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ECATS: Explainable-by-design concept-based anomaly detection for time series

Irene Ferfoglia, Gaia Saveri, Laura Nenzi, Luca Bortolussi

TL;DR

The paper addresses the need for explainable anomaly detection in time-series CPS data. It introduces ECATS, a neuro-symbolic, concept-based approach that represents concepts as $STL$ formulae and learns their embeddings via cross-attention to detect anomalies. The method yields both high classification performance and interpretable explanations expressed as STL concepts, providing local and global insights and demonstrating robustness on CPS benchmarks. This work advances trustworthy CPS monitoring by delivering human-readable, STL-based explanations while maintaining strong detection accuracy, with potential for extension to multivariate data and semi-supervised settings.

Abstract

Deep learning methods for time series have already reached excellent performances in both prediction and classification tasks, including anomaly detection. However, the complexity inherent in Cyber Physical Systems (CPS) creates a challenge when it comes to explainability methods. To overcome this inherent lack of interpretability, we propose ECATS, a concept-based neuro-symbolic architecture where concepts are represented as Signal Temporal Logic (STL) formulae. Leveraging kernel-based methods for STL, concept embeddings are learnt in an unsupervised manner through a cross-attention mechanism. The network makes class predictions through these concept embeddings, allowing for a meaningful explanation to be naturally extracted for each input. Our preliminary experiments with a simple CPS-based dataset show that our model is able to achieve great classification performance while ensuring local interpretability.

ECATS: Explainable-by-design concept-based anomaly detection for time series

TL;DR

The paper addresses the need for explainable anomaly detection in time-series CPS data. It introduces ECATS, a neuro-symbolic, concept-based approach that represents concepts as formulae and learns their embeddings via cross-attention to detect anomalies. The method yields both high classification performance and interpretable explanations expressed as STL concepts, providing local and global insights and demonstrating robustness on CPS benchmarks. This work advances trustworthy CPS monitoring by delivering human-readable, STL-based explanations while maintaining strong detection accuracy, with potential for extension to multivariate data and semi-supervised settings.

Abstract

Deep learning methods for time series have already reached excellent performances in both prediction and classification tasks, including anomaly detection. However, the complexity inherent in Cyber Physical Systems (CPS) creates a challenge when it comes to explainability methods. To overcome this inherent lack of interpretability, we propose ECATS, a concept-based neuro-symbolic architecture where concepts are represented as Signal Temporal Logic (STL) formulae. Leveraging kernel-based methods for STL, concept embeddings are learnt in an unsupervised manner through a cross-attention mechanism. The network makes class predictions through these concept embeddings, allowing for a meaningful explanation to be naturally extracted for each input. Our preliminary experiments with a simple CPS-based dataset show that our model is able to achieve great classification performance while ensuring local interpretability.
Paper Structure (24 sections, 11 equations, 14 figures, 2 algorithms)

This paper contains 24 sections, 11 equations, 14 figures, 2 algorithms.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Concept-based models
  4. Signal Temporal Logic
  5. A kernel for STL formulae
  6. ECATS architecture
  7. Cross-attention
  8. Concept-based explanation
  9. Local explanations
  10. Global explanations
  11. A post-processing step
  12. Experiments
  13. Setup
  14. Evaluation
  15. Conclusions
  16. ...and 9 more sections

Figures (14)

  • Figure 1: Architecture of ECATS. $V, K, Q$ are respectively the values, keys and query matrices typical of an attention mechanism.
  • Figure 2: Train cruise control trajectories. Blue trajectories are regular, red trajectories are anomalous.
  • Figure 3: The regular trajectory in the train cruise control dataset considered as example.
  • Figure 4: Robustness values for the explanation of the regular trajectory reported as example.
  • Figure 5: The anomalous trajectory in the train cruise control dataset considered as example.
  • ...and 9 more figures

Theorems & Definitions (1)

  • definition thmcounterdefinition