用小波图信号做符号推理，不靠神经网络也能高效学图数据。
Beyond Neural Networks: Symbolic Reasoning over Wavelet Logic Graph Signals
- 在图谱域用多尺度滤波和非线性压缩处理信号
- 合成数据和语言词图上性能媲美轻量GNN
- 支持可解释的符号逻辑推理，适合需要透明性的场景
我们提出一种完全非神经网络的学习框架，基于图拉普拉斯小波变换（GLWT）。不同于依赖卷积、循环或注意力机制的神经网络架构，本模型在图谱域内通过结构化多尺度滤波、非线性收缩及对小波系数的符号逻辑操作进行计算。定义在图节点上的信号经由GLWT分解，经可解释的非线性调制后重构，用于去噪和标记分类等下游任务。系统通过图小波激活上的领域专用符号语言（DSL）支持组合推理。在合成图去噪与语言词图任务上的实验表明，该方法性能可比轻量级GNN，且透明度与效率显著更高。本工作为图学习提供了原则性强、可解释且资源高效的非深度神经网络替代方案。
原文摘要 · Abstract (English)
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.
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