDITIONAL ATTRIBUTION ANALYSES

D.1 CONTROLLED DETECTION ABLATION

These analyses probe controlled detection, candidate-pool sensitivity, and whether teacher-relative syntactic signatures remain detectable across public training trajectories, including a masked-diffusion lineage.

D.1 CONTROLLED DETECTION ABLATION

  • In the 1.5–4B math cohort, all three profile variants reach AUC 1.000 and detect all nineteen students at zero false positives; in conversation, scaling raises AUC to 0.970 and detection from 14/19 to 17/19.In the 7–8B math cohort, SCOUT reaches AUC 0.993 and detects 20/21 students; threshold sweeps diagnose score separation, while Table 2 evaluates threshold transfer.Source: §D.1 · p. 42
  • Individual source-removed probe cells can have p⋆<0.05 without any false acceptance under the complete two-probe decision rule.Acceptance also requires the same selected candidate and significance on both probes.Source: §D.1 · p. 42, Table 17 · p. 43

D.2 CANDIDATE-POOL STRESS TEST WITH SOURCE RELATIVES

  • With an expanded sixteen-candidate pool, every output-only method selects DeepSeek-R1 for only 1/7 suspects, while DistillDetect retains 6/7 selections with the corresponding pre-distillation reference.Several output-only methods attain 7/7 with the original pool, making source resolution sensitive to close source relatives.Source: §D.2 · pp. 42–43, Table 18 · p. 43

E.1 THIRTEEN PUBLIC LADDERS

E.2 R1 DESCENDANT LINEAGES

  • Both R1-distilled parents and all twelve descendants have positive ∆GT on both probes; the signature persists but does not consistently strengthen during subsequent training.Seven of twelve descendants on OMI and three of twelve on s1 exceed their respective distilled parents.Source: §E.2 · p. 45

E.3 MASKED DIFFUSION LINEAGE

  • In the Dream-7B diffusion lineage, margins toward GPT-4o and Sonnet 3.5 rise after instruction tuning and remain positive for all four branches on both probes.The GPT-4o margins remain positive for the three branches other than SARDI even when SARDI's additional GPT-4o-mini SFT is excluded.Source: §E.3 · p. 45

F EXPERIMENTAL DETAILS

The experimental details specify how controlled cohorts and public lineages were assembled, how responses and candidate pools were prepared, and how attribution and detection were evaluated.

Controlled cohorts

  • Controlled math and conversation cohorts retain students whose post-SFT task performance exceeds their corresponding base models, using separate audit prompts.The study also constructs a 7–8B math cohort, and detection and abstention use both probe datasets.Source: F EXPERIMENTAL DETAILS · p. 46

Controlled SFT

  • Controlled students receive full-parameter SFT with a completion-only causal language-modeling objective, masking prompt tokens and truncating rather than packing examples.Llama-3.2-3B-Instruct uses its tokenizer's chat template; the other controlled backbones use plain-text formatting for both SFT and response generation.Source: F EXPERIMENTAL DETAILS · p. 46

Response generation

  • Locally generated responses use model-specific released configurations when available, so decoding settings may differ across models.SCOUT analyzes the first 2,000 characters; every response reaching the generation limit exceeds that analyzed prefix.Source: F EXPERIMENTAL DETAILS · p. 46

Candidate pools and response provenance

  • The retrospective evaluation uses domain-specific ten-candidate pools, with a different candidate and response provenance for conversation than for math.The math responses come from the DistillDetect bank; conversation responses are newly collected, and suspect and descendant responses are generated in the study's pipeline.Source: F EXPERIMENTAL DETAILS · pp. 46–47

Public models and checkpoint trajectories

  • Trajectory analyses use publicly released checkpoints and fixed candidate responses, profiles, and empirical nulls across checkpoints for each probe.The thirteen-candidate pool includes documented sources across trajectories; the Dream-7B analysis also evaluates four post-training branches.Source: F EXPERIMENTAL DETAILS · p. 47

Evaluation

  • Score-based evaluations aggregate prompt-level scores, fit thresholds on non-held-out cells, and require significance on both probes with the same selected candidate for detection.The LLM-judge protocol uses two judges, 200 prompts per probe, and a most-frequent model-level verdict; unparseable outputs count as NONE in open-set trials.Source: F EXPERIMENTAL DETAILS · pp. 47–48

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