# Relational Reasoning Networks

arXiv: https://arxiv.org/abs/2106.00393 · HTML: https://mlsanity.com/paper/2106.00393/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 86 references that are in the map.
- First posted on arXiv 1 Jun 2021.

## Builds on (most cited first, 30 of 33)

- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Embedding Entities and Relations for Learning and Inference in Knowledge Bases](https://mlsanity.com/paper/1412.6575/) (2014)
- [Complex Embeddings for Simple Link Prediction](https://mlsanity.com/paper/1606.06357/) (2016)
- [Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networks](https://mlsanity.com/paper/1810.02244/) (2018)
- [Convolutional 2D Knowledge Graph Embeddings](https://mlsanity.com/paper/1707.01476/) (2017)
- [Neural Probabilistic Logic Programming in DeepProbLog](https://mlsanity.com/paper/1907.08194/) (2019)
- [Interpretable Machine Learning: Fundamental Principles and 10 Grand Challenges](https://mlsanity.com/paper/2103.11251/) (2021)
- [The Expressive Power of Neural Networks: A View from the Width](https://mlsanity.com/paper/1709.02540/) (2017)
- [A Semantic Loss Function for Deep Learning with Symbolic Knowledge](https://mlsanity.com/paper/1711.11157/) (2017)
- [DeepPath: A Reinforcement Learning Method for Knowledge Graph Reasoning](https://mlsanity.com/paper/1707.06690/) (2017)
- [A Review of Relational Machine Learning for Knowledge Graphs](https://mlsanity.com/paper/1503.00759/) (2015)
- [Neurosymbolic AI: The 3rd Wave](https://mlsanity.com/paper/2012.05876/) (2020)
- [End-to-End Differentiable Proving](https://mlsanity.com/paper/1705.11040/) (2017)
- [Neural Logic Machines](https://mlsanity.com/paper/1904.11694/) (2019)
- [Harnessing Deep Neural Networks with Logic Rules](https://mlsanity.com/paper/1603.06318/) (2016)
- [Beta Embeddings for Multi-Hop Logical Reasoning in Knowledge Graphs](https://mlsanity.com/paper/2010.11465/) (2020)
- [Logic Tensor Networks for Semantic Image Interpretation](https://mlsanity.com/paper/1705.08968/) (2017)
- [The Logic of Graph Neural Networks](https://mlsanity.com/paper/2104.14624/) (2021)
- [Probabilistic Logic Neural Networks for Reasoning](https://mlsanity.com/paper/1906.08495/) (2019)
- [Hinge-Loss Markov Random Fields and Probabilistic Soft Logic](https://mlsanity.com/paper/1505.04406/) (2015)
- [A Semantic Matching Energy Function for Learning with Multi-relational Data](https://mlsanity.com/paper/1301.3485/) (2013)
- [Learning Reasoning Strategies in End-to-End Differentiable Proving](https://mlsanity.com/paper/2007.06477/) (2020)
- [Neural Enhanced Belief Propagation on Factor Graphs](https://mlsanity.com/paper/2003.01998/) (2020)
- [Knowledge Graph Embedding with Iterative Guidance from Soft Rules](https://mlsanity.com/paper/1711.11231/) (2017)
- [Efficient Probabilistic Logic Reasoning with Graph Neural Networks](https://mlsanity.com/paper/2001.11850/) (2020)
- [Social Adaptive Module for Weakly-supervised Group Activity Recognition](https://mlsanity.com/paper/2007.09470/) (2020)
- [Belief Propagation Neural Networks](https://mlsanity.com/paper/2007.00295/) (2020)
- [Integrating Learning and Reasoning with Deep Logic Models](https://mlsanity.com/paper/1901.04195/) (2019)
- [Relational Neural Machines](https://mlsanity.com/paper/2002.02193/) (2020)

## Built on by (most cited first, 4 of 4)

- [Neurosymbolic AI for Reasoning over Knowledge Graphs: A Survey](https://mlsanity.com/paper/2302.07200/) (2023)
- [Relational Concept Bottleneck Models](https://mlsanity.com/paper/2308.11991/) (2023)
- [Grounding Methods for Neural-Symbolic AI](https://mlsanity.com/paper/2507.08216/) (2025)
- [Enhancing Embedding Representations of Biomedical Data using Logic Knowledge](https://mlsanity.com/paper/2303.13566/) (2023)

## Abstract (arXiv)

Neuro-symbolic methods integrate neural architectures, knowledge representation and reasoning. However, they have been struggling at both dealing with the intrinsic uncertainty of the observations and scaling to real-world applications. This paper presents Relational Reasoning Networks (R2N), a novel end-to-end model that performs relational reasoning in the latent space of a deep learner architecture, where the representations of constants, ground atoms and their manipulations are learned in an integrated fashion. Unlike flat architectures like Knowledge Graph Embedders, which can only represent relations between entities, R2Ns define an additional computational structure, accounting for higher-level relations among the ground atoms. The considered relations can be explicitly known, like the ones defined by logic formulas, or defined as unconstrained correlations among groups of ground atoms. R2Ns can be applied to purely symbolic tasks or as a neuro-symbolic platform to integrate learning and reasoning in heterogeneous problems with both symbolic and feature-based represented entities. The proposed model overtakes the limitations of previous neuro-symbolic methods that have been either limited in terms of scalability or expressivity. The proposed methodology is shown to achieve state-of-the-art results in different experimental settings.