Beyond Neural Networks: Symbolic Reasoning over Wavelet Logic Graph Signals
This work offers an interpretable and efficient alternative to deep neural networks for graph learning, potentially benefiting domains requiring transparency, though it appears incremental as it builds on existing spectral graph methods.
The paper tackled the problem of learning on graphs by proposing a fully non-neural framework based on Graph Laplacian Wavelet Transforms, which achieved competitive performance against lightweight GNNs in tasks like denoising and token classification, with greater transparency and efficiency.
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.