In practical situations, the ensemble tree model is one of the most popular models along with neural networks. A soft tree is one of the variants of a decision tree. Instead of using a greedy method for searching splitting rules, the soft tree is trained using a gradient method in which the whole splitting operation is formulated in a differentiable form. Although ensembles of such soft trees have been increasingly used in recent years, little theoretical work has been done for understanding their behavior. In this paper, by considering an ensemble of infinite soft trees, we introduce and study the Tree Neural Tangent Kernel (TNTK), which provides new insights into the behavior of the infinite ensemble of soft trees. Using the TNTK, we succeed in theoretically finding several non-trivial properties, such as the effect of the oblivious tree structure and the degeneracy of the TNTK induced by the deepening of the trees. Moreover, we empirically examine the performance of an ensemble of infinite soft trees using the TNTK.

翻译：在实际情况下,混合树模型是神经网络中最受欢迎的模型之一。软树是决策树的变种之一。软树不是使用贪婪的方法来寻找分解规则,而是使用一种梯度方法来训练软树,整个分解作业以不同的形式形成。虽然近年来越来越多地使用这种软树的集合,但很少进行理论工作来了解它们的行为。在本文中,我们通过考虑无限软树的组合,引进和研究树神经凝固核心(TNTK),它为无限软树的组合行为提供了新的洞察。我们利用TNTK,在理论上成功地发现了一些非三维特性,例如模糊的树结构的影响和TNTK树的腐蚀。此外,我们从经验上研究了利用TNTK的无限软树群的性能。