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

arXiv: https://arxiv.org/abs/2609.26067 · HTML: https://mlsanity.com/paper/2609.26067/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 23 references that are in the map.
- First posted on arXiv 4 Aug 2026.

## Builds on (most cited first, 9 of 9)

- [Deep Compression: Compressing Deep Neural Networks with Pruning, Trained Quantization and Huffman Coding](https://mlsanity.com/paper/1510.00149/) (2015)
- [Learned Step Size Quantization](https://mlsanity.com/paper/1902.08153/) (2019)
- [Efficient Processing of Deep Neural Networks: A Tutorial and Survey](https://mlsanity.com/paper/1703.09039/) (2017)
- [Compressing Neural Networks with the Hashing Trick](https://mlsanity.com/paper/1504.04788/) (2015)
- [Chebyshev Polynomial-Based Kolmogorov-Arnold Networks: An Efficient Architecture for Nonlinear Function Approximation](https://mlsanity.com/paper/2405.07200/) (2024)
- [KAN or MLP: A Fairer Comparison](https://mlsanity.com/paper/2407.16674/) (2024)
- [KANEL'E: Kolmogorov-Arnold Networks for Efficient LUT-based Evaluation](https://mlsanity.com/paper/2512.12850/) (2025)
- [KANtize: Exploring Low-bit Quantization of Kolmogorov-Arnold Networks for Efficient Inference](https://mlsanity.com/paper/2603.17230/) (2026)
- [Shift-Invariant Attribute Scoring for Kolmogorov-Arnold Networks via Shapley Value](https://mlsanity.com/paper/2510.01663/) (2025)

## Abstract (arXiv)

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× and 17.6× with only 0.31 and 0.34 pp accuracy loss. On a 6.1M-edge convolutional KAGN, it achieves 19.9× 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× relative to dense INT4, without increasing cycle count or latency. The FuncCode implementation is available at https://github.com/OSU-STARLAB/FuncCode.