The neurons of Kolmogorov-Arnold Networks (KANs) perform a simple summation motivated by the Kolmogorov-Arnold representation theorem, which asserts that sum is the only fundamental multivariate function. In this work, we investigate the potential for identifying an alternative multivariate function for KAN neurons that may offer increased practical utility. Our empirical research involves testing various multivariate functions in KAN neurons across a range of benchmark Machine Learning tasks. Our findings indicate that substituting the sum with the average function in KAN neurons results in significant performance enhancements compared to traditional KANs. Our study demonstrates that this minor modification contributes to the stability of training by confining the input to the spline within the effective range of the activation function. Our implementation and experiments are available at: \url{https://github.com/Ghaith81/dropkan}

翻译：Kolmogorov-Arnold Networks (KANs) 的神经元执行简单的求和运算，其动机源于Kolmogorov-Arnold表示定理，该定理断言求和是唯一的基本多元函数。在本研究中，我们探讨了为KAN神经元识别一种可能具有更高实用价值的替代多元函数的潜力。我们的实证研究涉及在一系列基准机器学习任务中测试KAN神经元使用的各种多元函数。我们的研究结果表明，将KAN神经元中的求和函数替换为平均函数，相比传统KAN能带来显著的性能提升。我们的研究证明，这一微小修改通过将样条函数的输入限制在激活函数的有效范围内，有助于提升训练的稳定性。我们的实现和实验代码可在以下网址获取：\url{https://github.com/Ghaith81/dropkan}