KAN能否改进高能物理分类任务？Kolmogorov-Arnold网络应用于LHC物理实例
KAN we improve on HEP classification tasks? Kolmogorov-Arnold Networks applied to an LHC physics example
AI总结：
本研究将Kolmogorov-Arnold网络应用于LHC高能物理事件分类，发现其激活函数近似似然比，但参数效率不优于多层感知机，小型KAN以轻微性能损失换可解释性。
摘要：
最近，Kolmogorov-Arnold网络（KANs）被提出作为多层感知机的一种替代方案，声称在性能和可解释性方面具有优势。我们研究了一个典型的高能物理二元事件分类任务，包括高层特征，并评述了KANs在此背景下的性能和可解释性。与预期一致，我们发现单层KAN的学习激活函数类似于各自输入特征的单变量对数似然比。在更深的KAN中，第一层的激活与单层KAN中的不同，这表明更深的KAN学习到更复杂的数据表示，这一模式在其他深度学习架构中常见。我们研究了不同深度和宽度的KAN，并将其与多层感知机在性能和可训练参数数量方面进行比较。对于所选的分类任务，我们没有发现KAN在参数效率上更优。然而，小型KAN可能在可解释性方面提供优势，而这仅以适度的性能损失为代价。
英文摘要：
Recently, Kolmogorov-Arnold Networks (KANs) have been proposed as an alternative to multilayer perceptrons, suggesting advantages in performance and interpretability. We study a typical binary event classification task in high-energy physics including high-level features and comment on the performance and interpretability of KANs in this context. Consistent with expectations, we find that the learned activation functions of a one-layer KAN resemble the univariate log-likelihood ratios of the respective input features. In deeper KANs, the activations in the first layer differ from those in the one-layer KAN, which indicates that the deeper KANs learn more complex representations of the data, a pattern commonly observed in other deep-learning architectures. We study KANs with different depths and widths and we compare them to multilayer perceptrons in terms of performance and number of trainable parameters. For the chosen classification task, we do not find that KANs are more parameter efficient. However, small KANs may offer advantages in terms of interpretability that come at the cost of only a moderate loss in performance.
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