Information-Preserving Reformulation of Reasoning Traces for Antidistillation

1 Introduction

• Revealed reasoning traces can support user insight into model problem-solving, but exposing them makes them vulnerable to unauthorized distillation.The introduction notes that supervised fine-tuning on tens of thousands of reasoning traces can let students attain comparable reasoning capabilities.Source: §1 · p. 2
• Common protections hide reasoning traces or provide summaries, which hinder access to useful intermediate information; other approaches can reduce teacher performance or incur large-model training costs.PART is presented as an alternative intended to retain information while disrupting distillation.Source: §1 · p. 2
• PART uses a small auxiliary model to remove low-probability self-talk expressions and move sub-conclusions before their reasoning steps.The authors describe these changes as targeting token-level and structural patterns that support distillation while preserving information and human interpretability.Source: §1 · p. 2
• 90.1% of queries matched PART reformulations semantically, compared with 7.3% for the summary-based method.The evaluation also included lexical similarity; participants generally judged PART’s information comparable to the originals and preferred it over summaries for richer information.Source: §1 · p. 2
• A 32B student’s AIME 2024 score fell from 54.17 to 46.8 with PART-reformulated traces, a 13.5% degradation.The authors also report degradation across mathematics, coding, and scientific question answering benchmarks and across student-model sizes and dataset scales.Source: §1 · p. 3

2.1 Problem Formulation

• The transformation targets the reasoning trace while keeping the final answer unchanged, since the answer conveys the task outcome for users.The paper represents each output as y = (r, a), with reasoning trace r and final answer a.Source: §2.1 · p. 3
• The modified trace should degrade downstream performance of a student trained on the transformed dataset.This is the formulation’s distillation-interference objective.Source: §2.1 · p. 3
• The modified trace should remain human-readable and preserve as much useful information as possible from the original.The formulation describes this as an information-preservation objective.Source: §2.1 · p. 3

T Perf(SDT )

• The similarity threshold τ is intended to ensure the rewritten trace remains sufficiently faithful to the original from a human reader’s perspective.The formulation describes Sim as the similarity measure between original and rewritten traces.Source: T Perf(SDT ) · p. 3
• Self-talk tokens receive persistently lower predicted probabilities than average, despite conveying little reasoning content, and may exert disproportionate influence on updates.Figure 2 depicts token-level probabilities and tracks self-talk-token probabilities across training stages.Source: Figure 2 · p. 4

2.2 Reasoning Trace Reformulation

• The reformulation approach draws on the difference between how LLMs learn reasoning through supervised fine-tuning and how humans comprehend reasoning traces.The paper presents token-level and structural changes as complementary perspectives.Source: §2.2 · p. 4

1. Removing self-talk behaviors

• Low-probability tokens dominate the effective training signal because their gradients grow when the model poorly predicts them.Tokens the model already predicts confidently contribute negligible gradients and quickly fade from optimization.Source: §1 · pp. 4–5
• Self-talk expressions such as “Hmm” and “Wait” receive persistently low probabilities despite carrying little reasoning information, giving them disproportionate influence during updates.The analysis finds these expressions among low-probability tokens in teacher-generated traces.Source: §1 · p. 5
• Removing self-talk behaviors is intended to perturb gradients associated with low-probability tokens while incurring negligible information loss.The paper presents this rewrite as a way to affect the distillation process.Source: §1 · p. 5

2. Reordering the sub-conclusions

• Conclusion-before-process ordering can remain readable to humans, but makes distillation difficult because LLMs struggle to generate conclusions without first generating reasoning steps.The paper contrasts this approach with random shuffling, deletion, or irrelevant-step insertion, which compromise readability.Source: §2 · p. 5

2.3 Training a Compact Reformulation Model

• The reformulation model divides traces into segments, rewrites them individually, and concatenates them; it adds less than 1% of advanced reasoning models’ parameters and about 4% computational overhead.The compact model is fine-tuned on original traces paired with GPT-4o rewrites.Source: §2.3 · p. 5
• The compact model successfully removes self-talk and reorders sub-conclusions while preserving information, and PART is judged similarly informative to originals and preferred over summaries.Figure 3 reports higher lexical match ratios than the summary-based method at step and sentence levels.Source: §2.3 · p. 6, Figure 3 · p. 6

3 Quality of Reformulated Reasoning Traces

• PART’s reformulations are evaluated against originals and summaries using lexical similarity, semantic similarity, and human judgment to assess information preservation.The evaluation is intended to check that reformulations disrupt distillation while retaining information for users.Source: §3 · p. 6

3.1 Lexical Similarity

• At a 0.7 similarity threshold, PART achieves a 91% match ratio, compared with 18% for summary-based reformulations.The study uses fuzzy matching of original trace sentences or steps and reports that PART surpasses summaries across thresholds at both levels.Source: §3.1 · p. 6

3.2 Semantic Similarity

• 90.1% of queries match PART reformulations versus 7.3% for summaries, and average cosine similarity is 0.950 versus 0.889.Original traces are queries, while PART and summary reformulations are candidate documents.Source: §3.2 · p. 7

