# Neurosymbolic Decision Trees

arXiv: https://arxiv.org/abs/2503.08762 · HTML: https://mlsanity.com/paper/2503.08762/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning.
- Builds on 14 of its 38 references that are in the map.
- First posted on arXiv 11 Mar 2025.

## Placed in

- LLM reasoning / [Reasoning benchmarks and evaluation](https://mlsanity.com/lr/reasoning-benchmarks-and-evaluation/)

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

- [Neural Probabilistic Logic Programming in DeepProbLog](https://mlsanity.com/paper/1907.08194/) (2019)
- [Distilling a Neural Network Into a Soft Decision Tree](https://mlsanity.com/paper/1711.09784/) (2017)
- [On the Binding Problem in Artificial Neural Networks](https://mlsanity.com/paper/2012.05208/) (2020)
- [Learning Explanatory Rules from Noisy Data](https://mlsanity.com/paper/1711.04574/) (2017)
- [Write, Execute, Assess: Program Synthesis with a REPL](https://mlsanity.com/paper/1906.04604/) (2019)
- [NeurASP: Embracing Neural Networks into Answer Set Programming](https://mlsanity.com/paper/2307.07700/) (2023)
- [From Statistical Relational to Neurosymbolic Artificial Intelligence: a Survey](https://mlsanity.com/paper/2108.11451/) (2021)
- [Adaptive Neural Trees](https://mlsanity.com/paper/1807.06699/) (2018)
- [Neural Markov Logic Networks](https://mlsanity.com/paper/1905.13462/) (2019)
- [Synthesizing Datalog Programs Using Numerical Relaxation](https://mlsanity.com/paper/1906.00163/) (2019)
- [KLay: Accelerating Arithmetic Circuits for Neurosymbolic AI](https://mlsanity.com/paper/2410.11415/) (2024)
- [GradTree: Learning Axis-Aligned Decision Trees with Gradient Descent](https://mlsanity.com/paper/2305.03515/) (2023)
- [Simply Logical -- Intelligent Reasoning by Example (Fully Interactive Online Edition)](https://mlsanity.com/paper/2208.06823/) (2022)
- [Neurally-Guided Structure Inference](https://mlsanity.com/paper/1906.07304/) (2019)

## Abstract (arXiv)

Neurosymbolic (NeSy) AI studies the integration of neural networks (NNs) and symbolic reasoning based on logic. Usually, NeSy techniques focus on learning the neural, probabilistic and/or fuzzy parameters of NeSy models. Learning the symbolic or logical structure of such models has, so far, received less attention. We introduce neurosymbolic decision trees (NDTs), as an extension of decision trees together with a novel NeSy structure learning algorithm, which we dub NeuID3. NeuID3 adapts the standard top-down induction of decision tree algorithms and combines it with a neural probabilistic logic representation, inherited from the DeepProbLog family of models. The key advantage of learning NDTs with NeuID3 is the support of both symbolic and subsymbolic data (such as images), and that they can exploit background knowledge during the induction of the tree structure, In our experimental evaluation we demonstrate the benefits of NeSys structure learning over more traditonal approaches such as purely data-driven learning with neural networks.