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In practical situations, the tree ensemble is one of the most popular modelsalong with neural networks. A soft tree is a variant of a decision tree.Instead of using a greedy method for searching splitting rules, the soft treeis trained using a gradient method in which the entire splitting operation isformulated in a differentiable form. Although ensembles of such soft trees havebeen used increasingly in recent years, little theoretical work has been doneto understand their behavior. By considering an ensemble of infinite softtrees, this paper introduces and studies the Tree Neural Tangent Kernel (TNTK),which provides new insights into the behavior of the infinite ensemble of softtrees. Using the TNTK, we theoretically identify several non-trivialproperties, such as global convergence of the training, the equivalence of theoblivious tree structure, and the degeneracy of the TNTK induced by thedeepening of the trees.

A Neural Tangent Kernel Perspective of Infinite Tree Ensembles