FuncCode: Compressing Kolmogorov--Arnold Networks in Function Space with Hardware-Aware Quantization

Abstract

Kolmogorov--Arnold Networks (KANs) replace scalar edge weights with learnable univariate functions, increasing flexibility but also parameter memory because each edge stores multiple coefficients, often together with a separate base branch. We introduce FuncCode, a basis-agnostic compression approach that forms shared codebooks from sampled edge responses, codes the basis and base branches independently, and exports the resulting codebooks and per-edge indices in a quantized, bit-packed format. Across spline and polynomial KANs, sampled edge responses exhibit $13$--$35\%$ lower effective rank than their coefficient representations. Further replicated controls show that function-space clustering alone is statistically tied with coefficient-space clustering; the consistent accuracy gain comes from preserving the distinct sharing structure of the two branches. On a ten-seed MNIST benchmark, FuncCode compresses spline and GRAM KANs by $31.6\times$ and $17.6\times$ with only $0.31$ and $0.34$ pp accuracy loss. On a 6.1M-edge convolutional KAGN, it achieves $19.9\times$ compression while remaining within $0.54$ pp of dense accuracy on CIFAR-10 and $1.89$ pp on CIFAR-100. After compression, per-edge indices account for up to $99.4\%$ of stored weight bits, making the representation index-bound. Across nine bit-exact FPGA accelerators, FuncCode reduces SplineKAN post-route weight memory by $3.87\times$ relative to dense INT4, without increasing cycle count or latency. The FuncCode implementation is available at https://github.com/OSU-STARLAB/FuncCode.