Neuro-Symbolic Signal Processing: A quest for optimal models

Abstract

This dissertation explores how signal processing and artificial intelligence (AI) can be combined to develop models that are not only accurate, but also reliable, interpretable, and computationally efficient. Signal processing underlies many technologies in modern society, ranging from speech recognition and seismic analysis to cardiovascular monitoring. In recent decades, Deep Learning (DL) has transformed the field by enabling major advances in tasks such as medical image analysis and automated diagnosis. However, despite its success, DL also introduced important limitations, including poor interpretability, dependence on large amounts of high-quality data, vulnerability to bias, and reduced robustness in real-world conditions. The dissertation argues that many of these limitations arise from an overreliance on purely data-driven approaches. Through a historical analysis of the field, three major paradigms are identified: symbolic methods, hybrid approaches, and deep learning methods. While DL models are highly powerful, the transition away from symbolic reasoning has often come at the cost of transparency and reliability. To address this imbalance, the dissertation proposes neuro-symbolic signal processing as a promising direction that combines the strengths of both symbolic reasoning and neural networks. The core of the dissertation presents three major contributions. First, the Continuous Wavelet Transform (CWT), a classical symbolic method for frequency analysis, was redesigned for modern hardware, resulting in the fast Continuous Wavelet Transform (fCWT). This implementation achieved a 34–120× speedup without loss of accuracy, enabling real-time and resource-efficient analysis on devices such as wearables and edge systems. By combining interpretability with computational efficiency, fCWT demonstrates that classical signal processing methods remain highly relevant in modern AI applications. Second, the dissertation investigates how the reliability and generalizability of DL models can be improved. Using ambulatory single-lead ECG segmentation as a challenging case study, the NALA model was developed using Active Learning. Instead of relying on massive datasets, NALA iteratively selected the most informative and uncertain examples for annotation, creating a smaller but highly diverse training set. This strategy improved segmentation accuracy from 64% to 94%, demonstrating that data quality and diversity are more important than dataset size alone. Finally, the dissertation introduces ALADIN, a neuro-symbolic AI system for arrhythmia diagnosis. ALADIN combines DL-based ECG analysis with symbolic rules and heuristics, enabling both flexibility and interpretability. The system was externally validated on 13,780 patients across multiple devices and patient populations and significantly outperformed several state-of-the-art DL models, including models trained on substantially larger datasets. ALADIN achieved diagnostic performance comparable to human cardiologists and exceeded the performance of most individual experts. Overall, the dissertation demonstrates that accurate, robust, interpretable, and sustainable signal processing systems can be achieved by integrating symbolic reasoning with deep learning, highlighting neuro-symbolic AI as a promising future direction for the field.