# pix2rule: End-to-end Neuro-symbolic Rule Learning

arXiv: https://arxiv.org/abs/2106.07487 · HTML: https://mlsanity.com/paper/2106.07487/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 41 of its 76 references that are in the map.
- First posted on arXiv 14 Jun 2021.

## Builds on (most cited first, 30 of 41)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [Distributed Representations of Words and Phrases and their Compositionality](https://mlsanity.com/paper/1310.4546/) (2013)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [On the Properties of Neural Machine Translation: Encoder-Decoder Approaches](https://mlsanity.com/paper/1409.1259/) (2014)
- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (2016)
- [Object-Centric Learning with Slot Attention](https://mlsanity.com/paper/2006.15055/) (2020)
- [Neural Turing Machines](https://mlsanity.com/paper/1410.5401/) (2014)
- [Neural Probabilistic Logic Programming in DeepProbLog](https://mlsanity.com/paper/1907.08194/) (2019)
- [MONet: Unsupervised Scene Decomposition and Representation](https://mlsanity.com/paper/1901.11390/) (2019)
- [The Neuro-Symbolic Concept Learner: Interpreting Scenes, Words, and Sentences From Natural Supervision](https://mlsanity.com/paper/1904.12584/) (2019)
- [Memory Networks](https://mlsanity.com/paper/1410.3916/) (2014)
- [A simple neural network module for relational reasoning](https://mlsanity.com/paper/1706.01427/) (2017)
- [Neural-Symbolic VQA: Disentangling Reasoning from Vision and Language Understanding](https://mlsanity.com/paper/1810.02338/) (2018)
- [Learning Explanatory Rules from Noisy Data](https://mlsanity.com/paper/1711.04574/) (2017)
- [Graph Matching Networks for Learning the Similarity of Graph Structured Objects](https://mlsanity.com/paper/1904.12787/) (2019)
- [Neural-Symbolic Learning and Reasoning: A Survey and Interpretation](https://mlsanity.com/paper/1711.03902/) (2017)
- [End-to-End Differentiable Proving](https://mlsanity.com/paper/1705.11040/) (2017)
- [Neural Logic Machines](https://mlsanity.com/paper/1904.11694/) (2019)
- [An Attentive Survey of Attention Models](https://mlsanity.com/paper/1904.02874/) (2019)
- [Logical Neural Networks](https://mlsanity.com/paper/2006.13155/) (2020)
- [Neural Symbolic Machines: Learning Semantic Parsers on Freebase with Weak Supervision](https://mlsanity.com/paper/1611.00020/) (2016)
- [Neural Programmer-Interpreters](https://mlsanity.com/paper/1511.06279/) (2015)
- [Inferring Algorithmic Patterns with Stack-Augmented Recurrent Nets](https://mlsanity.com/paper/1503.01007/) (2015)
- [Neural Production Systems: Learning Rule-Governed Visual Dynamics](https://mlsanity.com/paper/2103.01937/) (2021)
- [Classical Planning in Deep Latent Space: Bridging the Subsymbolic-Symbolic Boundary](https://mlsanity.com/paper/1705.00154/) (2017)
- [Learning Physical Graph Representations from Visual Scenes](https://mlsanity.com/paper/2006.12373/) (2020)
- [From Word to Sense Embeddings: A Survey on Vector Representations of Meaning](https://mlsanity.com/paper/1805.04032/) (2018)
- [An Explicitly Relational Neural Network Architecture](https://mlsanity.com/paper/1905.10307/) (2019)

## Built on by (most cited first, 9 of 9)

- [Neuro-Symbolic AI in 2024: A Systematic Review](https://mlsanity.com/paper/2501.05435/) (2025)
- [TELLER: A Trustworthy Framework for Explainable, Generalizable and Controllable Fake News Detection](https://mlsanity.com/paper/2402.07776/) (2024)
- [Neuro-Symbolic AI: Explainability, Challenges, and Future Trends](https://mlsanity.com/paper/2411.04383/) (2024)
- [Neuro-symbolic Rule Learning in Real-world Classification Tasks](https://mlsanity.com/paper/2303.16674/) (2023)
- [Neural DNF-MT: A Neuro-symbolic Approach for Learning Interpretable and Editable Policies](https://mlsanity.com/paper/2501.03888/) (2025)
- [Learning Type-Generalized Actions for Symbolic Planning](https://mlsanity.com/paper/2308.04867/) (2023)
- [Neural Logic Networks for Interpretable Classification](https://mlsanity.com/paper/2508.08172/) (2025)
- [Bridging the Gap: Representation Spaces in Neuro-Symbolic AI](https://mlsanity.com/paper/2411.04393/) (2024)
- [Disentangling Neural Disjunctive Normal Form Models](https://mlsanity.com/paper/2507.10546/) (2025)

## Abstract (arXiv)

Humans have the ability to seamlessly combine low-level visual input with high-level symbolic reasoning often in the form of recognising objects, learning relations between them and applying rules. Neuro-symbolic systems aim to bring a unifying approach to connectionist and logic-based principles for visual processing and abstract reasoning respectively. This paper presents a complete neuro-symbolic method for processing images into objects, learning relations and logical rules in an end-to-end fashion. The main contribution is a differentiable layer in a deep learning architecture from which symbolic relations and rules can be extracted by pruning and thresholding. We evaluate our model using two datasets: subgraph isomorphism task for symbolic rule learning and an image classification domain with compound relations for learning objects, relations and rules. We demonstrate that our model scales beyond state-of-the-art symbolic learners and outperforms deep relational neural network architectures.