LTBs-KAN: Linear-Time B-splines Kolmogorov-Arnold Networks

2026-04-23

AI Summary

This work addresses the inefficiency of Kolmogorov–Arnold Networks (KANs) arising from the recursive evaluation of B-spline basis functions, which hinders their practical deployment. To overcome this limitation, the authors propose Linear-Time B-spline KANs (LTBs-KAN), which achieve linear-time complexity in B-spline computation for the first time. The method further incorporates a product-sum matrix factorization strategy that substantially reduces both parameter count and computational overhead while preserving model expressiveness. Empirical evaluations on MNIST, Fashion-MNIST, and CIFAR-10 demonstrate that LTBs-KAN enables highly efficient forward inference and yields compact model sizes, achieving competitive accuracy with significantly enhanced practicality.

Technology Category

• Machine Learning: Kernel Methods
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

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.

Problem

• Kolmogorov-Arnold Networks
• B-splines
• computational efficiency
• time complexity
• neural network architecture

Innovation

• Linear-time complexity
• B-splines
• Kolmogorov-Arnold Networks
• Parameter reduction
• Matrix factorization