A Theoretical Analysis of Detecting Large Model-Generated Time Series

2025-11-10

AI Summary

Time-series large models (TSLMs) pose risks of synthetic data misuse, yet reliable detection methods remain scarce. Method: We propose the “uncertainty contraction” hypothesis—that TSLMs exhibit systematic decay in predictive uncertainty over recursive forecasting steps, unlike genuine time series. Leveraging this theoretical insight, we design UCE (Uncertainty Contraction Estimator), a white-box detector that aggregates uncertainty metrics across multi-step prefix predictions to identify synthetic sequences. Contribution/Results: We provide theoretical justification for the fundamental distributional divergence underlying this phenomenon. Extensive evaluation across 32 diverse, cross-domain datasets demonstrates that UCE significantly outperforms existing state-of-the-art detectors, exhibiting strong generalization and robustness. UCE establishes a novel, interpretable, and verifiable paradigm for time-series provenance verification.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Sequential Decision Making
• Multiagent Systems: Multiagent Systems under Uncertainty

Application Category

• Web Mining and Content Analysis: Web data provenance, reliability, and authenticity
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

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.

Problem

• Detecting synthetic time series generated by large AI models
• Addressing modality differences between text and time series data
• Identifying uncertainty contraction patterns in model-generated sequences

Innovation

• Detects synthetic time series via uncertainty contraction
• Proposes white-box Uncertainty Contraction Estimator detector
• Analyzes distribution differences in recursive forecasting