Kolmogorov-Arnold 傅里叶网络
Kolmogorov-Arnold Fourier Networks
AI总结：
针对KAN网络参数爆炸和高维任务中高频特征捕获能力不足的问题，提出Kolmogorov-Arnold傅里叶网络（KAF），通过谱重参数化将局部B样条表示转换为全局自适应谱表示，引入可训练随机傅里叶特征和自适应混合GELU-傅里叶激活机制，在CV、NLP、音频和PDE求解任务上取得最优性能。
摘要：
尽管基于Kolmogorov-Arnold的可解释网络（KAN）具有强大的理论表达能力，但在高维任务中面临严重的参数爆炸和捕获高频特征能力有限的问题。为解决这些问题，我们提出了Kolmogorov-Arnold傅里叶网络（KAF），通过谱重参数化从根本上重新定义了KAN范式。我们的主要贡献包括：（1）提出从局部的、基于网格的B样条表示到全局的、自适应的谱表示的基础基变换。这一转变改变了网络的归纳偏置，将参数复杂度从$O(G)$降低到$O(1)$，同时保持表达能力；（2）引入通过谱对齐策略初始化的可训练随机傅里叶特征（RFF），使模型能够打破固定核的平滑性限制，准确捕获高频分量；（3）实现自适应混合GELU-傅里叶激活机制，在训练过程中逐步增强频率表示。大量实验证明了KAF在计算机视觉（CV）、自然语言处理（NLP）、音频和偏微分方程（PDE）求解任务上的优越性，以更高的效率实现了最先进的性能。代码可在https://github.com/kolmogorovArnoldFourierNetwork/KAF获取。
英文摘要：
Although Kolmogorov-Arnold-based interpretable networks (KANs) possess strong theoretical expressiveness, they suffer from severe parameter explosion and limited ability to capture high-frequency features in high-dimensional tasks. To address these issues, we propose the Kolmogorov-Arnold Fourier Network (KAF), which fundamentally redefines the KAN paradigm through spectral reparameterization. Our key contributions include: (1) proposing a fundamental basis transformation from the local, grid-based B-spline representation to a global, adaptive spectral representation. This shift changes the network's inductive bias, reducing parameter complexity from $O(G)$ to $O(1)$ while preserving expressiveness; (2) introducing trainable Random Fourier Features (RFF) initialized via a spectral alignment strategy, which allows the model to break the smoothness limitation of fixed kernels and accurately capture high-frequency components; and (3) implementing an adaptive hybrid GELU-Fourier activation mechanism that progressively enhances frequency representation during training. Comprehensive experiments demonstrate the superiority of KAF across computer vision (CV), natural language processing (NLP), audio, and partial differential equation (PDE) solving tasks, achieving state-of-the-art performance with improved efficiency. The code is available at https://github.com/kolmogorovArnoldFourierNetwork/KAF.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
