PolyKAN: Efficient Fused GPU Operators for Polynomial Kolmogorov-Arnold Network Variants

Kolmogorov-Arnold Networks (KANs) promise higher expressive capability and stronger interpretability than Multi-Layer Perceptron, particularly in the domain of AI for Science. However, practical adoption has been hindered by low GPU utilization of existing parallel implementations. To address this challenge, we present a GPU-accelerated operator library, named PolyKAN which is the first general open-source implementation of KAN and its variants. PolyKAN fuses the forward and backward passes of polynomial KAN layers into a concise set of optimized CUDA kernels. Four orthogonal techniques underpin the design: (i) lookup-table with linear interpolation that replaces runtime expensive math-library functions; (ii) 2D tiling to expose thread-level parallelism with preserving memory locality; (iii) a two-stage reduction scheme converting scattered atomic updates into a single controllable merge step; and (iv) coefficient-layout reordering yielding unit-stride reads under the tiled schedule. Using a KAN variant, Chebyshev KAN, as a case-study, PolyKAN delivers 1.2--10× faster inference and 1.4--12× faster training than a Triton + cuBLAS baseline, with identical accuracy on speech, audio-enhancement, and tabular-regression workloads on both highend GPU and consumer-grade GPU.