# Learning Binary Decision Trees by Argmin Differentiation

arXiv: https://arxiv.org/abs/2010.04627 · HTML: https://mlsanity.com/paper/2010.04627/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Oct 2020.

## Built on by (most cited first, 11 of 11)

- [Deep Differentiable Logic Gate Networks](https://mlsanity.com/paper/2210.08277/) (2022)
- [Learning Accurate Decision Trees with Bandit Feedback via Quantized Gradient Descent](https://mlsanity.com/paper/2102.07567/) (2021)
- [GradTree: Learning Axis-Aligned Decision Trees with Gradient Descent](https://mlsanity.com/paper/2305.03515/) (2023)
- [NCART: Neural Classification and Regression Tree for Tabular Data](https://mlsanity.com/paper/2307.12198/) (2023)
- [Learning a Decision Tree Algorithm with Transformers](https://mlsanity.com/paper/2402.03774/) (2024)
- [Vanilla Gradient Descent for Oblique Decision Trees](https://mlsanity.com/paper/2408.09135/) (2024)
- [Hierarchical Retrieval at Scale: Bridging Transparency and Efficiency](https://mlsanity.com/paper/2502.07971/) (2025)
- [Learning Compact Boolean Networks](https://mlsanity.com/paper/2602.05830/) (2026)
- [OF-AE: Oblique Forest AutoEncoders](https://mlsanity.com/paper/2301.00880/) (2023)
- [Improving the Validity of Decision Trees as Explanations](https://mlsanity.com/paper/2306.06777/) (2023)
- [Approximation-Free Differentiable Oblique Decision Trees](https://mlsanity.com/paper/2605.07837/) (2026)

## Abstract (arXiv)

We address the problem of learning binary decision trees that partition data for some downstream task. We propose to learn discrete parameters (i.e., for tree traversals and node pruning) and continuous parameters (i.e., for tree split functions and prediction functions) simultaneously using argmin differentiation. We do so by sparsely relaxing a mixed-integer program for the discrete parameters, to allow gradients to pass through the program to continuous parameters. We derive customized algorithms to efficiently compute the forward and backward passes. This means that our tree learning procedure can be used as an (implicit) layer in arbitrary deep networks, and can be optimized with arbitrary loss functions. We demonstrate that our approach produces binary trees that are competitive with existing single tree and ensemble approaches, in both supervised and unsupervised settings. Further, apart from greedy approaches (which do not have competitive accuracies), our method is faster to train than all other tree-learning baselines we compare with. The code for reproducing the results is available at https://github.com/vzantedeschi/LatentTrees.