HKAN：无反向传播的分层科莫戈罗夫-阿诺德网络
HKAN: Hierarchical Kolmogorov-Arnold Network without Backpropagation
AI总结：
HKAN通过非迭代的随机学习方法，在不依赖反向传播的情况下，实现了与KAN相当甚至更优的回归性能和稳定性。
摘要：
本文介绍了分层科莫戈罗夫-阿诺德网络（HKAN），一种新型的网络架构，为最近提出的科莫戈罗夫-阿诺德网络（KAN）提供了有竞争力的替代方案。不同于KAN依赖反向传播，HKAN采用随机学习方法，其基函数的参数固定，线性聚合通过最小二乘回归进行优化。HKAN采用分层多堆叠框架，每一层通过解决一系列线性回归问题来细化前一层的预测。这种非迭代训练方法简化了计算并消除了损失函数局部极小点的敏感性。实验结果表明，HKAN在各种回归任务中表现出与KAN相当甚至更优的准确性和稳定性，同时提供了变量重要性的见解。所提出的方法无缝整合了理论洞察与实际应用，为神经网络建模提供了一种稳健且高效的替代方案。
英文摘要：
This paper introduces the Hierarchical Kolmogorov-Arnold Network (HKAN), a novel network architecture that offers a competitive alternative to the recently proposed Kolmogorov-Arnold Network (KAN). Unlike KAN, which relies on backpropagation, HKAN adopts a randomized learning approach, where the parameters of its basis functions are fixed, and linear aggregations are optimized using least-squares regression. HKAN utilizes a hierarchical multi-stacking framework, with each layer refining the predictions from the previous one by solving a series of linear regression problems. This non-iterative training method simplifies computation and eliminates sensitivity to local minima in the loss function. Empirical results show that HKAN delivers comparable, if not superior, accuracy and stability relative to KAN across various regression tasks, while also providing insights into variable importance. The proposed approach seamlessly integrates theoretical insights with practical applications, presenting a robust and efficient alternative for neural network modeling.
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。
