Beyond Neural Networks: Symbolic Reasoning over Wavelet Logic Graph Signals

Recent advances in spectral learning and graph signal processing have enabled powerful techniques for analyzing data defined on irregular domains such as social networks, transportation systems, biological interaction graphs, and linguistic structures [4, 9]. Central to these developments is the use of the graph Laplacian operator, whose eigensystem defines a Fourier-like basis for signals on graphs. This has laid the foundation for spectral filtering, multiscale decomposition, and efficient data representation on non-Euclidean domains. While spectral graph methods have traditionally been explored in a fixed, analytic setting, recent years have seen a resurgence in their application as components of deep learning architectures--such as graph convolutional networks (GCNs) [10], graph attention networks (GATs) [11], and graph transformers [12]. These models often rely on parametric transformations over graph Laplacian eigenspaces or message-passing mechanisms inspired by spectral filters. However, they remain computationally intensive, opaque, and data-hungry--posing challenges in interpretability, robustness, and deployment on low-resource devices.