Motivated by the increasing risks of data misuse and fabrication, we investigate the problem of identifying synthetic time series generated by Time-Series Large Models (TSLMs) in this work. While there are extensive researches on detecting model generated text, we find that these existing methods are not applicable to time series data due to the fundamental modality difference, as time series usually have lower information density and smoother probability distributions than text data, which limit the discriminative power of token-based detectors. To address this issue, we examine the subtle distributional differences between real and model-generated time series and propose the contraction hypothesis, which states that model-generated time series, unlike real ones, exhibit progressively decreasing uncertainty under recursive forecasting. We formally prove this hypothesis under theoretical assumptions on model behavior and time series structure. Model-generated time series exhibit progressively concentrated distributions under recursive forecasting, leading to uncertainty contraction. We provide empirical validation of the hypothesis across diverse datasets. Building on this insight, we introduce the Uncertainty Contraction Estimator (UCE), a white-box detector that aggregates uncertainty metrics over successive prefixes to identify TSLM‑generated time series. Extensive experiments on 32 datasets show that UCE consistently outperforms state-of-the-art baselines, offering a reliable and generalizable solution for detecting model-generated time series.

Large Language Models (LLMs) have been widely adopted to enhance Task-Oriented Dialogue Systems (TODS) by modeling complex language patterns and delivering contextually appropriate responses. However, this integration introduces significant privacy risks, as LLMs, functioning as soft knowledge bases that compress extensive training data into rich knowledge representations, can inadvertently memorize training dialogue data containing not only identifiable information such as phone numbers but also entire dialogue-level events like complete travel schedules. Despite the critical nature of this privacy concern, how LLM memorization is inherited in developing task bots remains unexplored. In this work, we address this gap through a systematic quantitative study that involves evaluating existing training data extraction attacks, analyzing key characteristics of task-oriented dialogue modeling that render existing methods ineffective, and proposing novel attack techniques tailored for LLM-based TODS that enhance both response sampling and membership inference. Experimental results demonstrate the effectiveness of our proposed data extraction attack. Our method can extract thousands of training labels of dialogue states with best-case precision exceeding 70%. Furthermore, we provide an in-depth analysis of training data memorization in LLM-based TODS by identifying and quantifying key influencing factors and discussing targeted mitigation strategies.