This report extends the Spectral Neuro-Symbolic Reasoning (Spectral NSR) framework by introducing three semantically grounded enhancements: (1) transformer-based node merging using contextual embeddings (e.g., Sentence-BERT, SimCSE) to reduce redundancy, (2) sentence-level entailment validation with pretrained NLI classifiers (e.g., RoBERTa, DeBERTa) to improve edge quality, and (3) alignment with external knowledge graphs (e.g., ConceptNet, Wikidata) to augment missing context. These modifications enhance graph fidelity while preserving the core spectral reasoning pipeline. Experimental results on ProofWriter, EntailmentBank, and CLUTRR benchmarks show consistent accuracy gains (up to +3.8\%), improved generalization to adversarial cases, and reduced inference noise. The novelty lies in performing semantic and symbolic refinement entirely upstream of the spectral inference stage, enabling efficient, interpretable, and scalable reasoning without relying on quadratic attention mechanisms. In summary, this work extends the Spectral NSR framework with modular, semantically grounded preprocessing steps that improve graph quality without altering the core spectral reasoning engine. The result is a more robust, interpretable, and scalable reasoning system suitable for deployment in open-domain and real-world settings.

翻译：本报告通过引入三种基于语义的增强方法，扩展了谱神经符号推理（Spectral NSR）框架：（1）利用上下文嵌入（如Sentence-BERT、SimCSE）的基于Transformer的节点合并，以减少冗余；（2）使用预训练自然语言推理分类器（如RoBERTa、DeBERTa）进行句子级蕴含验证，以提升边质量；（3）与外部知识图谱（如ConceptNet、Wikidata）对齐，以补充缺失的上下文。这些改进在保持核心谱推理流程的同时，增强了图的保真度。在ProofWriter、EntailmentBank和CLUTRR基准测试上的实验结果表明，该方法实现了稳定的准确率提升（最高达+3.8%），增强了对对抗性案例的泛化能力，并降低了推理噪声。其创新性在于将语义与符号精炼完全置于谱推理阶段的上游，从而实现了高效、可解释且可扩展的推理，而无需依赖二次注意力机制。总之，本研究通过模块化、基于语义的预处理步骤扩展了Spectral NSR框架，在不改变核心谱推理引擎的情况下提升了图的质量。最终构建了一个更鲁棒、可解释且可扩展的推理系统，适用于开放域和实际场景的部署。