Optimal Estimation of Watermark Proportions in Hybrid AI-Human Texts
Xiang LiGarrett WenWeiqing HeJiayuan WuQi LongWeijie J. Su
Sep 2026
Machine LearningNatural Language ProcessingData Science
Abstract
Text watermarks in large language models (LLMs) are an increasingly important tool for detecting synthetic text and distinguishing human-written content from LLM-generated text. While most existing studies focus on determining whether entire texts are watermarked, many real-world scenarios involve mixed-source texts, which blend human-written and watermarked content. In this paper, we address the problem of optimally estimating the watermark proportion in mixed-source texts. We cast this problem as estimating the proportion parameter in a mixture model based on \emph{pivotal statistics}. First, we show that this parameter is not even identifiable in certain watermarking schemes, let alone consistently estimable. In stark contrast, for watermarking methods that employ continuous pivotal statistics for detection, we demonstrate that the proportion parameter is identifiable under mild conditions. We propose efficient estimators for this class of methods, which include several popular unbiased watermarks as examples, and derive minimax lower bounds for any measurable estimator based on pivotal statistics, showing that our estimators achieve these lower bounds. Through evaluations on both synthetic data and mixed-source text generated by open-source models, we demonstrate that our proposed estimators consistently achieve high estimation accuracy.
Agile - denoting "the quality of being agile, readiness for motion, nimbleness, activity, dexterity in motion" - software development methods are attempting to offer an answer to the eager business community asking for lighter weight along with faster and nimbler software development processes. This is especially the case with the rapidly growing and volatile Internet software industry as well as for the emerging mobile application environment. The new agile methods have evoked substantial amount of literature and debates. However, academic research on the subject is still scarce, as most of existing publications are written by practitioners or consultants. The aim of this publication is to begin filling this gap by systematically reviewing the existing literature on agile software development methodologies. This publication has three purposes. First, it proposes a definition and a classification of agile software development approaches. Second, it analyses ten software development methods that can be characterized as being "agile" against the defined criterion. Third, it compares these methods and highlights their similarities and differences. Based on this analysis, future research needs are identified and discussed.
P. Abrahamsson, O. Salo, Jussi Ronkainen et al.· arXiv.org· 728 citations· ⚡54
Context: Software startups are newly created companies with no operating history and fast in producing cutting-edge technologies. These companies develop software under highly uncertain conditions, tackling fast-growing markets under severe lack of resources. Therefore, software startups present a unique combination of characteristics which pose several challenges to software development activities. Objective: This study aims to structure and analyze the literature on software development in startup companies, determining thereby the potential for technology transfer and identifying software development work practices reported by practitioners and researchers. Method: We conducted a systematic mapping study, developing a classification schema, ranking the selected primary studies according their rigor and relevance, and analyzing reported software development work practices in startups. Results: A total of 43 primary studies were identified and mapped, synthesizing the available evidence on software development in startups. Only 16 studies are entirely dedicated to software development in startups, of which 10 result in a weak contribution (advice and implications (6); lesson learned (3); tool (1)). Nineteen studies focus on managerial and organizational factors. Moreover, only 9 studies exhibit high scientific rigor and relevance. From the reviewed primary studies, 213 software engineering work practices were extracted, categorized and analyzed. Conclusion: This mapping study provides the first systematic exploration of the state-of-art on software startup research. The existing body of knowledge is limited to a few high quality studies. Furthermore, the results indicate that software engineering work practices are chosen opportunistically, adapted and configured to provide value under the constrains imposed by the startup context.
Nicolò Paternoster, Carmine Giardino, M. Unterkalmsteiner et al.· Information and Software Tec...· 394 citations· ⚡54
A new machine-learning framework aims to improve the success rate of computational protein design while moving away from results that reproduce sequences found in nature.
MIT News · Artificial Intelligence· news.mit.eduAug 24, 2026
