让KAN网络自动更新网格，提升性能并识别异常输入
Automatic Grid Updates for Kolmogorov-Arnold Networks using Layer Histograms
- 用层直方图动态调整KAN的领域网格，实现数据驱动更新
- 在4个任务上超越或媲美已有KAN和MLP模型，包括科学方程学习
- 可同时用于检测分布外输入，适合需要可解释性的场景
Kolmogorov-Arnold网络（KAN）因其可解释性和在符号方程学习中的高精度而受到关注。与MLP不同，KAN采用可训练的参数化激活函数，但其原始架构需人工调整网络的域网格（称为“域网格”），增加了训练负担。典型KAN层无法自主根据前层输出范围变化动态更新域。本文提出的AdaptKAN通过层直方图算法实现数据驱动的网格自适应更新，显著降低用户干预。该方法还可在多种场景下用于检测分布外（OOD）输入。实验表明，AdaptKAN在四个任务中表现优于或匹配现有KAN及MLP：从Feynman数据集学习科学方程、基于冻结特征的图像分类、学习控制李雅普诺夫函数，以及在OpenOOD v1.5基准上检测分布外输入。
原文摘要 · Abstract (English)
Kolmogorov-Arnold Networks (KANs) are a class of neural networks that have received increased attention in recent literature. In contrast to MLPs, KANs leverage parameterized, trainable activation functions and offer several benefits including improved interpretability and higher accuracy on learning symbolic equations. However, the original KAN architecture requires adjustments to the domain discretization of the network (called the "domain grid") during training, creating extra overhead for the user in the training process. Typical KAN layers are not designed with the ability to autonomously update their domains in a data-driven manner informed by the changing output ranges of previous layers. As an added benefit, this histogram algorithm may also be applied towards detecting out-of-distribution (OOD) inputs in a variety of settings. We demonstrate that AdaptKAN exceeds or matches the performance of prior KAN architectures and MLPs on four different tasks: learning scientific equations from the Feynman dataset, image classification from frozen features, learning a control Lyapunov function, and detecting OOD inputs on the OpenOOD v1.5 benchmark.
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