# BiKAN: Restoring Collapsed Basis of Binary Kolmogorov--Arnold Networks

arXiv: https://arxiv.org/abs/2608.01490 · HTML: https://mlsanity.com/paper/2608.01490/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 18 references that are in the map.
- First posted on arXiv 2 Aug 2026.

## Builds on (most cited first, 8 of 8)

- [Bi-Real Net: Enhancing the Performance of 1-bit CNNs With Improved Representational Capability and Advanced Training Algorithm](https://mlsanity.com/paper/1808.00278/) (2018)
- [ReActNet: Towards Precise Binary Neural Network with Generalized Activation Functions](https://mlsanity.com/paper/2003.03488/) (2020)
- [Forward and Backward Information Retention for Accurate Binary Neural Networks](https://mlsanity.com/paper/1909.10788/) (2019)
- [LogicNets: Co-Designed Neural Networks and Circuits for Extreme-Throughput Applications](https://mlsanity.com/paper/2004.03021/) (2020)
- [WRPN: Wide Reduced-Precision Networks](https://mlsanity.com/paper/1709.01134/) (2017)
- [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)
- [BiKA: Kolmogorov-Arnold-Network-inspired Ultra Lightweight Neural Network Hardware Accelerator](https://mlsanity.com/paper/2602.23455/) (2026)

## Abstract (arXiv)

Binarizing a polynomial Kolmogorov--Arnold Network (KAN) not only changes parameter precision, but also alters the function space available to each layer. When activations are restricted to -1,+1, all even powers reduce to 1 and all odd powers reduce to x, causing the elementwise polynomial basis to collapse to constant and first-order responses. We refer to this structural failure as Spatial Orthogonality Collapse. Our proposed BiKAN addresses this critical issue by augmenting each binary KAN layer with selected degree-2 Walsh characters. Fixed circular channel rolls generate pairwise parities, and learned binary projections mix them using the same XNOR--popcount operations as the remaining W1A1 paths. This restores explicit pairwise coordinates without learned routing or multiplier-based feature generation. Experiments on CIFAR-10 confirms that removing parity reduces accuracy by 1.23 points over five paired seeds (p=0.003), the gain increases as width decreases, and accuracy improves monotonically as more parity planes are added. At an equal ~11.9M-parameter budget, parity outperforms conventional widening by 3.09 points (p<10-4). At W1A1, BiKAN reaches 99.48%, 84.38%, and 55.81% on MNIST, CIFAR-10, and CIFAR-100, respectively. Post-route Zynq-7020 FPGA results show that the repair remains hardware-efficient; the convolutional design cuts DSP usage from 164 to 72 and estimated compute-core latency from 401 to 54.8 ms, while the power-of-two-aware dense design achieves zero-DSP inference with a 0.03-point accuracy loss. The BiKAN implementation is available at https://github.com/OSU-STARLAB/BiKAN.