A Fully Spectral Neuro-Symbolic Reasoning Architecture with Graph Signal Processing as the Computational Backbone

TL;DR

This paper introduces a novel fully spectral neuro-symbolic reasoning architecture that uses Graph Signal Processing as its core computational framework, enhancing logical consistency, interpretability, and efficiency.

Contribution

It formulates the entire reasoning process in the spectral domain using GSP, integrating symbolic logic and neural inference in a unified mathematical framework.

Findings

Improves logical consistency and interpretability over existing models.

Demonstrates computational efficiency on benchmark datasets.

Provides a mathematically grounded spectral reasoning framework.

Abstract

We propose a fully spectral, neuro\-symbolic reasoning architecture that leverages Graph Signal Processing (GSP) as the primary computational backbone for integrating symbolic logic and neural inference. Unlike conventional reasoning models that treat spectral graph methods as peripheral components, our approach formulates the entire reasoning pipeline in the graph spectral domain. Logical entities and relationships are encoded as graph signals, processed via learnable spectral filters that control multi-scale information propagation, and mapped into symbolic predicates for rule-based inference. We present a complete mathematical framework for spectral reasoning, including graph Fourier transforms, band-selective attention, and spectral rule grounding. Experiments on benchmark reasoning datasets (ProofWriter, EntailmentBank, bAbI, CLUTRR, and ARC-Challenge) demonstrate improvements in logical consistency, interpretability, and computational efficiency over state\-of\-the\-art neuro\-symbolic models. Our results suggest that GSP provides a mathematically grounded and computationally efficient substrate for robust and interpretable reasoning systems.