Beyond Neural Networks: Symbolic Reasoning over Wavelet Logic Graph Signals

TL;DR

This paper introduces a non-neural, graph spectral domain framework using Wavelet Transforms for graph signals, enabling interpretable reasoning and competitive performance in denoising and token classification tasks.

Contribution

It presents a novel, fully non neural approach based on Graph Laplacian Wavelet Transforms that supports symbolic reasoning and offers transparency and efficiency.

Findings

Competitive performance on synthetic graph denoising

Effective symbolic reasoning with a domain-specific language

Greater transparency and resource efficiency than lightweight GNNs

Abstract

We present a fully non neural learning framework based on Graph Laplacian Wavelet Transforms (GLWT). Unlike traditional architectures that rely on convolutional, recurrent, or attention based neural networks, our model operates purely in the graph spectral domain using structured multiscale filtering, nonlinear shrinkage, and symbolic logic over wavelet coefficients. Signals defined on graph nodes are decomposed via GLWT, modulated with interpretable nonlinearities, and recombined for downstream tasks such as denoising and token classification. The system supports compositional reasoning through a symbolic domain-specific language (DSL) over graph wavelet activations. Experiments on synthetic graph denoising and linguistic token graphs demonstrate competitive performance against lightweight GNNs with far greater transparency and efficiency. This work proposes a principled, interpretable, and resource-efficient alternative to deep neural architectures for learning on graphs.