# LLM-Assisted Logic Rule Learning: Scaling Human Expertise for Time Series Anomaly Detection

arXiv: https://arxiv.org/abs/2601.19255 · HTML: https://mlsanity.com/paper/2601.19255/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 49 references that are in the map.
- First posted on arXiv 27 Jan 2026.

## Builds on (most cited first, 30 of 30)

- [Large Language Models as Optimizers](https://mlsanity.com/paper/2309.03409/) (2023)
- [Time-LLM: Time Series Forecasting by Reprogramming Large Language Models](https://mlsanity.com/paper/2310.01728/) (2023)
- [Large Language Models Are Zero-Shot Time Series Forecasters](https://mlsanity.com/paper/2310.07820/) (2023)
- [Anomaly Transformer: Time Series Anomaly Detection with Association Discrepancy](https://mlsanity.com/paper/2110.02642/) (2021)
- [Evolution of Heuristics: Towards Efficient Automatic Algorithm Design Using Large Language Model](https://mlsanity.com/paper/2401.02051/) (2024)
- [Deep Learning for Time Series Anomaly Detection: A Survey](https://mlsanity.com/paper/2211.05244/) (2022)
- [DCdetector: Dual Attention Contrastive Representation Learning for Time Series Anomaly Detection](https://mlsanity.com/paper/2306.10347/) (2023)
- [LLM and Simulation as Bilevel Optimizers: A New Paradigm to Advance Physical Scientific Discovery](https://mlsanity.com/paper/2405.09783/) (2024)
- [Representing Numbers in NLP: a Survey and a Vision](https://mlsanity.com/paper/2103.13136/) (2021)
- [A Comprehensive Review of Multimodal Large Language Models: Performance and Challenges Across Different Tasks](https://mlsanity.com/paper/2408.01319/) (2024)
- [Can LLMs Understand Time Series Anomalies?](https://mlsanity.com/paper/2410.05440/) (2024)
- [ImDiffusion: Imputed Diffusion Models for Multivariate Time Series Anomaly Detection](https://mlsanity.com/paper/2307.00754/) (2023)
- [The first step is the hardest: Pitfalls of Representing and Tokenizing Temporal Data for Large Language Models](https://mlsanity.com/paper/2309.06236/) (2023)
- [Large Language Models can Deliver Accurate and Interpretable Time Series Anomaly Detection](https://mlsanity.com/paper/2405.15370/) (2024)
- [Large Language Model Guided Knowledge Distillation for Time Series Anomaly Detection](https://mlsanity.com/paper/2401.15123/) (2024)
- [FunBO: Discovering Acquisition Functions for Bayesian Optimization with FunSearch](https://mlsanity.com/paper/2406.04824/) (2024)
- [Can LLMs Serve As Time Series Anomaly Detectors?](https://mlsanity.com/paper/2408.03475/) (2024)
- [CrossLinear: Plug-and-Play Cross-Correlation Embedding for Time Series Forecasting with Exogenous Variables](https://mlsanity.com/paper/2505.23116/) (2025)
- [Argos: Agentic Time-Series Anomaly Detection with Autonomous Rule Generation via Large Language Models](https://mlsanity.com/paper/2501.14170/) (2025)
- [Unraveling the "Anomaly" in Time Series Anomaly Detection: A Self-supervised Tri-domain Solution](https://mlsanity.com/paper/2311.11235/) (2023)
- [A Comparative Study on Unsupervised Anomaly Detection for Time Series: Experiments and Analysis](https://mlsanity.com/paper/2209.04635/) (2022)
- [Precursor-of-Anomaly Detection for Irregular Time Series](https://mlsanity.com/paper/2306.15489/) (2023)
- [AAD-LLM: Adaptive Anomaly Detection Using Large Language Models](https://mlsanity.com/paper/2411.00914/) (2024)
- [Robust and Explainable Detector of Time Series Anomaly via Augmenting Multiclass Pseudo-Anomalies](https://mlsanity.com/paper/2505.20765/) (2025)
- [mTSBench: Benchmarking Multivariate Time Series Anomaly Detection and Model Selection at Scale](https://mlsanity.com/paper/2506.21550/) (2025)
- [Forecasting in multivariate irregularly sampled time series with missing values](https://mlsanity.com/paper/2004.03398/) (2020)
- [Daily Physical Activity Monitoring -- Adaptive Learning from Multi-source Motion Sensor Data](https://mlsanity.com/paper/2405.16395/) (2024)
- [KDSelector: A Knowledge-Enhanced and Data-Efficient Model Selector Learning Framework for Time Series Anomaly Detection](https://mlsanity.com/paper/2503.12478/) (2025)
- [Moon: A Modality Conversion-based Efficient Multivariate Time Series Anomaly Detection](https://mlsanity.com/paper/2510.01970/) (2025)
- [SOCRATES: Simulation Optimization with Correlated Replicas and Adaptive Trajectory Evaluations](https://mlsanity.com/paper/2511.00685/) (2025)

## Built on by (most cited first, 2 of 2)

- [An Explainable LLM Agent Layer for Open-World Anomaly Detection in Oil Wells](https://mlsanity.com/paper/2608.04041/) (2026)
- [Auto-Formalizing Neuro-Symbolic Predictors](https://mlsanity.com/paper/2610.01519/) (2026)

## Abstract (arXiv)

Time series anomaly detection is critical for supply chain management to take proactive operations, but faces challenges: classical unsupervised anomaly detection based on exploiting data patterns often yields results misaligned with business requirements and domain knowledge, while manual expert analysis cannot scale to millions of products in the supply chain. We propose a framework that leverages large language models (LLMs) to systematically encode human expertise into interpretable, logic-based rules for detecting anomaly patterns in supply chain time series data. Our approach operates in three stages: 1) LLM-based labeling of training data instructed by domain knowledge, 2) automated generation and iterative improvements of symbolic rules through LLM-driven optimization, and 3) rule augmentation with business-relevant anomaly categories supported by LLMs to enhance interpretability. The experiment results showcase that our approach outperforms the unsupervised learning methods in both detection accuracy and interpretability. Furthermore, compared to direct LLM deployment for time series anomaly detection, our approach provides consistent, deterministic results with low computational latency and cost, making it ideal for production deployment. The proposed framework thus demonstrates how LLMs can bridge the gap between scalable automation and expert-driven decision-making in operational settings.