# DICE: Detecting In-distribution Contamination in LLM's Fine-tuning Phase for Math Reasoning

arXiv: https://arxiv.org/abs/2406.04197 · HTML: https://mlsanity.com/paper/2406.04197/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 31 of its 41 references that are in the map.
- First posted on arXiv 6 Jun 2024.

## Placed in

- LLM reasoning / [Mathematical reasoning](https://mlsanity.com/lr/mathematical-reasoning/)

## Builds on (most cited first, 30 of 31)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Sentence-BERT: Sentence Embeddings using Siamese BERT-Networks](https://mlsanity.com/paper/1908.10084/) (2019)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Extracting Training Data from Large Language Models](https://mlsanity.com/paper/2012.07805/) (2020)
- [Survey of Hallucination in Natural Language Generation](https://mlsanity.com/paper/2202.03629/) (2022)
- [LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Code](https://mlsanity.com/paper/2403.07974/) (2024)
- [LongBench: A Bilingual, Multitask Benchmark for Long Context Understanding](https://mlsanity.com/paper/2308.14508/) (2023)
- [Are NLP Models really able to Solve Simple Math Word Problems?](https://mlsanity.com/paper/2103.07191/) (2021)
- [PAL: Program-aided Language Models](https://mlsanity.com/paper/2211.10435/) (2022)
- [Scalable Extraction of Training Data from (Production) Language Models](https://mlsanity.com/paper/2311.17035/) (2023)
- [Detecting Pretraining Data from Large Language Models](https://mlsanity.com/paper/2310.16789/) (2023)
- [Dynamic Prompt Learning via Policy Gradient for Semi-structured Mathematical Reasoning](https://mlsanity.com/paper/2209.14610/) (2022)
- [A Diverse Corpus for Evaluating and Developing English Math Word Problem Solvers](https://mlsanity.com/paper/2106.15772/) (2021)
- [Data Contamination: From Memorization to Exploitation](https://mlsanity.com/paper/2203.08242/) (2022)
- [Proving Test Set Contamination in Black Box Language Models](https://mlsanity.com/paper/2310.17623/) (2023)
- [A Careful Examination of Large Language Model Performance on Grade School Arithmetic](https://mlsanity.com/paper/2405.00332/) (2024)
- [Benchmarking Foundation Models with Language-Model-as-an-Examiner](https://mlsanity.com/paper/2306.04181/) (2023)
- [Benchmarking Benchmark Leakage in Large Language Models](https://mlsanity.com/paper/2404.18824/) (2024)
- [DyVal: Dynamic Evaluation of Large Language Models for Reasoning Tasks](https://mlsanity.com/paper/2309.17167/) (2023)
- [KoLA: Carefully Benchmarking World Knowledge of Large Language Models](https://mlsanity.com/paper/2306.09296/) (2023)
- [Benchmark Self-Evolving: A Multi-Agent Framework for Dynamic LLM Evaluation](https://mlsanity.com/paper/2402.11443/) (2024)
- [Memorization vs. Generalization: Quantifying Data Leakage in NLP Performance Evaluation](https://mlsanity.com/paper/2102.01818/) (2021)
- [LatestEval: Addressing Data Contamination in Language Model Evaluation through Dynamic and Time-Sensitive Test Construction](https://mlsanity.com/paper/2312.12343/) (2023)
- ["According to ...": Prompting Language Models Improves Quoting from Pre-Training Data](https://mlsanity.com/paper/2305.13252/) (2023)
- [KIEval: A Knowledge-grounded Interactive Evaluation Framework for Large Language Models](https://mlsanity.com/paper/2402.15043/) (2024)
- [Evading Data Contamination Detection for Language Models is (too) Easy](https://mlsanity.com/paper/2402.02823/) (2024)
- [TRUCE: Private Benchmarking to Prevent Contamination and Improve Comparative Evaluation of LLMs](https://mlsanity.com/paper/2403.00393/) (2024)

## Built on by (most cited first, 11 of 11)

- [Recent Advances in Large Langauge Model Benchmarks against Data Contamination: From Static to Dynamic Evaluation](https://mlsanity.com/paper/2502.17521/) (2025)
- [A Survey on Data Contamination for Large Language Models](https://mlsanity.com/paper/2502.14425/) (2025)
- [Detecting Training Data of Large Language Models via Expectation Maximization](https://mlsanity.com/paper/2410.07582/) (2024)
- [On The Fragility of Benchmark Contamination Detection in Reasoning Models](https://mlsanity.com/paper/2510.02386/) (2025)
- [VeriEquivBench: An Equivalence Score for Ground-Truth-Free Evaluation of Formally Verifiable Code](https://mlsanity.com/paper/2510.06296/) (2025)
- [Self-Improvement of Large Language Models: A Technical Overview and Future Outlook](https://mlsanity.com/paper/2603.25681/) (2026)
- [Establishing Trustworthy LLM Evaluation via Shortcut Neuron Analysis](https://mlsanity.com/paper/2506.04142/) (2025)
- [The Illusion of Reasoning: Exposing Evasive Data Contamination in LLMs via Zero-CoT Truncation](https://mlsanity.com/paper/2605.21856/) (2026)
- [LogitTrace: Detecting Benchmark Contamination via Layerwise Logit Trajectories](https://mlsanity.com/paper/2509.20909/) (2025)
- [AdEval: Alignment-based Dynamic Evaluation to Mitigate Data Contamination in Large Language Models](https://mlsanity.com/paper/2501.13983/) (2025)
- [Benchmark Contamination: A Taxonomy Organized by Defeated Mitigation](https://mlsanity.com/paper/2608.29463/) (2026)

## Abstract (arXiv)

The advancement of large language models (LLMs) relies on evaluation using public benchmarks, but data contamination can lead to overestimated performance. Previous researches focus on detecting contamination by determining whether the model has seen the exact same data during training. Besides, prior work has already shown that even training on data similar to benchmark data inflates performance, namely In-distribution contamination. In this work, we argue that in-distribution contamination can lead to the performance drop on OOD benchmarks. To effectively detect in-distribution contamination, we propose DICE, a novel method that leverages the internal states of LLMs to locate-then-detect the contamination. DICE first identifies the most sensitive layer to contamination, then trains a classifier based on the internal states of that layer. Experiments reveal DICE's high accuracy in detecting in-distribution contamination across various LLMs and math reasoning datasets. We also show the generalization capability of the trained DICE detector, which is able to detect contamination across multiple benchmarks with similar distributions. Additionally, we find that DICE's predictions correlate with the performance of LLMs fine-tuned by either us or other organizations, achieving a coefficient of determination (R2) between 0.61 and 0.75. The code and data are available at https://github.com/THU-KEG/DICE.