Subrat Prasad Panda

Subrat Prasad Panda, Blaise Genest, Arvind Easwaran et al.

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 DTSemNet, a novel semantically equivalent and invertible encoding for (hard, oblique) DTs as Neural Networks (NNs), that uses standard vanilla gradient descent. Experiments across various classification and regression benchmarks show that oblique DTs learned using 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 DTSemNet can learn DT policies as efficiently as NN policies in the Reinforcement Learning (RL) setup with physical inputs (dimensions $\leq32$). The code is available at https://github.com/CPS-research-group/dtsemnet.

Subrat Prasad Panda, Blaise Genest, Arvind Easwaran

Decision Trees (DTs) are widely used in safety-critical domains such as medical diagnosis, valued for their interpretability and effectiveness on tabular data. However, training accurate oblique DTs is challenging due to complex optimization landscapes and overfitting risks, particularly in regression. Recent advances have introduced differentiable formulations that enable gradient-based training and joint optimization of decision boundaries and leaf regressors. Yet, existing approaches typically rely on approximations, either through probabilistic softening of boundaries (soft DTs) or quantized gradients such as the Straight-Through Estimator (STE). To overcome these limitations, we propose DTSemNet, a novel, semantically equivalent, and invertible representation of hard oblique DTs as neural networks. DTSemNet enables end-to-end training with standard gradient descent, eliminating the need for approximations in both classification and regression. While classification aligns naturally with this formulation, regression remains challenging due to the joint optimization of internal nodes and leaf regressors. To address this, we analyze the limitations of STE and introduce an annealed Top-k method that provides accurate gradient signals without approximation. Extensive experiments on classification and regression benchmarks show that DTSemNet-trained oblique DTs outperform state-of-the-art differentiable DTs. Furthermore, we demonstrate that DTSemNet can serve as programmatic DT policies in reinforcement learning environments, thereby broadening their applicability.