# Min-K%++: Improved Baseline for Detecting Pre-Training Data from Large Language Models

arXiv: https://arxiv.org/abs/2404.02936 · HTML: https://mlsanity.com/paper/2404.02936/

## Key facts

- Cited by 103 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 50 references that are in the map.
- First posted on arXiv 3 Apr 2024.

## Builds on (most cited first, 30 of 36)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [OPT: Open Pre-trained Transformer Language Models](https://mlsanity.com/paper/2205.01068/) (2022)
- [The Pile: An 800GB Dataset of Diverse Text for Language Modeling](https://mlsanity.com/paper/2101.00027/) (2020)
- [Membership Inference Attacks against Machine Learning Models](https://mlsanity.com/paper/1610.05820/) (2016)
- [Extracting Training Data from Large Language Models](https://mlsanity.com/paper/2012.07805/) (2020)
- [Pythia: A Suite for Analyzing Large Language Models Across Training and Scaling](https://mlsanity.com/paper/2304.01373/) (2023)
- [Enhancing The Reliability of Out-of-distribution Image Detection in Neural Networks](https://mlsanity.com/paper/1706.02690/) (2017)
- [Membership Inference Attacks From First Principles](https://mlsanity.com/paper/2112.03570/) (2021)
- [Quantifying Memorization Across Neural Language Models](https://mlsanity.com/paper/2202.07646/) (2022)
- [Extracting Training Data from Diffusion Models](https://mlsanity.com/paper/2301.13188/) (2023)
- [DetectGPT: Zero-Shot Machine-Generated Text Detection using Probability Curvature](https://mlsanity.com/paper/2301.11305/) (2023)
- [GPT-NeoX-20B: An Open-Source Autoregressive Language Model](https://mlsanity.com/paper/2204.06745/) (2022)
- [Detecting Pretraining Data from Large Language Models](https://mlsanity.com/paper/2310.16789/) (2023)
- [Membership Inference Attacks against Language Models via Neighbourhood Comparison](https://mlsanity.com/paper/2305.18462/) (2023)
- [Proving Test Set Contamination in Black Box Language Models](https://mlsanity.com/paper/2310.17623/) (2023)
- [Demystifying Prompts in Language Models via Perplexity Estimation](https://mlsanity.com/paper/2212.04037/) (2022)
- [Do Membership Inference Attacks Work on Large Language Models?](https://mlsanity.com/paper/2402.07841/) (2024)
- [OpenOOD v1.5: Enhanced Benchmark for Out-of-Distribution Detection](https://mlsanity.com/paper/2306.09301/) (2023)
- [Quantifying Privacy Risks of Masked Language Models Using Membership Inference Attacks](https://mlsanity.com/paper/2203.03929/) (2022)
- [What Language Model Architecture and Pretraining Objective Work Best for Zero-Shot Generalization?](https://mlsanity.com/paper/2204.05832/) (2022)
- [On the Importance of Difficulty Calibration in Membership Inference Attacks](https://mlsanity.com/paper/2111.08440/) (2021)
- [The Privacy Onion Effect: Memorization is Relative](https://mlsanity.com/paper/2206.10469/) (2022)
- [Privacy Auditing with One (1) Training Run](https://mlsanity.com/paper/2305.08846/) (2023)

