Signal2Symbol: Neuro-Symbolic Temporal Reasoning for Explainable Physiological Time-Series Anomaly Detection

Naser Mansour; Sidahmed Benabderrahmane; Ameer Rahwan

cs.LGSep 20, 2026

Signal2Symbol: Neuro-Symbolic Temporal Reasoning for Explainable Physiological Time-Series Anomaly Detection

Authors: Naser Mansour, Sidahmed Benabderrahmane, Ameer Rahwan

Organizations: New York University, NYUAD, Computer Science Department, Division of Science. · Koc University, Faculty of Medicine, Turkey.

Abstract

Physiological time series such as electrocardiograms (ECG) and electroencephalograms (EEG) exhibit complex temporal structure, substantial acquisition variability, and a strong need for transparent decision-making. Although deep models can achieve high detection performance, they often provide limited insight into why a segment is anomalous, how local anomalies relate over time, and whether a detection belongs to a broader recurring pattern. We propose Signal2Symbol, a neuro-symbolic framework for explainable biosignal anomaly detection. The method first converts ECG/EEG signals into symbolic sequences using either a learned VQ-VAE (Vector Quantized Variational Autoencoder) codebook or a SAX (Symbolic Aggregate approXimation) baseline. It then constructs bigram enriched token-window transactions and scores anomalies through rare itemset evidence derived from minimal rare itemset mining. Detected anomalous windows are merged into intervals and related using Allen interval algebra, enabling composite temporal explanations such as escalation chains, artifact overlap, and cross-channel synchrony. Finally, we introduce a rare temporal concept lattice based on Formal Concept Analysis (FCA), which groups anomalous intervals by shared rare symbolic evidence, Allen temporal relations, channel context, and robustness attributes. The resulting Galois lattice compresses many local detections into interpretable families of temporal-symbolic anomalies. We evaluate on three public benchmarks: MIT-BIH Arrhythmia (beat-level ECG), PTB-XL (record-level ECG), and the Bonn EEG dataset (segment-level EEG). We stress-test robustness under additive noise and baseline-wander perturbations. The results highlight the value of neuro-symbolic tokenization for temporal anomaly analysis and show that Allen/FCA reasoning provides compact, interpretable summaries of local detections.

Figures & tables

Fig. 1 : Signal2Symbol pipeline. Raw ECG/EEG signals are tokenized using SAX or VQ-VAE, transformed into bigram-enriched symbolic transactions, scored by rare-pattern evidence, merged into intervals, related through Allen algebra, and organized into FCA/Galois lattices for visual explanation.

Fig. 2 : VQ-VAE tokenization. Each ECG beat or EEG window is encoded, assigned to the nearest codebook prototype, reconstructed through a decoder, and represented as a symbolic token aligned with timestamps.

Interval	$R_{1}$	$R_{2}$	long-duration	escalation	overlap-artifact
$A_{1}$	$\times$		$\times$
$A_{2}$	$\times$		$\times$		$\times$
$A_{3}$		$\times$		$\times$
$A_{4}$		$\times$		$\times$	$\times$
$A_{5}$	$\times$	$\times$	$\times$	$\times$

TABLE I : Toy Formal Context mapping anomaly intervals to attributes.

Fig. 3 : Concept lattice of the toy formal context in Table I .

Dataset	Method	AUROC $\uparrow$	AUPRC $\uparrow$
MIT-BIH	IF (200 trees)	0.790	0.405
	LOF ( $k\!=\!20$ )	0.737	0.423
	USAD	0.750	0.341
	SAX+Rare	0.605	0.198
	Signal2Symbol (VQ-VAE+Rare)	0.818	0.547
PTB-XL	IF (200 trees)	0.546	0.615

TABLE II : Detection results across ECG and EEG datasets. MIT-BIH is evaluated at beat-level, PTB-XL at record-level (lead II only), and Bonn at segment-level.

Setting	AUROC $\uparrow$	AUPRC $\uparrow$	Notes
Tokenizer
SAX ( $\|\Sigma\|\!=\!5,P\!=\!16$ )	0.579	0.911	fixed discretization
SAX ( $\|\Sigma\|\!=\!6,P\!=\!16$ )	0.536	0.898	larger alphabet
SAX ( $\|\Sigma\|\!=\!6,P\!=\!20$ )	0.512	0.891	more segments
VQ-VAE ( $K\!=\!128$ )	0.710	0.959	learned codebook
VQ-VAE ( $K\!=\!256$ )	0.710	0.959	saturates at $K\!=\!128$

TABLE III : Ablation study: effect of tokenizer, alphabet size, and PAA resolution on Bonn EEG.

Fig. 4 : Sensitivity of AUROC and AUPRC to the support threshold

\tau

on the Bonn EEG dataset. The VQ-VAE model exhibits remarkable stability across lower thresholds.

