KAN：科尔莫戈罗夫-阿诺德网络
KAN: Kolmogorov-Arnold Networks
AI总结：
受科尔莫戈罗夫-阿诺德表示定理启发提出KANs替代MLPs，以边端可学习样条单变量函数替代线性权重，在准确性（小模型性能更优、缩放律更快）和可解释性（可视化、辅助定律发现）上更优，为深度学习模型改进提供新方向。
摘要：
受科尔莫戈罗夫-阿诺德表示定理启发，我们提出科尔莫戈罗夫-阿诺德网络（KANs）作为多层感知机（MLPs）的潜在替代方案。MLPs在节点（“神经元”）上使用固定激活函数，而KANs在边（“权重”）上使用可学习的激活函数。KANs完全没有线性权重——每个权重参数都被替换为以样条函数参数化的单变量函数。我们证明，这一看似简单的改变使KANs在准确性和可解释性方面优于MLPs。准确性方面，小得多的KANs在数据拟合和PDE求解中可达到与大得多的MLPs相当或更好的准确性；理论和实证上，KANs的神经缩放律比MLPs更快。可解释性方面，KANs可直观可视化，且易于与人类用户交互。通过数学和物理领域的两个例子，KANs被证明是帮助科学家（重新）发现数学和物理定律的有用协作工具。总之，KANs是MLPs的潜在替代方案，为进一步改进当今严重依赖MLPs的深度学习模型带来了机遇。
英文摘要：
Inspired by the Kolmogorov-Arnold representation theorem, we propose Kolmogorov-Arnold Networks (KANs) as promising alternatives to Multi-Layer Perceptrons (MLPs). While MLPs have fixed activation functions on nodes ("neurons"), KANs have learnable activation functions on edges ("weights"). KANs have no linear weights at all -- every weight parameter is replaced by a univariate function parametrized as a spline. We show that this seemingly simple change makes KANs outperform MLPs in terms of accuracy and interpretability. For accuracy, much smaller KANs can achieve comparable or better accuracy than much larger MLPs in data fitting and PDE solving. Theoretically and empirically, KANs possess faster neural scaling laws than MLPs. For interpretability, KANs can be intuitively visualized and can easily interact with human users. Through two examples in mathematics and physics, KANs are shown to be useful collaborators helping scientists (re)discover mathematical and physical laws. In summary, KANs are promising alternatives for MLPs, opening opportunities for further improving today's deep learning models which rely heavily on MLPs.
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。