## Built on by (most cited first, 30 of 103)

- [A Comprehensive Survey in LLM(-Agent) Full Stack Safety: Data, Training and Deployment](https://mlsanity.com/paper/2504.15585/) (2025)
- [H-CoT: Hijacking the Chain-of-Thought Safety Reasoning Mechanism to Jailbreak Large Reasoning Models, Including OpenAI o1/o3, DeepSeek-R1, and Gemini 2.0 Flash Thinking](https://mlsanity.com/paper/2502.12893/) (2025)
- [INCLUDE: Evaluating Multilingual Language Understanding with Regional Knowledge](https://mlsanity.com/paper/2411.19799/) (2024)
- [RWKU: Benchmarking Real-World Knowledge Unlearning for Large Language Models](https://mlsanity.com/paper/2406.10890/) (2024)
- [Blind Baselines Beat Membership Inference Attacks for Foundation Models](https://mlsanity.com/paper/2406.16201/) (2024)
- [ReCaLL: Membership Inference via Relative Conditional Log-Likelihoods](https://mlsanity.com/paper/2406.15968/) (2024)
- [Position: LLM Unlearning Benchmarks are Weak Measures of Progress](https://mlsanity.com/paper/2410.02879/) (2024)
- [Discrete Diffusion in Large Language and Multimodal Models: A Survey](https://mlsanity.com/paper/2506.13759/) (2025)
- [SoK: Membership Inference Attacks on LLMs are Rushing Nowhere (and How to Fix It)](https://mlsanity.com/paper/2406.17975/) (2024)
- [Pretraining Data Detection for Large Language Models: A Divergence-based Calibration Method](https://mlsanity.com/paper/2409.14781/) (2024)
- [Membership Inference Attacks Cannot Prove that a Model Was Trained On Your Data](https://mlsanity.com/paper/2409.19798/) (2024)
- [Is My Data in Your Retrieval Database? Membership Inference Attacks Against Retrieval Augmented Generation](https://mlsanity.com/paper/2405.20446/) (2024)
- [Seq vs Seq: An Open Suite of Paired Encoders and Decoders](https://mlsanity.com/paper/2507.11412/) (2025)
- [Towards Label-Only Membership Inference Attack against Pre-trained Large Language Models](https://mlsanity.com/paper/2502.18943/) (2025)
- [Exposing Privacy Gaps: Membership Inference Attack on Preference Data for LLM Alignment](https://mlsanity.com/paper/2407.06443/) (2024)
- [Context-Aware Membership Inference Attacks against Pre-trained Large Language Models](https://mlsanity.com/paper/2409.13745/) (2024)
- [Con-ReCall: Detecting Pre-training Data in LLMs via Contrastive Decoding](https://mlsanity.com/paper/2409.03363/) (2024)
- [Vid-SME: Membership Inference Attacks against Large Video Understanding Models](https://mlsanity.com/paper/2506.03179/) (2025)
- [Can Watermarking Large Language Models Prevent Copyrighted Text Generation and Hide Training Data?](https://mlsanity.com/paper/2407.17417/) (2024)
- [Semantic Membership Inference Attack against Large Language Models](https://mlsanity.com/paper/2406.10218/) (2024)
- [Beware of Calibration Data for Pruning Large Language Models](https://mlsanity.com/paper/2410.17711/) (2024)
- [How Contaminated Is Your Benchmark? Quantifying Dataset Leakage in Large Language Models with Kernel Divergence](https://mlsanity.com/paper/2502.00678/) (2025)
- [Privacy Attacks on Image AutoRegressive Models](https://mlsanity.com/paper/2502.02514/) (2025)
- [The Emperor's New Clothes in Benchmarking? A Rigorous Examination of Mitigation Strategies for LLM Benchmark Data Contamination](https://mlsanity.com/paper/2503.16402/) (2025)
- [Detecting Training Data of Large Language Models via Expectation Maximization](https://mlsanity.com/paper/2410.07582/) (2024)
- [Beyond Next Token Probabilities: Learnable, Fast Detection of Hallucinations and Data Contamination on LLM Output Distributions](https://mlsanity.com/paper/2503.14043/) (2025)
- [SALAD: Systematic Assessment of Machine Unlearning on LLM-Aided Hardware Design](https://mlsanity.com/paper/2506.02089/) (2025)
- [Jr. AI Scientist and Its Risk Report: Autonomous Scientific Exploration from a Baseline Paper](https://mlsanity.com/paper/2511.04583/) (2025)
- [Unveiling Over-Memorization in Finetuning LLMs for Reasoning Tasks](https://mlsanity.com/paper/2508.04117/) (2025)
- [Constrained Entropic Unlearning: A Primal-Dual Framework for Large Language Models](https://mlsanity.com/paper/2506.05314/) (2025)

## Abstract (arXiv)

The problem of pre-training data detection for large language models (LLMs) has received growing attention due to its implications in critical issues like copyright violation and test data contamination. Despite improved performance, existing methods (including the state-of-the-art, Min-K%) are mostly developed upon simple heuristics and lack solid, reasonable foundations. In this work, we propose a novel and theoretically motivated methodology for pre-training data detection, named Min-K%++. Specifically, we present a key insight that training samples tend to be local maxima of the modeled distribution along each input dimension through maximum likelihood training, which in turn allow us to insightfully translate the problem into identification of local maxima. Then, we design our method accordingly that works under the discrete distribution modeled by LLMs, whose core idea is to determine whether the input forms a mode or has relatively high probability under the conditional categorical distribution. Empirically, the proposed method achieves new SOTA performance across multiple settings. On the WikiMIA benchmark, Min-K%++ outperforms the runner-up by 6.2% to 10.5% in detection AUROC averaged over five models. On the more challenging MIMIR benchmark, it consistently improves upon reference-free methods while performing on par with reference-based method that requires an extra reference model.