MonoKAN让神经网络预测更可解释且保证单调性,适合需要可信决策的场景。
MonoKAN: Certified Monotonic Kolmogorov-Arnold Network
- 用分段三次埃尔米特样条实现输入输出单调性约束
- 在多数基准上性能超越现有单调MLP方法
- 兼具可解释性与可证明的单调性,适合高可靠性应用
人工神经网络(ANN)在模式识别和复杂问题求解中取得显著进展,但其可解释性仍是关键挑战,尤其在需透明与问责的应用中。尽管可解释AI(XAI)有所发展,仅可解释仍不足;某些场景要求模型预测符合专家设定的约束,如部分单调性。虽然传统多层感知机(MLP)有单调方法,但难以同时满足可解释性与可证明的单调性。近期提出的基于样条参数化可学习激活函数的柯尔莫哥洛夫-阿诺德网络(KAN)更具可解释性。本文在此基础上提出新架构MonoKAN,通过立方埃尔米特样条确保单调性,并结合正权重线性组合,使网络保持输入输出间的单调关系。实验表明,MonoKAN不仅提升可解释性,还在多数基准上优于最先进的单调MLP方法。
原文摘要 · Abstract (English)
Artificial Neural Networks (ANNs) have significantly advanced various fields by effectively recognizing patterns and solving complex problems. Despite these advancements, their interpretability remains a critical challenge, especially in applications where transparency and accountability are essential. To address this, explainable AI (XAI) has made progress in demystifying ANNs, yet interpretability alone is often insufficient. In certain applications, model predictions must align with expert-imposed requirements, sometimes exemplified by partial monotonicity constraints. While monotonic approaches are found in the literature for traditional Multi-layer Perceptrons (MLPs), they still face difficulties in achieving both interpretability and certified partial monotonicity. Recently, the Kolmogorov-Arnold Network (KAN) architecture, based on learnable activation functions parametrized as splines, has been proposed as a more interpretable alternative to MLPs. Building on this, we introduce a novel ANN architecture called MonoKAN, which is based on the KAN architecture and achieves certified partial monotonicity while enhancing interpretability. To achieve this, we employ cubic Hermite splines, which guarantee monotonicity through a set of straightforward conditions. Additionally, by using positive weights in the linear combinations of these splines, we ensure that the network preserves the monotonic relationships between input and output. Our experiments demonstrate that MonoKAN not only enhances interpretability but also improves predictive performance across the majority of benchmarks, outperforming state-of-the-art monotonic MLP approaches.
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