揭示分段线性KAN与ReLU网络的等价转换关系
Relating Piecewise Linear Kolmogorov Arnold Networks to ReLU Networks
- 构建了分段线性KAN与ReLU网络间的显式双向转换方法
- 证明二者在表达能力上完全等价，可互相精确转换
- 为理解KAN的数学本质提供新视角，适合模型分析者
Kolmogorov-Arnold网络是一类新型神经网络架构，有望克服维度灾难并具备可解释性优势（arXiv:2404.19756）。本文研究了采用分段线性（一元实函数）的KAN与ReLU网络之间的联系。我们提供了将分段线性KAN转化为ReLU网络以及反之亦然的完全显式构造方法。
原文摘要 · Abstract (English)
Kolmogorov-Arnold Networks are a new family of neural network architectures which holds promise for overcoming the curse of dimensionality and has interpretability benefits (arXiv:2404.19756). In this paper, we explore the connection between Kolmogorov Arnold Networks (KANs) with piecewise linear (univariate real) functions and ReLU networks. We provide completely explicit constructions to convert a piecewise linear KAN into a ReLU network and vice versa.
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