Oblique Decision Trees from Derivatives of ReLU Networks

TL;DR

This paper introduces locally constant networks, a neural architecture that can implicitly realize oblique decision trees with parameter sharing, enabling improved training and performance on molecular property tasks.

Contribution

The paper establishes the equivalence between locally constant networks and decision trees, and demonstrates their advantages in parameter sharing and training efficiency.

Findings

Outperforms existing methods in molecular property classification.

Implicitly models oblique decision trees with fewer parameters.

Enables use of deep network tools like DropConnect for decision trees.

Abstract

We show how neural models can be used to realize piece-wise constant functions such as decision trees. The proposed architecture, which we call locally constant networks, builds on ReLU networks that are piece-wise linear and hence their associated gradients with respect to the inputs are locally constant. We formally establish the equivalence between the classes of locally constant networks and decision trees. Moreover, we highlight several advantageous properties of locally constant networks, including how they realize decision trees with parameter sharing across branching / leaves. Indeed, only $M$ neurons suffice to implicitly model an oblique decision tree with $2^M$ leaf nodes. The neural representation also enables us to adopt many tools developed for deep networks (e.g., DropConnect (Wan et al., 2013)) while implicitly training decision trees. We demonstrate that our method outperforms alternative techniques for training oblique decision trees in the context of molecular property classification and regression tasks.