LTBs-KAN: Linear-Time B-splines Kolmogorov-Arnold Networks
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866914503444135936 |
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| author | Merin-Martinez, Eduardo Said Mendez-Vazquez, Andres Rodriguez-Tello, Eduardo |
| author_facet | Merin-Martinez, Eduardo Said Mendez-Vazquez, Andres Rodriguez-Tello, Eduardo |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_22034 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | LTBs-KAN: Linear-Time B-splines Kolmogorov-Arnold Networks Merin-Martinez, Eduardo Said Mendez-Vazquez, Andres Rodriguez-Tello, Eduardo Machine Learning Computer Vision and Pattern Recognition Neural and Evolutionary Computing 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. |
| title | LTBs-KAN: Linear-Time B-splines Kolmogorov-Arnold Networks |
| topic | Machine Learning Computer Vision and Pattern Recognition Neural and Evolutionary Computing |
| url | https://arxiv.org/abs/2604.22034 |