3.3 Human Judgment

• Participants judged PART similarly informative to original traces and clearly preferred it over summary-based reformulations for information richness.The study collected 124 comparisons from 31 completed questionnaires.Source: §3.3 · p. 7

4.1 Setup

• The evaluation distills student models of different sizes and families on two datasets, then tests MATH-500, AIME 2024, LiveCodeBench v2, and GPQA-Diamond.The tasks cover mathematical reasoning, code generation, and scientific question answering.Source: §4.1 · p. 7

4.2 Results

• 32B students score 54.17 to 46.88 on AIME 2024 with PART, a 13.5% degradation; performance degrades consistently across benchmarks and student sizes.Table 1 reports benchmark performance; more negative ∆ indicates stronger antidistillation effects.Source: §4.2 · p. 7, Table 1 · p. 8
• Qwen2.5-Math-7B scores decrease by 7.67 on average and Qwen2.5-7B-Instruct scores by 10.19, showing effectiveness across student-model types.Source: §4.2 · p. 8

4.3 Effectiveness of the Reformulation Model

• A 1.5B reformulation model trained on Bespoke-Stratos-17k reforms OpenThoughts-114k traces that still significantly degrade student performance.Its traces reach 88% lexical match at threshold 0.7 and 0.94 average semantic cosine similarity, close to GPT-4o reformulations and above the summary-based method.Source: §4.3 · p. 8

4.4 Detectability

• Self-talk keyword frequency falls from 2.9% in original traces to 0.4% after reformulation, enabling a threshold classifier to reach F1 0.93 and TPR 88.3% at 1% FPR.Source: §4.4 · p. 8

4.5 Robustness to Data Scale

• Across different data scales, PART consistently degrades distilled-model performance; even many reformulated traces underperform fewer original traces.Source: §4.5 · p. 9, Figure 4 · p. 9

• PART is an information-preserving reformulation of reasoning traces designed for antidistillation.Source: §5 · p. 9
• The method removes self-talk tokens and reorders sub-conclusions before their supporting process.Source: §5 · p. 9
• PART retains original-trace information and substantially outperforms summary-based methods across lexical, semantic, and human-judgment evaluations.Source: §5 · p. 9
• Distillation on reformulated traces consistently degrades student performance across benchmarks, model sizes, and data scales.The paper presents PART as a practical way to balance interpretability with protection of model intellectual property.Source: §5 · p. 9

A Related Work

• Reasoning distillation uses reasoning traces to train smaller models, with prior work reporting strong distilled models and large-scale trace datasets.Examples include O1 Journey and DeepSeek-R1.Source: A Related Work · p. 13
• Watermarking manipulates generation sampling to make text detectable, whereas its primary emphasis is post-hoc detection rather than interfering with distillation.Prior work explores detecting watermarks after distillation.Source: A Related Work · p. 13
• Unlearnable-data methods modify training inputs, but the passage says they are unsuitable when an attacker’s prompts cannot be altered and are typically limited to classification.PART instead modifies model generation without task-specific designs.Source: A Related Work · p. 13
• Earlier antidistillation methods alter sampling or teacher parameters and were demonstrated only on students below 4B; PART is reported effective up to 32B.The cited approaches are Antidistillation Sampling [STF+25] and DOGe [LTQ+25].Source: A Related Work · p. 13

B Prompts

• The self-talk prompt rewrites only self-talk expressions declaratively, avoids first-person phrasing, and preserves other text without adding information.Source: B Prompts · p. 13
• The reordering prompt extracts a small set of important sub-conclusions, then moves their corresponding sentences before the reasoning processes.Source: B Prompts · p. 14

C Hyperparameter

• Training hyperparameters use larger learning rates for smaller models.Source: Table 2 · p. 14
• AIME24 evaluation uses more responses per query because the problem set is small.Source: Table 3 · p. 14

D Example of Reformulated Reasoning Trace

• The example trace considers whether three people form a connected communication graph through direct links or an intermediary.Source: D Example of Reformulated Reasoning… · p. 15

E Lexical Similarity

• The three-person communication problem is framed as checking whether everyone is connected directly or through the third person.Each consecutive pair in the chain must be within R.Source: E Lexical Similarity · p. 15
• The clock-angle reformulation retains the possible second 110-degree angle and the formula for the angle between the hands.The original step uses self-talk to revisit the possibility; the matched version states the check directly.Source: E Lexical Similarity · p. 15
• The reformulated erased-number problem retains the consecutive-integers setup, the remaining average, and the answer choices.The matched version omits the original's closing “Hmm.”Source: E Lexical Similarity · p. 15
• The reformulated graph-transformation check retains the x = -1 test that rules out option E and supports option D.Both versions also note that option E works at x = 0.Source: E Lexical Similarity · p. 16
• The reformulated ranking trace retains the values for Thuy, Jose, and Kareem and the conclusion that Kareem is largest.The reformulation repeats the three values before stating the final order.Source: E Lexical Similarity · p. 16