重新思考KANs中神经元的功能
Rethinking the Function of Neurons in KANs
AI总结：
本研究探讨了KANs中神经元多元函数的替代方案，发现用平均函数替代求和能将样条输入限制在激活函数有效范围内，从而显著提升模型性能与训练稳定性。
摘要：
Kolmogorov-Arnold Networks（KANs）的神经元执行简单的求和操作，这源于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神经元寻找一种可能提供更高实用性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Machine Learning任务中测试KAN神经元内的各种多元函数。研究结果表明，在KAN神经元中用平均函数替代求和，与传统KANs相比带来了显著的性能提升。我们的研究表明，这一微小修改通过将样条的输入限制在激活函数的有效范围内，从而有助于训练的稳定性。我们的实现和实验可在以下网址获取：https://github.com/Ghaith81/dropkan
英文摘要：
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}
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