# A Theoretical Analysis of Detecting Large Model-Generated Time Series

arXiv: https://arxiv.org/abs/2511.07104 · HTML: https://mlsanity.com/paper/2511.07104/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 38 references that are in the map.
- First posted on arXiv 10 Nov 2025.

## Builds on (most cited first, 18 of 18)

- [Membership Inference Attacks From First Principles](https://mlsanity.com/paper/2112.03570/) (2021)
- [DetectGPT: Zero-Shot Machine-Generated Text Detection using Probability Curvature](https://mlsanity.com/paper/2301.11305/) (2023)
- [One Fits All:Power General Time Series Analysis by Pretrained LM](https://mlsanity.com/paper/2302.11939/) (2023)
- [Release Strategies and the Social Impacts of Language Models](https://mlsanity.com/paper/1908.09203/) (2019)
- [Large Language Models Are Zero-Shot Time Series Forecasters](https://mlsanity.com/paper/2310.07820/) (2023)
- [GLTR: Statistical Detection and Visualization of Generated Text](https://mlsanity.com/paper/1906.04043/) (2019)
- [MOMENT: A Family of Open Time-series Foundation Models](https://mlsanity.com/paper/2402.03885/) (2024)
- [Paraphrasing evades detectors of AI-generated text, but retrieval is an effective defense](https://mlsanity.com/paper/2303.13408/) (2023)
- [Time-MoE: Billion-Scale Time Series Foundation Models with Mixture of Experts](https://mlsanity.com/paper/2409.16040/) (2024)
- [Spotting LLMs With Binoculars: Zero-Shot Detection of Machine-Generated Text](https://mlsanity.com/paper/2401.12070/) (2024)
- [DetectLLM: Leveraging Log Rank Information for Zero-Shot Detection of Machine-Generated Text](https://mlsanity.com/paper/2306.05540/) (2023)
- [Automatic Detection of Machine Generated Text: A Critical Survey](https://mlsanity.com/paper/2011.01314/) (2020)
- [On the Turing Completeness of Modern Neural Network Architectures](https://mlsanity.com/paper/1901.03429/) (2019)
- [DNA-GPT: Divergent N-Gram Analysis for Training-Free Detection of GPT-Generated Text](https://mlsanity.com/paper/2305.17359/) (2023)
- [Intrinsic Dimension Estimation for Robust Detection of AI-Generated Texts](https://mlsanity.com/paper/2306.04723/) (2023)
- [Towards Neural Scaling Laws for Time Series Foundation Models](https://mlsanity.com/paper/2410.12360/) (2024)
- [Detecting Subtle Differences between Human and Model Languages Using Spectrum of Relative Likelihood](https://mlsanity.com/paper/2406.19874/) (2024)
- [Towards Understanding the Universality of Transformers for Next-Token Prediction](https://mlsanity.com/paper/2410.03011/) (2024)

## Built on by (most cited first, 3 of 3)

- [When AI Settles Down: Late-Stage Stability as a Signature of AI-Generated Text Detection](https://mlsanity.com/paper/2601.04833/) (2026)
- [Minimizing Mismatch Risk: A Prototype-Based Routing Framework for Zero-shot LLM-generated Text Detection](https://mlsanity.com/paper/2602.01240/) (2026)
- [Detecting Diffusion-Generated Time Series Under Generator Shift](https://mlsanity.com/paper/2605.28355/) (2026)

## Abstract (arXiv)

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.