# Yet Another Representation of Binary Decision Trees: A Mathematical Demonstration

arXiv: https://arxiv.org/abs/2101.07077 · HTML: https://mlsanity.com/paper/2101.07077/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 46 references that are in the map.
- First posted on arXiv 18 Jan 2021.

## Builds on (most cited first, 15 of 15)

- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [From Softmax to Sparsemax: A Sparse Model of Attention and Multi-Label Classification](https://mlsanity.com/paper/1602.02068/) (2016)
- [Neural Oblivious Decision Ensembles for Deep Learning on Tabular Data](https://mlsanity.com/paper/1909.06312/) (2019)
- [Adaptively Sparse Transformers](https://mlsanity.com/paper/1909.00015/) (2019)
- [Entity Embeddings of Categorical Variables](https://mlsanity.com/paper/1604.06737/) (2016)
- [Deep Neural Decision Trees](https://mlsanity.com/paper/1806.06988/) (2018)
- [The Tree Ensemble Layer: Differentiability meets Conditional Computation](https://mlsanity.com/paper/2002.07772/) (2020)
- [Explaining the Success of AdaBoost and Random Forests as Interpolating Classifiers](https://mlsanity.com/paper/1504.07676/) (2015)
- [A Regularized Framework for Sparse and Structured Neural Attention](https://mlsanity.com/paper/1705.07704/) (2017)
- [On Controllable Sparse Alternatives to Softmax](https://mlsanity.com/paper/1810.11975/) (2018)
- [Sigsoftmax: Reanalysis of the Softmax Bottleneck](https://mlsanity.com/paper/1805.10829/) (2018)
- [Efficient non-greedy optimization of decision trees](https://mlsanity.com/paper/1511.04056/) (2015)
- [The Power of Unbiased Recursive Partitioning: A Unifying View of CTree, MOB, and GUIDE](https://mlsanity.com/paper/1906.10179/) (2019)
- [Representation of ordered trees with a given degree distribution](https://mlsanity.com/paper/1807.00371/) (2018)
- [Convergence of a Relaxed Variable Splitting Coarse Gradient Descent Method for Learning Sparse Weight Binarized Activation Neural Networks](https://mlsanity.com/paper/1901.09731/) (2019)

## Built on by (most cited first, 2 of 2)

- [Pegasus: A Universal Framework for Scalable Deep Learning Inference on the Dataplane](https://mlsanity.com/paper/2506.05779/) (2025)
- [Stella Nera: A Differentiable Maddness-Based Hardware Accelerator for Efficient Approximate Matrix Multiplication](https://mlsanity.com/paper/2311.10207/) (2023)

## Abstract (arXiv)

A decision tree looks like a simple directed acyclic computational graph, where only the leaf nodes specify the output values and the non-terminals specify their tests or split conditions. From the numerical perspective, we express decision trees in the language of computational graph. We explicitly parameterize the test phase, traversal phase and prediction phase of decision trees based on the bitvectors of non-terminal nodes. As shown, the decision tree is a shallow binary network in some sense. Especially, we introduce the bitvector matrix to implement the tree traversal in numerical approach, where the core is to convert the logical `AND' operation to arithmetic operations. And we apply this numerical representation to extend and unify diverse decision trees in concept.