# PDR: A Plug-and-Play Positional Decay Framework for LLM Pre-training Data Detection

arXiv: https://arxiv.org/abs/2601.06827 · HTML: https://mlsanity.com/paper/2601.06827/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 25 references that are in the map.
- First posted on arXiv 11 Jan 2026.

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

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [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)
- [Membership Inference Attacks From First Principles](https://mlsanity.com/paper/2112.03570/) (2021)
- [GPT-NeoX-20B: An Open-Source Autoregressive Language Model](https://mlsanity.com/paper/2204.06745/) (2022)
- [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)
- [Quantifying Privacy Risks of Masked Language Models Using Membership Inference Attacks](https://mlsanity.com/paper/2203.03929/) (2022)
- [On the Importance of Difficulty Calibration in Membership Inference Attacks](https://mlsanity.com/paper/2111.08440/) (2021)
- [Use of LLMs for Illicit Purposes: Threats, Prevention Measures, and Vulnerabilities](https://mlsanity.com/paper/2308.12833/) (2023)
- [DE-COP: Detecting Copyrighted Content in Language Models Training Data](https://mlsanity.com/paper/2402.09910/) (2024)
- [Scalable Membership Inference Attacks via Quantile Regression](https://mlsanity.com/paper/2307.03694/) (2023)
- [ReCaLL: Membership Inference via Relative Conditional Log-Likelihoods](https://mlsanity.com/paper/2406.15968/) (2024)
- [Towards More Realistic Membership Inference Attacks on Large Diffusion Models](https://mlsanity.com/paper/2306.12983/) (2023)
- [Membership Inference Attacks on Large-Scale Models: A Survey](https://mlsanity.com/paper/2503.19338/) (2025)
- [MIA-Tuner: Adapting Large Language Models as Pre-training Text Detector](https://mlsanity.com/paper/2408.08661/) (2024)
- [Range Membership Inference Attacks](https://mlsanity.com/paper/2408.05131/) (2024)

## Abstract (arXiv)

Detecting pre-training data in Large Language Models (LLMs) is crucial for auditing data privacy and copyright compliance, yet it remains challenging in black-box, zero-shot settings where computational resources and training data are scarce. While existing likelihood-based methods have shown promise, they typically aggregate token-level scores using uniform weights, thereby neglecting the inherent information-theoretic dynamics of autoregressive generation. In this paper, we hypothesize and empirically validate that memorization signals are heavily skewed towards the high-entropy initial tokens, where model uncertainty is highest, and decay as context accumulates. To leverage this linguistic property, we introduce Positional Decay Reweighting (PDR), a training-free and plug-and-play framework. PDR explicitly reweights token-level scores to amplify distinct signals from early positions while suppressing noise from later ones. Extensive experiments show that PDR acts as a robust prior and can usually enhance a wide range of advanced methods across multiple benchmarks.