# Neural Networks are Decision Trees

arXiv: https://arxiv.org/abs/2210.05189 · HTML: https://mlsanity.com/paper/2210.05189/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 31 references that are in the map.
- First posted on arXiv 11 Oct 2022.

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

- [Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization](https://mlsanity.com/paper/1610.02391/) (2016)
- [Learning Deep Features for Discriminative Localization](https://mlsanity.com/paper/1512.04150/) (2015)
- [Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Maps](https://mlsanity.com/paper/1312.6034/) (2013)
- [Visualizing and Understanding Convolutional Networks](https://mlsanity.com/paper/1311.2901/) (2013)
- [YOLO9000: Better, Faster, Stronger](https://mlsanity.com/paper/1612.08242/) (2016)
- [Grad-CAM++: Improved Visual Explanations for Deep Convolutional Networks](https://mlsanity.com/paper/1710.11063/) (2017)
- [Top-down Neural Attention by Excitation Backprop](https://mlsanity.com/paper/1608.00507/) (2016)
- [Distilling a Neural Network Into a Soft Decision Tree](https://mlsanity.com/paper/1711.09784/) (2017)
- [Eigen-CAM: Class Activation Map using Principal Components](https://mlsanity.com/paper/2008.00299/) (2020)
- [Convolutional Networks with Adaptive Inference Graphs](https://mlsanity.com/paper/1711.11503/) (2017)
- [Tropical Geometry of Deep Neural Networks](https://mlsanity.com/paper/1805.07091/) (2018)
- [Use HiResCAM instead of Grad-CAM for faithful explanations of convolutional neural networks](https://mlsanity.com/paper/2011.08891/) (2020)
- [Deep Neural Decision Trees](https://mlsanity.com/paper/1806.06988/) (2018)
- [Beyond Sparsity: Tree Regularization of Deep Models for Interpretability](https://mlsanity.com/paper/1711.06178/) (2017)
- [Deep Feature Factorization For Concept Discovery](https://mlsanity.com/paper/1806.10206/) (2018)
- [Mad Max: Affine Spline Insights into Deep Learning](https://mlsanity.com/paper/1805.06576/) (2018)
- [Network of Experts for Large-Scale Image Categorization](https://mlsanity.com/paper/1604.06119/) (2016)
- [NBDT: Neural-Backed Decision Trees](https://mlsanity.com/paper/2004.00221/) (2020)
- [Deciding How to Decide: Dynamic Routing in Artificial Neural Networks](https://mlsanity.com/paper/1703.06217/) (2017)
- [Unwrapping The Black Box of Deep ReLU Networks: Interpretability, Diagnostics, and Simplification](https://mlsanity.com/paper/2011.04041/) (2020)
- [Blockout: Dynamic Model Selection for Hierarchical Deep Networks](https://mlsanity.com/paper/1512.05246/) (2015)
- [Towards Interpretable ANNs: An Exact Transformation to Multi-Class Multivariate Decision Trees](https://mlsanity.com/paper/2003.04675/) (2020)

## Built on by (most cited first, 17 of 17)

- [Interpretable Concept Bottlenecks to Align Reinforcement Learning Agents](https://mlsanity.com/paper/2401.05821/) (2024)
- [SoK: A Systematic Evaluation of Backdoor Trigger Characteristics in Image Classification](https://mlsanity.com/paper/2302.01740/) (2023)
- [Unwrapping All ReLU Networks](https://mlsanity.com/paper/2305.09424/) (2023)
- [Establishing Trustworthiness: Rethinking Tasks and Model Evaluation](https://mlsanity.com/paper/2310.05442/) (2023)
- [Dynamic Normativity: Necessary and Sufficient Conditions for Value Alignment](https://mlsanity.com/paper/2406.11039/) (2024)
- [Prophecy: Inferring Formal Properties from Neuron Activations](https://mlsanity.com/paper/2509.21677/) (2025)
- [The Topos of Transformer Networks](https://mlsanity.com/paper/2403.18415/) (2024)
- [Myths and Legends in High-Performance Computing](https://mlsanity.com/paper/2301.02432/) (2023)
- [Efficient Multi-stage Inference on Tabular Data](https://mlsanity.com/paper/2303.11580/) (2023)
- [LEURN: Learning Explainable Univariate Rules with Neural Networks](https://mlsanity.com/paper/2303.14937/) (2023)
- [Model of models -- Part 1](https://mlsanity.com/paper/2308.04600/) (2023)
- [High-Level Parallelism and Nested Features for Dynamic Inference Cost and Top-Down Attention](https://mlsanity.com/paper/2308.05128/) (2023)
- [Extracting PAC Decision Trees from Black Box Binary Classifiers: The Gender Bias Case Study on BERT-based Language Models](https://mlsanity.com/paper/2412.10513/) (2024)
- [Even Faster Hyperbolic Random Forests: A Beltrami-Klein Wrapper Approach](https://mlsanity.com/paper/2506.04360/) (2025)
- [Poisson Hyperplane Processes with Rectified Linear Units](https://mlsanity.com/paper/2601.05586/) (2026)
- [Late Breaking Results: Conversion of Neural Networks into Logic Flows for Edge Computing](https://mlsanity.com/paper/2601.22151/) (2026)
- [The Hamilton-Jacobi Theory of Deep Learning](https://mlsanity.com/paper/2605.28983/) (2026)

## Abstract (arXiv)

In this manuscript, we show that any neural network with any activation function can be represented as a decision tree. The representation is equivalence and not an approximation, thus keeping the accuracy of the neural network exactly as is. We believe that this work provides better understanding of neural networks and paves the way to tackle their black-box nature. We share equivalent trees of some neural networks and show that besides providing interpretability, tree representation can also achieve some computational advantages for small networks. The analysis holds both for fully connected and convolutional networks, which may or may not also include skip connections and/or normalizations.