Dataset	Intervals	Concepts	Compression $\uparrow$	Intent $\downarrow$
Bonn EEG	2061	40	51.5 $\times$	3.2
MIT-BIH	2154	32	67.3 $\times$	4.1
PTB-XL	585	144	4.1 $\times$	4.0

TABLE IV : Explanation quality across datasets. Compression is the ratio of detected anomaly intervals to retained iceberg-lattice concepts; Intent is the mean number of attributes per retained concept.

Method	Clean AUROC	Noise $\Delta$	Wander $\Delta$
SAX+Rare ( $\|\Sigma\|\!=\!5$ )	0.579	$-$ 0.002	$-$ 0.024
VQ-VAE+Rare ( $K\!=\!128$ )	0.710	0.000	0.000

TABLE V : Robustness (

\Delta

AUROC vs. clean) on Bonn EEG. Noise column reports worst-case

\Delta

across SNR

\in\{5,10,20\}

dB; Wander column across amplitudes

\in\{0.1,0.3,0.5\}

Fig. 5 : Rare Temporal Concept Lattice generated from 30 anomaly intervals on Bonn EEG (Set E, Seizure). The FCA lattice compresses individual detections into a hierarchy of concepts based on shared temporal attributes (e.g., long-duration ) and rare symbolic patterns (

R_{i}

). Deeper nodes represent more specific anomaly signatures.

Time-Series Anomaly Detection

Time-Series Anomaly Detection identifies unusual patterns or events in sequential data, from sensor readings and network traffic to health and industrial telemetry.

See all 203 papers

Detecting Time Series Anomalies Like an Expert: A Multi-Agent LLM Framework with Specialized Analyzers
May 7, 2026Hyeongwon Kang, Jeongseob Kim, Jinwoo Park +1LLM-Based Time Series Anomaly Detection Interpretable Anomaly Detection
Department of Industrial and Management Engineering Korea University · Mirae Asset Securities · Department of Industrial Engineering Seoul National University
Unsupervised Symbolic Anomaly Detection
Mar 18, 2026Md Maruf Hossain, Tim Katzke, Simon Klüttermann +1Unsupervised Anomaly Detection Anomaly Detection
TU Dortmund University, Dortmund, Germany · Research Center Trustworthy Data Science and Security, UA Ruhr, Germany
Conditional Attribution for Root Cause Analysis in Time-Series Anomaly Detection
Apr 19, 2026Shashank Mishra, Karan Patil, Cedric Schockaert +2Feature Attribution Interpretable Anomaly Detection
German Research Center for Artificial Intelligence (DFKI), Kaiserslautern, Germany · Rheinland-Pfälzische Technische Universität Kaiserslautern-Landau, Germany · Paul Wurth S.A, Luxembourg

May 7, 2026J/K move · Enter open · S save

Detecting Time Series Anomalies Like an Expert: A Multi-Agent LLM Framework with Specialized Analyzers

Hyeongwon Kang, Jeongseob Kim, Jinwoo Park, Pilsung Kang

Department of Industrial and Management Engineering Korea University · Mirae Asset Securities · Department of Industrial Engineering Seoul National University

LLM-Based Time Series Anomaly Detection Interpretable Anomaly Detection Multi-Agent Systems Time-Series Anomaly Detection

Open paper AskPDF arXiv

Recent studies have explored large language models for time-series anomaly detection, yet existing approaches often rely on a single general-purpose model to directly infer anomaly indices or intervals, limiting controllability, interpretability, and reliability for complex anomaly patterns. We propose SAGE (Specialized Analyzer Group for Expert-like Detection), a multi-agent framework for structured anomaly diagnosis in univariate time series. It decomposes anomaly analysis into four specialized Analyzers for point, structural, seasonal, and pattern anomalies. Each Analyzer applies family-specific numerical tools and diagnostic visualizations to generate evidence, while an evidence-grounded Detector consolidates the evidence into confidence-scored anomaly records with intervals and candidate types. A Supervisor then converts these structured records into analyst-facing diagnostic reports. SAGE further constructs synthetic in-context examples from normal-reference training segments, without using real anomalous segments or anomaly-type labels as in-context examples. Across three benchmarks, SAGE achieves the best average performance among strong ML/DL and language-model-based baselines. Ablation studies and human evaluation further show that the proposed framework improves detection reliability and the practical usefulness of diagnostic outputs.

Abstract

Time-Series Anomaly Detection

Explore similar work

Detecting Time Series Anomalies Like an Expert: A Multi-Agent LLM Framework with Specialized Analyzers

Unsupervised Symbolic Anomaly Detection

Conditional Attribution for Root Cause Analysis in Time-Series Anomaly Detection