# Detecting Distillation Data from Reasoning Models

arXiv: https://arxiv.org/abs/2510.04850 · HTML: https://mlsanity.com/paper/2510.04850/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Placed in Prompting and chain-of-thought reasoning, one of 17 directions in LLM reasoning.
- Builds on 19 of its 51 references that are in the map.
- First posted on arXiv 6 Oct 2025.

## Placed in

- LLM reasoning / [Prompting and chain-of-thought reasoning](https://mlsanity.com/lr/prompting-and-chain-of-thought-reasoning/)
- Knowledge distillation / [Knowledge distillation for LLMs](https://mlsanity.com/distill/knowledge-distillation-for-llms/)

## Builds on (most cited first, 19 of 19)

- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Gemini 2.5: Pushing the Frontier with Advanced Reasoning, Multimodality, Long Context, and Next Generation Agentic Capabilities](https://mlsanity.com/paper/2507.06261/) (2025)
- [Mistral 7B](https://mlsanity.com/paper/2310.06825/) (2023)
- [s1: Simple test-time scaling](https://mlsanity.com/paper/2501.19393/) (2025)
- [OpenAI o1 System Card](https://mlsanity.com/paper/2412.16720/) (2024)
- [Gemma: Open Models Based on Gemini Research and Technology](https://mlsanity.com/paper/2403.08295/) (2024)
- [LIMO: Less is More for Reasoning](https://mlsanity.com/paper/2502.03387/) (2025)
- [Training Language Models to Self-Correct via Reinforcement Learning](https://mlsanity.com/paper/2409.12917/) (2024)
- [DeepSeek-Prover-V1.5: Harnessing Proof Assistant Feedback for Reinforcement Learning and Monte-Carlo Tree Search](https://mlsanity.com/paper/2408.08152/) (2024)
- [Quantifying Privacy Risks of Masked Language Models Using Membership Inference Attacks](https://mlsanity.com/paper/2203.03929/) (2022)
- [Benchmark Data Contamination of Large Language Models: A Survey](https://mlsanity.com/paper/2406.04244/) (2024)
- [Use of LLMs for Illicit Purposes: Threats, Prevention Measures, and Vulnerabilities](https://mlsanity.com/paper/2308.12833/) (2023)
- [Estimating Contamination via Perplexity: Quantifying Memorisation in Language Model Evaluation](https://mlsanity.com/paper/2309.10677/) (2023)
- [QFFT, Question-Free Fine-Tuning for Adaptive Reasoning](https://mlsanity.com/paper/2506.12860/) (2025)
- [Beyond Scaling Law: A Data-Efficient Distillation Framework for Reasoning](https://mlsanity.com/paper/2508.09883/) (2025)
- [Slow Tuning and Low-Entropy Masking for Safe Chain-of-Thought Distillation](https://mlsanity.com/paper/2508.09666/) (2025)
- [Can Large Models Teach Student Models to Solve Mathematical Problems Like Human Beings? A Reasoning Distillation Method via Multi-LoRA Interaction](https://mlsanity.com/paper/2508.13037/) (2025)

## Built on by (most cited first, 4 of 4)

- [Reference-Based Distillation Detection in LLMs](https://mlsanity.com/paper/2607.09692/) (2026)
- [TokenPrint: A Calibrated Token-Space Fingerprint for Language-Model Provenance](https://mlsanity.com/paper/2608.08139/) (2026)
- [Metacognitive Behavioral Tuning of Large Language Models for Multi-Hop Question Answering](https://mlsanity.com/paper/2602.22508/) (2026)
- [WildTrace: Evaluating Training Data Detection in Realistic Large-Scale LLM Post-Training](https://mlsanity.com/paper/2610.16152/) (2026)

## Abstract (arXiv)

Reasoning distillation has emerged as a prevailing paradigm for transferring reasoning capabilities from large reasoning models to small language models. Yet, reasoning distillation risks data contamination: benchmark data may inadvertently be included in the distillation data, thereby inflating model performance metrics. In this work, we formally define the distillation data detection task, which determines whether a given question is included in the model's distillation data. The unique challenge of this task lies in the partial availability of distillation data. To address this, we propose Token Probability Deviation (TPD), a detection method that leverages the probability patterns of output tokens generated by the model instead of input tokens. Our method is motivated by the observation that seen questions tend to elicit more near-deterministic tokens generated by the models than unseen ones. Our TPD score is thus designed to quantify the token-level deviation of generated tokens from a high-confidence reference probability. Consequently, seen questions can yield substantially lower TPD scores than unseen ones, enabling strong detection performance. Extensive experiments demonstrate the effectiveness of our approach, improving detection AUC by up to 31% on distillation datasets.