提出线性时间B样条KAN，速度和参数量显著降低。
LTBs-KAN: Linear-Time B-splines Kolmogorov-Arnold Networks
- 用线性时间B样条替代递归计算，加速模型推理
- 在多个数据集上实现更快训练与更少参数，性能不降
- 适合对效率敏感的深度学习应用
Kolmogorov-Arnold网络（KANs）是一种新兴神经网络架构，相较于多层感知机（MLPs）具备更强的可解释性和表达能力。然而，由于B样条函数计算具有递归特性，KANs的运行速度远低于MLPs，限制了其实际应用。本文提出一种新型基样条线性时间KAN（LTBs-KAN），实现了线性复杂度。不同于以往依赖Boor-Mansfield-Cox样条算法或其他高计算开销数学方法的做法，本方法大幅降低了计算负担。此外，在前向传播中通过乘积-求和矩阵分解进一步压缩模型参数，且不牺牲性能。在MNIST、Fashion-MNIST和CIFAR-10上的实验表明，当作为构建模块使用时，LTBs-KAN相比其他KAN实现展现出更优的时间复杂度与参数减少效果。
原文摘要 · Abstract (English)
Kolmogorov-Arnold Networks (KANs) are a recent neural network architecture offering an alternative to Multilayer Perceptrons (MLPs) with improved explainability and expressibility. However, KANs are significantly slower than MLPs due to the recursive nature of B-spline function computations, limiting their application. This work addresses these issues by proposing a novel base-spline Linear-Time B-splines Kolmogorov-Arnold Network (LTBs-KAN) with linear complexity. Unlike previous methods that rely on the Boor-Mansfield-Cox spline algorithm or other computationally intensive mathematical functions, our approach significantly reduces the computational burden. Additionally, we further reduce model's parameter through product-of-sums matrix factorization in the forward pass without sacrificing performance. Experiments on MNIST, Fashion-MNIST and CIFAR-10 demonstrate that LTBs-KAN achieves good time complexity and parameter reduction, when used as building architectural blocks, compared to other KAN implementations.
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