AI 中文总结
针对二元KAN的空间正交性坍缩问题，提出添加二次沃尔什字符的BiKAN，在图像分类任务上提升准确率，且硬件效率优异。
AI 中文摘要
对多项式柯尔莫哥洛夫-阿诺尔德网络（KAN）进行二值化处理，不仅会改变参数精度，还会改变每一层可使用的函数空间。当激活值被限制为{-1,+1}时，所有偶次幂都会简化为1，所有奇次幂都会简化为x，这导致逐元素多项式基坍缩为常数和一阶响应，我们将这种结构故障称为空间正交性坍缩。我们提出的BiKAN通过为每个二元KAN层添加选定的二次沃尔什字符来解决这一关键问题：固定的循环通道滚动生成成对奇偶性，学习到的二元投影使用与其余W1A1路径相同的XNOR-计数量操作对其进行混合，这无需学习路由或基于乘法器的特征生成即可恢复显式成对坐标。在CIFAR-10上的实验证实，移除奇偶性会使五个配对种子的准确率降低1.23个百分点（p=0.003），且随着网络宽度减小，增益会增大；随着添加更多奇偶平面，准确率单调提升。在约1190万参数的相同预算下，奇偶性方法的性能比传统加宽方法高3.09个百分点（p<10^-4）。在W1A1设置下，BiKAN在MNIST、CIFAR-10和CIFAR-100上分别达到99.48%、84.38%和55.81%的准确率。路由后的Zynq-7020 FPGA结果显示，该修复方案仍具备硬件效率：卷积设计将DSP使用量从164降至72，估计计算核心延迟从401 ms降至54.8 ms；而感知2的幂的密集设计实现了零DSP推理，仅存在0.03个百分点的准确率损失。BiKAN的实现代码可在指定网址获取。
英文摘要
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 $\sim$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.
