LSS-SKAN: Efficient Kolmogorov-Arnold Networks based on Single-Parameterized Function (2410.14951v1)

Abstract: The recently proposed Kolmogorov-Arnold Networks (KAN) networks have attracted increasing attention due to their advantage of high visualizability compared to MLP. In this paper, based on a series of small-scale experiments, we proposed the Efficient KAN Expansion Principle (EKE Principle): allocating parameters to expand network scale, rather than employing more complex basis functions, leads to more efficient performance improvements in KANs. Based on this principle, we proposed a superior KAN termed SKAN, where the basis function utilizes only a single learnable parameter. We then evaluated various single-parameterized functions for constructing SKANs, with LShifted Softplus-based SKANs (LSS-SKANs) demonstrating superior accuracy. Subsequently, extensive experiments were performed, comparing LSS-SKAN with other KAN variants on the MNIST dataset. In the final accuracy tests, LSS-SKAN exhibited superior performance on the MNIST dataset compared to all tested pure KAN variants. Regarding execution speed, LSS-SKAN outperformed all compared popular KAN variants. Our experimental codes are available at https://github.com/chikkkit/LSS-SKAN and SKAN's Python library (for quick construction of SKAN in python) codes are available at https://github.com/chikkkit/SKAN .