Hardware-Oriented Inference Complexity of Kolmogorov-Arnold Networks

A new research paper tackles a critical bottleneck in the adoption of Kolmogorov-Arnold Networks (KANs): understanding their true computational cost on specialized hardware. While KANs have shown promise as a powerful alternative to traditional Multi-Layer Perceptrons (MLPs), their unique, learnable activation function structure makes standard GPU-focused metrics like FLOPs insufficient for real-world deployment. In latency-sensitive fields like optical communications, where dedicated hardware accelerators are preferred, engineers need better tools to estimate resource consumption—such as power and chip area—before the costly design and synthesis stage.

To solve this, the authors propose three new, platform-independent complexity metrics: Real Multiplications (RM), Bit Operations (BOP), and Number of Additions and Bit-Shifts (NABS). These formulas can be calculated directly from a KAN's architecture—its grid size, polynomial order, and spline type—allowing for an apples-to-apples comparison with other neural networks early in the design process. The analysis extends across multiple KAN variants, including B-spline, Gaussian Radial Basis Function (GRBF), Chebyshev, and Fourier KANs. This work provides a crucial missing link, enabling hardware engineers and ML researchers to make informed architectural choices and optimize KANs for efficient deployment in power-constrained, real-time applications.