KANtize: Exploring Low-bit Quantization of Kolmogorov-Arnold Networks for Efficient Inference

Kolmogorov-Arnold Networks (KANs) have gained attention for their potential to outperform Multi-Layer Perceptrons (MLPs) in terms of parameter efficiency and interpretability. Unlike traditional MLPs, KANs use learnable non-linear activation functions, typically spline functions, expressed as linear combinations of basis splines (B-splines). B-spline coefficients serve as the model's learnable parameters. However, evaluating these spline functions increases computational complexity during inference. Conventional quantization reduces this complexity by lowering the numerical precision of parameters and activations. However, the impact of quantization on KANs, and especially its effectiveness in reducing computational complexity, is largely unexplored, particularly for quantization levels below 8 bits. The study investigates the impact of low-bit quantization on KANs and its impact on computational complexity and hardware efficiency. Results show that B-splines can be quantized to 2-3 bits with negligible loss in accuracy, significantly reducing computational complexity. Hence, we investigate the potential of using low-bit quantized precomputed tables as a replacement for the recursive B-spline algorithm. This approach aims to further reduce the computational complexity of KANs and enhance hardware efficiency while maintaining accuracy. For example, ResKAN18 achieves a 50x reduction in BitOps without loss of accuracy using low-bit-quantized B-spline tables. Additionally, precomputed 8-bit lookup tables improve GPU inference speedup by up to 2.9x, while on FPGA-based systolic-array accelerators, reducing B-spline table precision from 8 to 3 bits cuts resource usage by 36%, increases clock frequency by 50%, and enhances speedup by 1.24x. On a 28nm FD-SOI ASIC, reducing the B-spline bit-width from 16 to 3 bits achieves 72% area reduction and 50% higher maximum frequency.