Beyond Neural Networks: Symbolic Reasoning over Wavelet Logic Graph Signals
On the map: LLM reasoning → Knowledge- and tool-augmented reasoning
Abstract (arXiv)
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.
Key facts. No citing papers in the map yet (data through 14 Oct 2026). Placed in Knowledge- and tool-augmented reasoning, one of 17 directions in LLM reasoning. Builds on 4 of its 11 references that are in the map. First posted on arXiv 27 Jul 2025.
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4 of 11 references.
References · 4
- 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,361
- 2017Graph Attention Networkscited by 8,923
- 2020A Generalization of Transformer Networks to Graphscited by 661
- 2017Graph Signal Processing: Overview, Challenges and Applicationscited by 413
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- 2025From Eigenmodes to Proofs: Integrating Graph Spectral Operators with Symbolic Interpretable Reasoning
- 2025A Fully Spectral Neuro-Symbolic Reasoning Architecture with Graph Signal Processing as the Computational Backbone
- 2026Teaching LLMs to See Graphs: Unifying Text and Structural Reasoning
- 2025Spectral Neuro-Symbolic Reasoning II: Semantic Node Merging, Entailment Filtering, and Knowledge Graph Alignment
- 2026Beyond One-Size-Fits-All: Adaptive Subgraph Denoising for Zero-Shot Graph Learning with Large Language Models
- 2025A Graph Talks, But Who's Listening? Rethinking Evaluations for Graph-Language Models
- 2023Frameless Graph Knowledge Distillation
- 2022Graph-based Neural Modules to Inspect Attention-based Architectures: A Position Paper