# GSLAD: Prototype-Regularized Graph Structure Learning for Multivariate Time Series Anomaly Detection

arXiv: https://arxiv.org/abs/2609.15483 · HTML: https://mlsanity.com/paper/2609.15483/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 32 references that are in the map.
- First posted on arXiv 14 Sep 2026.

## Builds on (most cited first, 13 of 13)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Anomaly Transformer: Time Series Anomaly Detection with Association Discrepancy](https://mlsanity.com/paper/2110.02642/) (2021)
- [Graph Structure Learning for Robust Graph Neural Networks](https://mlsanity.com/paper/2005.10203/) (2020)
- [Graph Neural Network-Based Anomaly Detection in Multivariate Time Series](https://mlsanity.com/paper/2106.06947/) (2021)
- [A Deep Neural Network for Unsupervised Anomaly Detection and Diagnosis in Multivariate Time Series Data](https://mlsanity.com/paper/1811.08055/) (2018)
- [Multivariate Time-series Anomaly Detection via Graph Attention Network](https://mlsanity.com/paper/2009.02040/) (2020)
- [1D Convolutional Neural Networks and Applications: A Survey](https://mlsanity.com/paper/1905.03554/) (2019)
- [Towards Unsupervised Deep Graph Structure Learning](https://mlsanity.com/paper/2201.06367/) (2022)
- [CATCH: Channel-Aware multivariate Time Series Anomaly Detection via Frequency Patching](https://mlsanity.com/paper/2410.12261/) (2024)
- [A Survey on Graph Structure Learning: Progress and Opportunities](https://mlsanity.com/paper/2103.03036/) (2021)
- [GSLB: The Graph Structure Learning Benchmark](https://mlsanity.com/paper/2310.05174/) (2023)
- [GCAD: Anomaly Detection in Multivariate Time Series from the Perspective of Granger Causality](https://mlsanity.com/paper/2501.13493/) (2025)
- [DyEdgeGAT: Dynamic Edge via Graph Attention for Early Fault Detection in IIoT Systems](https://mlsanity.com/paper/2307.03761/) (2023)

## Built on by (most cited first, 1 of 1)

- [Graph-Spectral Flow Matching for Multivariate Time Series Anomaly Detection](https://mlsanity.com/paper/2609.36765/) (2026)

## Abstract (arXiv)

Unsupervised multivariate time series anomaly detection methods typically identify anomalies through forecasting, reconstruction, or representation discrepancies. However, industrial faults may first alter inter-variable structural patterns while individual trajectories remain close to normal, resulting in weak anomaly signals. In this paper, we propose GSLAD, a prototype-regularized graph structure learning framework that uses structural deviations for anomaly scoring. GSLAD adopts a two-phase training strategy. First, a condition-aware graph learner and a graph-based forecaster are optimized with predictive supervision. The inferred normal graphs are then clustered into multiple structural prototypes representing different normal operating regimes, with edge-wise variability characterizing structural uncertainty. Deviations from these prototypes regularize the graph learner in the second phase, encouraging stable and regime-specific structural patterns. During inference, uncertainty-normalized structural deviation is combined with predictive deviation for anomaly scoring. Experiments on four industrial benchmarks demonstrate strong overall performance of GSLAD and confirm the effectiveness of structural deviation for anomaly detection and diagnosis.