Quantum Spectral Reasoning: A Non-Neural Architecture for Interpretable Machine Learning

TL;DR

This paper introduces a quantum spectral machine learning architecture that uses spectral methods and symbolic reasoning, providing an interpretable, physics-inspired alternative to neural networks for analyzing signals.

Contribution

It presents a novel non-neural, spectral-based architecture that transforms signals into symbolic representations for interpretable reasoning, bridging physics, spectral approximation, and AI.

Findings

Achieves competitive accuracy on time-series tasks

Maintains interpretability and data efficiency

Provides a modular, mathematically formalized system

Abstract

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.