Decision Trees (DTs) constitute one of the major highly non-linear AI models, valued, e.g., for their efficiency on tabular data. Learning accurate DTs is, however, complicated, especially for oblique DTs, and does take a significant training time. Further, DTs suffer from overfitting, e.g., they proverbially "do not generalize" in regression tasks. Recently, some works proposed ways to make (oblique) DTs differentiable. This enables highly efficient gradient-descent algorithms to be used to learn DTs. It also enables generalizing capabilities by learning regressors at the leaves simultaneously with the decisions in the tree. Prior approaches to making DTs differentiable rely either on probabilistic approximations at the tree's internal nodes (soft DTs) or on approximations in gradient computation at the internal node (quantized gradient descent). In this work, we propose \textit{DTSemNet}, a novel \textit{sem}antically equivalent and invertible encoding for (hard, oblique) DTs as Neural \textit{Net}works (NNs), that uses standard vanilla gradient descent. Experiments across various classification and regression benchmarks show that oblique DTs learned using \textit{DTSemNet} are more accurate than oblique DTs of similar size learned using state-of-the-art techniques. Further, DT training time is significantly reduced. We also experimentally demonstrate that \textit{DTSemNet} can learn DT policies as efficiently as NN policies in the Reinforcement Learning (RL) setup with physical inputs (dimensions $\leq32$).
Results on Classification Datasets with Small DTs
Results on Classification Datasets with Large DTs
Results on Regression Datasets
Results on Reinforcement Learning Environments
Loss Landscape
The loss landscape of DTSemNet and DGT for MNIST, when
varying the parameters around the trained parameters along two random
directions. The flatter the loss landscape, the better the generalization.
