HKAN用随机参数+线性回归替代反向传播，训练更快更稳。
HKAN: Hierarchical Kolmogorov-Arnold Network without Backpropagation
- 基础函数参数固定，通过最小二乘法优化线性组合。
- 多层堆叠结构在回归任务中精度媲美甚至超越KAN。
- 无需迭代训练，适合追求高效稳定的模型应用者。
本文提出层次化柯尔莫哥洛夫-阿诺德网络（HKAN），作为近期提出的柯尔莫哥洛夫-阿诺德网络（KAN）的有力替代方案。与依赖反向传播的KAN不同，HKAN采用随机学习策略：其基函数参数固定，仅通过最小二乘回归优化线性加权。该网络采用分层多级堆叠结构，每层通过求解一系列线性回归问题对前一层预测进行精细化修正。这种非迭代训练方式简化了计算过程，避免了损失函数中局部极小值的敏感性。实验证明，HKAN在多种回归任务中表现相当甚至更优，兼具高准确率和稳定性，并能揭示变量重要性。该方法将理论洞见与实际应用无缝融合，为神经网络建模提供了高效稳健的新选择。
原文摘要 · Abstract (English)
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.
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