# Relational Neural Machines

arXiv: https://arxiv.org/abs/2002.02193 · HTML: https://mlsanity.com/paper/2002.02193/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Feb 2020.

## Built on by (most cited first, 19 of 19)

- [From Statistical Relational to Neurosymbolic Artificial Intelligence: a Survey](https://mlsanity.com/paper/2108.11451/) (2021)
- [Interpretable Neural-Symbolic Concept Reasoning](https://mlsanity.com/paper/2304.14068/) (2023)
- [Modular Design Patterns for Hybrid Learning and Reasoning Systems: a taxonomy, patterns and use cases](https://mlsanity.com/paper/2102.11965/) (2021)
- [Towards Data-and Knowledge-Driven Artificial Intelligence: A Survey on Neuro-Symbolic Computing](https://mlsanity.com/paper/2210.15889/) (2022)
- [EXplainable Neural-Symbolic Learning (X-NeSyL) methodology to fuse deep learning representations with expert knowledge graphs: the MonuMAI cultural heritage use case](https://mlsanity.com/paper/2104.11914/) (2021)
- [Differentiable Inductive Logic Programming for Structured Examples](https://mlsanity.com/paper/2103.01719/) (2021)
- [A Comprehensive Survey on Self-Interpretable Neural Networks](https://mlsanity.com/paper/2501.15638/) (2025)
- [Differentiable Rule Induction with Learned Relational Features](https://mlsanity.com/paper/2201.06515/) (2022)
- [Naturally Supervised 3D Visual Grounding with Language-Regularized Concept Learners](https://mlsanity.com/paper/2404.19696/) (2024)
- [A Critical Review of Inductive Logic Programming Techniques for Explainable AI](https://mlsanity.com/paper/2112.15319/) (2021)
- [Relational Reasoning Networks](https://mlsanity.com/paper/2106.00393/) (2021)
- [DeepPSL: End-to-end perception and reasoning](https://mlsanity.com/paper/2109.13662/) (2021)
- [Knowledge Enhanced Neural Networks for relational domains](https://mlsanity.com/paper/2205.15762/) (2022)
- [LogicMP: A Neuro-symbolic Approach for Encoding First-order Logic Constraints](https://mlsanity.com/paper/2309.15458/) (2023)
- [Grounding Methods for Neural-Symbolic AI](https://mlsanity.com/paper/2507.08216/) (2025)
- [Knowledge Enhanced Graph Neural Networks for Graph Completion](https://mlsanity.com/paper/2303.15487/) (2023)
- [Parallel Neurosymbolic Integration with Concordia](https://mlsanity.com/paper/2306.00480/) (2023)
- [EM-NeSy: Expectation Maximization for Neurosymbolic Learning](https://mlsanity.com/paper/2606.14463/) (2026)
- [Parallel Noising in Neural Markov Logic Networks](https://mlsanity.com/paper/2607.19126/) (2026)

## Abstract (arXiv)

Deep learning has been shown to achieve impressive results in several tasks where a large amount of training data is available. However, deep learning solely focuses on the accuracy of the predictions, neglecting the reasoning process leading to a decision, which is a major issue in life-critical applications. Probabilistic logic reasoning allows to exploit both statistical regularities and specific domain expertise to perform reasoning under uncertainty, but its scalability and brittle integration with the layers processing the sensory data have greatly limited its applications. For these reasons, combining deep architectures and probabilistic logic reasoning is a fundamental goal towards the development of intelligent agents operating in complex environments. This paper presents Relational Neural Machines, a novel framework allowing to jointly train the parameters of the learners and of a First--Order Logic based reasoner. A Relational Neural Machine is able to recover both classical learning from supervised data in case of pure sub-symbolic learning, and Markov Logic Networks in case of pure symbolic reasoning, while allowing to jointly train and perform inference in hybrid learning tasks. Proper algorithmic solutions are devised to make learning and inference tractable in large-scale problems. The experiments show promising results in different relational tasks.