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Black-Box Membership Inference via Word-Level Probability Estimation

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Updated 2 h ago · first seen 11 Sept 2026

paper_01M294FPPMRF2TMMNFKTAF3Z50

Published: 11 Sept 2026; T1 · 2 h ago
arXiv: 2609.10611; T1 · 2 h ago
Category: cs.CR; T1 · 2 h ago

Abstract

Membership inference attacks (MIAs) have emerged as critical tools for auditing privacy risks in large language models (LLMs), aiming to determine whether a given text was included in a model's training corpus. However, most existing MIAs require access to per-token logits or probabilities, making them inapplicable in practice to proprietary LLMs that expose only textual continuations. To address this underexplored setting, we propose Word-level Probability MIA (WPMIA), a statistically principled MIA for strict black-box privacy auditing. WPMIA estimates word-level generation probabilities via Monte Carlo sampling with local kernel smoothing, then aggregates these estimates into a sequence-level likelihood estimator. Furthermore, WPMIA constructs the likelihood conditioned on different prefixes, thereby amplifying the distributional differences between members and non-members. We evaluate WPMIA across various open-source LLMs and find that it consistently outperforms existing black-box baselines. Importantly, we also evaluate WPMIA on modern proprietary LLMs, including GPT-5-Chat, Gemini-2.5-Flash, and Claude-4.5-Haiku, achieving an average TPR@5\%FPR of 42.0 across these models. These results offer a sound foundation for future research on strict black-box membership inference. Code is available at \href{https://github.com/niusj03/WPMIA}{https://github.com/niusj03/WPMIA}.

Authors 3

Shengjie Niu, Yeheng Ge, Jian Huang

Specification

Official page: arxiv.org/abs/2609.10611
Source:arXiv (Atom API + RSS)T1observed 2 h agohigh
Arxiv announce type: cross
Source:arXiv (Atom API + RSS)T1observed 2 h agohigh
arXiv id: 2609.10611
Source:arXiv (Atom API + RSS)T1observed 2 h agohigh
Categories: cs.CR, cs.LG, stat.ML
Source:arXiv (Atom API + RSS)T1observed 2 h agohigh
PDF: arxiv.org/pdf/2609.10611
Source:arXiv (Atom API + RSS)T1observed 2 h agohigh
Primary category: cs.CR
Source:arXiv (Atom API + RSS)T1observed 2 h agohigh
Published: 11 Sept 2026
Source:arXiv (Atom API + RSS)T1observed 2 h agohigh

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Provenance

Attributed facts

Source tiers

T19

Freshest observation

2 h ago

Conflicts

None

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Claim history

9 claims · 9 properties

Official pageofficial_url1

Claim history for Official page
Value	Valid from → to	Status	Source	Confidence	Extractor
https://arxiv.org/abs/2609.10611	11 Sept 2026 21:02 UTC → current	current	arXiv (Atom API + RSS)T1	high	deterministic

Abstractabstract1

Claim history for Abstract
Value	Valid from → to	Status	Source	Confidence	Extractor
Membership inference attacks (MIAs) have emerged as critical tools for auditing privacy risks in large language models (LLMs), aiming to determine whether a given text was included in a model's training corpus. However, most existing MIAs require access to per-token logits or probabilities, making them inapplicable in practice to proprietary LLMs that expose only textual continuations. To address this underexplored setting, we propose Word-level Probability MIA (WPMIA), a statistically principled MIA for strict black-box privacy auditing. WPMIA estimates word-level generation probabilities via Monte Carlo sampling with local kernel smoothing, then aggregates these estimates into a sequence-level likelihood estimator. Furthermore, WPMIA constructs the likelihood conditioned on different prefixes, thereby amplifying the distributional differences between members and non-members. We evaluate WPMIA across various open-source LLMs and find that it consistently outperforms existing black-box baselines. Importantly, we also evaluate WPMIA on modern proprietary LLMs, including GPT-5-Chat, Gemini-2.5-Flash, and Claude-4.5-Haiku, achieving an average TPR@5\%FPR of 42.0 across these models. These results offer a sound foundation for future research on strict black-box membership inference. Code is available at \href{https://github.com/niusj03/WPMIA}{https://github.com/niusj03/WPMIA}.	11 Sept 2026 21:02 UTC → current	current	arXiv (Atom API + RSS)T1	high	deterministic

Arxiv announce typearxiv_announce_type1

Claim history for Arxiv announce type
Value	Valid from → to	Status	Source	Confidence	Extractor
cross	11 Sept 2026 21:02 UTC → current	current	arXiv (Atom API + RSS)T1	high	deterministic

arXiv idarxiv_id1

Claim history for arXiv id
Value	Valid from → to	Status	Source	Confidence	Extractor
2609.10611	11 Sept 2026 21:02 UTC → current	current	arXiv (Atom API + RSS)T1	high	deterministic

Authorsauthors1

Claim history for Authors
Value	Valid from → to	Status	Source	Confidence	Extractor
Shengjie Niu, Yeheng Ge, Jian Huang	11 Sept 2026 21:02 UTC → current	current	arXiv (Atom API + RSS)T1	high	deterministic

Categoriescategories1

Claim history for Categories
Value	Valid from → to	Status	Source	Confidence	Extractor
cs.CR, cs.LG, stat.ML	11 Sept 2026 21:02 UTC → current	current	arXiv (Atom API + RSS)T1	high	deterministic

PDFpdf_url1

Claim history for PDF
Value	Valid from → to	Status	Source	Confidence	Extractor
https://arxiv.org/pdf/2609.10611	11 Sept 2026 21:02 UTC → current	current	arXiv (Atom API + RSS)T1	high	deterministic

Primary categoryprimary_category1

Claim history for Primary category
Value	Valid from → to	Status	Source	Confidence	Extractor
cs.CR	11 Sept 2026 21:02 UTC → current	current	arXiv (Atom API + RSS)T1	high	deterministic

Publishedpublished_at1

Claim history for Published
Value	Valid from → to	Status	Source	Confidence	Extractor
11 Sept 2026	11 Sept 2026 21:02 UTC → current	current	arXiv (Atom API + RSS)T1	high	deterministic

Claims are temporal and append-only: a new observation closes the previous claim (valid_to) instead of overwriting it. Conflicting claims from different sources are kept side by side and flagged — never averaged. Methodology →

Source documents
Source	Document	Type	Tier	Last observed	Snapshots
arXiv (Atom API + RSS)	rss.arxiv.org/rss/cs.LG	feed	T1· Official	47 min ago	1

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