用双曲几何提升模糊推理系统可解释性与精度
HyperANFIS: Enhancing Rule Representation and Interpretability in Adaptive Neuro-Fuzzy Systems via Hyperbolic Geometry
- 在双曲空间中学习规则原型并进行推理，增强表示能力
- 在多个数据集上均优于标准ANFIS，预测准确率更高
- 保持可解释的IF-THEN规则生成，适合需要透明决策场景
自适应神经模糊推理系统（ANFIS）是一种具备可解释性的推理框架，能够生成明确的若-则模糊规则，适用于需要透明推理的任务。然而，现有ANFIS模型通常在欧氏空间中构建规则前提并执行推理，限制了其表示能力和预测性能。为此，我们提出双曲神经模糊推理系统（HyperANFIS），即ANFIS的双曲扩展。HyperANFIS保留传统ANFIS的模糊语义与核心架构，同时在双曲空间中进行规则原型学习、规则激活和结论聚合。它仍能生成可解释的若-则规则。通过利用双曲几何的表示特性，HyperANFIS强化了模糊推理过程，从而提升了预测准确性、规则间协同能力及可解释规则的可信度。实验结果表明，HyperANFIS在所有数据集上均持续优于标准ANFIS基线及其多种变体，同时生成更高质量的模糊规则。
原文摘要 · Abstract (English)
The adaptive neuro-fuzzy inference system (ANFIS) is an interpretable reasoning framework capable of generating explicit IF-THEN fuzzy rules, making it suitable for tasks requiring transparent reasoning. However, existing ANFIS models generally construct rule antecedents and perform inference in Euclidean space, limiting their representational capacity and predictive performance. To address this issue, we propose Hyperbolic ANFIS (HyperANFIS), a hyperbolic extension of ANFIS. HyperANFIS preserves the fuzzy semantics and core architecture of conventional ANFIS while performing rule-prototype learning, rule activation, and consequent aggregation in hyperbolic space. It also retains the ability to generate interpretable IF-THEN rules. By exploiting the representational properties of hyperbolic geometry, HyperANFIS strengthens the fuzzy inference process, thereby improving predictive accuracy, inter-rule collaboration, and the credibility of its interpretable rules. Experimental results show that HyperANFIS consistently outperforms the standard ANFIS baseline and various ANFIS variants across all datasets, while also generating higher-quality fuzzy rules.
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