用图信号处理构建可解释的神经符号推理系统
A Fully Spectral Neuro-Symbolic Reasoning Architecture with Graph Signal Processing as the Computational Backbone
- 在图谱域全程处理逻辑实体与关系，通过可学习谱滤波器实现多尺度信息传播
- 在多个基准数据集上提升逻辑一致性与推理效率，优于现有神经符号模型
- 适合需要高可解释性与数学严谨性的复杂推理任务研究者
我们提出一种全谱神经符号推理架构，以图信号处理（GSP）作为核心计算基础，整合符号逻辑与神经推理。不同于传统模型将谱图方法视为辅助组件，本方法将整个推理流程置于图谱域中：逻辑实体与关系编码为图信号，经可学习的谱滤波器处理以控制多尺度信息传播，并映射为可用于规则推理的符号谓词。本文构建了完整的谱推理数学框架，包括图傅里叶变换、带通注意力机制和谱规则对齐。在ProofWriter、EntailmentBank、bAbI、CLUTRR和ARC-Challenge等基准数据集上的实验表明，该方法在逻辑一致性、可解释性和计算效率方面均优于当前最先进神经符号模型。结果表明，GSP为鲁棒且可解释的推理系统提供了数学坚实且高效的计算基础。
原文摘要 · Abstract (English)
We propose a fully spectral, neuro\-symbolic reasoning architecture that leverages Graph Signal Processing (GSP) as the primary computational backbone for integrating symbolic logic and neural inference. Unlike conventional reasoning models that treat spectral graph methods as peripheral components, our approach formulates the entire reasoning pipeline in the graph spectral domain. Logical entities and relationships are encoded as graph signals, processed via learnable spectral filters that control multi-scale information propagation, and mapped into symbolic predicates for rule-based inference. We present a complete mathematical framework for spectral reasoning, including graph Fourier transforms, band-selective attention, and spectral rule grounding. Experiments on benchmark reasoning datasets (ProofWriter, EntailmentBank, bAbI, CLUTRR, and ARC-Challenge) demonstrate improvements in logical consistency, interpretability, and computational efficiency over state\-of\-the\-art neuro\-symbolic models. Our results suggest that GSP provides a mathematically grounded and computationally efficient substrate for robust and interpretable reasoning systems.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。