Quantum Spectral Reasoning: A Non-Neural Architecture for Interpretable Machine Learning
This work offers a transparent and physically grounded alternative to deep learning models for researchers and practitioners needing interpretable, reasoning-capable machine learning, though it is incremental in combining existing spectral and symbolic techniques.
The authors tackled the problem of interpretable machine learning by proposing a non-neural architecture using quantum spectral methods, which achieved competitive accuracy in tasks like time-series anomaly detection and symbolic classification while maintaining interpretability and data efficiency.
We propose a novel machine learning architecture that departs from conventional neural network paradigms by leveraging quantum spectral methods, specifically Pade approximants and the Lanczos algorithm, for interpretable signal analysis and symbolic reasoning. The core innovation of our approach lies in its ability to transform raw time-domain signals into sparse, physically meaningful spectral representations without the use of backpropagation, high-dimensional embeddings, or data-intensive black-box models. Through rational spectral approximation, the system extracts resonant structures that are then mapped into symbolic predicates via a kernel projection function, enabling logical inference through a rule-based reasoning engine. This architecture bridges mathematical physics, sparse approximation theory, and symbolic artificial intelligence, offering a transparent and physically grounded alternative to deep learning models. We develop the full mathematical formalism underlying each stage of the pipeline, provide a modular algorithmic implementation, and demonstrate the system's effectiveness through comparative evaluations on time-series anomaly detection, symbolic classification, and hybrid reasoning tasks. Our results show that this spectral-symbolic architecture achieves competitive accuracy while maintaining interpretability and data efficiency, suggesting a promising new direction for physically-informed, reasoning-capable machine learning.