UKAN: UNBOUNDED KOLMOGOROV-ARNOLD NETWORKS
Keywords: KAN, Acceleration, Unbounded KAN, Grid Free, Function Approximation
TL;DR: Dynamically-generated B-spline coefficients for grid free KAN.
Abstract: We present Unbounded Kolmogorov-Arnold Networks (UKANs), a novel algorithm that eliminates the need for bounded grids in traditional Kolmogorov-Arnold Networks (KANs). The key innovation is a coefficient generator (CG) model that dynamically produces B-spline coefficients, operating on an infinite symmetric grid. UKANs integrate multilayer-perceptrons with KANs, using positional encoding of grid groups as input to the CG model. This approach enables function approximation on unbounded domains without data normalization. Additionally, to reduce UKAN and KAN computational cost, we introduce a GPU-accelerated library that reduces B-spline evaluation complexity by a factor of $\mathcal{O}(\text{grid size})$ compared to existing libraries, enabling efficient large-scale learning. Our experiments on regression, classification, and generative tasks demonstrate UKANs' effectiveness, while benchmarks confirm superior memory and computational efficiency compared to existing methods. This work advances function approximation techniques, offering a flexible solution for complex, large-scale learning problems.
Primary Area: other topics in machine learning (i.e., none of the above)
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Submission Number: 8208
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