# Empowering Decision Trees via Shape Function Branching

arXiv: https://arxiv.org/abs/2510.19040 · HTML: https://mlsanity.com/paper/2510.19040/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 53 references that are in the map.
- First posted on arXiv 21 Oct 2025.

## Builds on (most cited first, 22 of 22)

- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Towards A Rigorous Science of Interpretable Machine Learning](https://mlsanity.com/paper/1702.08608/) (2017)
- [Tabular Data: Deep Learning is Not All You Need](https://mlsanity.com/paper/2106.03253/) (2021)
- [Neural Additive Models: Interpretable Machine Learning with Neural Nets](https://mlsanity.com/paper/2004.13912/) (2020)
- [Interpretable machine learning: definitions, methods, and applications](https://mlsanity.com/paper/1901.04592/) (2019)
- [InterpretML: A Unified Framework for Machine Learning Interpretability](https://mlsanity.com/paper/1909.09223/) (2019)
- [When Do Neural Nets Outperform Boosted Trees on Tabular Data?](https://mlsanity.com/paper/2305.02997/) (2023)
- [Coordinate Descent Algorithms](https://mlsanity.com/paper/1502.04759/) (2015)
- [Generalized and Scalable Optimal Sparse Decision Trees](https://mlsanity.com/paper/2006.08690/) (2020)
- [NODE-GAM: Neural Generalized Additive Model for Interpretable Deep Learning](https://mlsanity.com/paper/2106.01613/) (2021)
- [Interpretability of machine learning based prediction models in healthcare](https://mlsanity.com/paper/2002.08596/) (2020)
- [Neural Basis Models for Interpretability](https://mlsanity.com/paper/2205.14120/) (2022)
- [How Interpretable and Trustworthy are GAMs?](https://mlsanity.com/paper/2006.06466/) (2020)
- [ExKMC: Expanding Explainable k-Means Clustering](https://mlsanity.com/paper/2006.02399/) (2020)
- [Large Scale Prediction with Decision Trees](https://mlsanity.com/paper/2104.13881/) (2021)
- [Assessing the Local Interpretability of Machine Learning Models](https://mlsanity.com/paper/1902.03501/) (2019)
- [Hierarchical Shrinkage: improving the accuracy and interpretability of tree-based methods](https://mlsanity.com/paper/2202.00858/) (2022)
- [Sparse learning with CART](https://mlsanity.com/paper/2006.04266/) (2020)
- [Scalable Optimal Multiway-Split Decision Trees with Constraints](https://mlsanity.com/paper/2302.06812/) (2023)
- [Near Optimal Decision Trees in a SPLIT Second](https://mlsanity.com/paper/2502.15988/) (2025)
- [Breiman meets Bellman: Non-Greedy Decision Trees with MDPs](https://mlsanity.com/paper/2309.12701/) (2023)
- [NeurCAM: Interpretable Neural Clustering via Additive Models](https://mlsanity.com/paper/2408.13361/) (2024)

## Abstract (arXiv)

Decision trees are prized for their interpretability and strong performance on tabular data. Yet, their reliance on simple axis-aligned linear splits often forces deep, complex structures to capture non-linear feature effects, undermining human comprehension of the constructed tree. To address this limitation, we propose a novel generalization of a decision tree, the Shape Generalized Tree (SGT), in which each internal node applies a learnable axis-aligned shape function to a single feature, enabling rich, non-linear partitioning in one split. As users can easily visualize each node's shape function, SGTs are inherently interpretable and provide intuitive, visual explanations of the model's decision mechanisms. To learn SGTs from data, we propose ShapeCART, an efficient induction algorithm for SGTs. We further extend the SGT framework to bivariate shape functions (S2GT) and multi-way trees (SGTK), and present Shape2CART and ShapeCARTK, extensions to ShapeCART for learning S2GTs and SGTKs, respectively. Experiments on various datasets show that SGTs achieve superior performance with reduced model size compared to traditional axis-aligned linear trees.