# Equivalent and Compact Representations of Neural Network Controllers With Decision Trees

arXiv: https://arxiv.org/abs/2304.06049 · HTML: https://mlsanity.com/paper/2304.06049/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 43 references that are in the map.
- First posted on arXiv 11 Apr 2023.

## Builds on (most cited first, 14 of 14)

- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Playing Atari with Deep Reinforcement Learning](https://mlsanity.com/paper/1312.5602/) (2013)
- [OpenAI Gym](https://mlsanity.com/paper/1606.01540/) (2016)
- [Do Deep Nets Really Need to be Deep?](https://mlsanity.com/paper/1312.6184/) (2013)
- [Adversarial Attacks on Neural Network Policies](https://mlsanity.com/paper/1702.02284/) (2017)
- [Distilling a Neural Network Into a Soft Decision Tree](https://mlsanity.com/paper/1711.09784/) (2017)
- [Beta-CROWN: Efficient Bound Propagation with Per-neuron Split Constraints for Complete and Incomplete Neural Network Robustness Verification](https://mlsanity.com/paper/2103.06624/) (2021)
- [Fast and Complete: Enabling Complete Neural Network Verification with Rapid and Massively Parallel Incomplete Verifiers](https://mlsanity.com/paper/2011.13824/) (2020)
- [Verifiable Reinforcement Learning via Policy Extraction](https://mlsanity.com/paper/1805.08328/) (2018)
- [Verisig: verifying safety properties of hybrid systems with neural network controllers](https://mlsanity.com/paper/1811.01828/) (2018)
- [Oblique Decision Trees from Derivatives of ReLU Networks](https://mlsanity.com/paper/1909.13488/) (2019)
- [One-Shot Reachability Analysis of Neural Network Dynamical Systems](https://mlsanity.com/paper/2209.11827/) (2022)
- [Towards Interpretable ANNs: An Exact Transformation to Multi-Class Multivariate Decision Trees](https://mlsanity.com/paper/2003.04675/) (2020)
- [Bounding the Complexity of Formally Verifying Neural Networks: A Geometric Approach](https://mlsanity.com/paper/2012.11761/) (2020)

## Abstract (arXiv)

Over the past decade, neural network (NN)-based controllers have demonstrated remarkable efficacy in a variety of decision-making tasks. However, their black-box nature and the risk of unexpected behaviors pose a challenge to their deployment in real-world systems requiring strong guarantees of correctness and safety. We address these limitations by investigating the transformation of NN-based controllers into equivalent soft decision tree (SDT)-based controllers and its impact on verifiability. In contrast to existing work, we focus on discrete-output NN controllers including rectified linear unit (ReLU) activation functions as well as argmax operations. We then devise an exact yet efficient transformation algorithm which automatically prunes redundant branches. We first demonstrate the practical efficacy of the transformation algorithm applied to an autonomous driving NN controller within OpenAI Gym's CarRacing environment. Subsequently, we evaluate our approach using two benchmarks from the OpenAI Gym environment. Our results indicate that the SDT transformation can benefit formal verification, showing runtime improvements of up to 21 × and 2 × for MountainCar-v0 and CartPole-v1, respectively.