# Recurrent Relational Networks

arXiv: https://arxiv.org/abs/1711.08028 · HTML: https://mlsanity.com/paper/1711.08028/

## Key facts

- Cited by 72 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Nov 2017.

## Built on by (most cited first, 30 of 72)

- [Combinatorial optimization and reasoning with graph neural networks](https://mlsanity.com/paper/2102.09544/) (2021)
- [Hierarchical Reasoning Model](https://mlsanity.com/paper/2506.21734/) (2025)
- [NeurASP: Embracing Neural Networks into Answer Set Programming](https://mlsanity.com/paper/2307.07700/) (2023)
- [Dirichlet Diffusion Score Model for Biological Sequence Generation](https://mlsanity.com/paper/2305.10699/) (2023)
- [StepGame: A New Benchmark for Robust Multi-Hop Spatial Reasoning in Texts](https://mlsanity.com/paper/2204.08292/) (2022)
- [Coupling Large Language Models with Logic Programming for Robust and General Reasoning from Text](https://mlsanity.com/paper/2307.07696/) (2023)
- [Artificial Kuramoto Oscillatory Neurons](https://mlsanity.com/paper/2410.13821/) (2024)
- [Deep Learning Methods for Abstract Visual Reasoning: A Survey on Raven's Progressive Matrices](https://mlsanity.com/paper/2201.12382/) (2022)
- [Learning Iterative Reasoning through Energy Diffusion](https://mlsanity.com/paper/2406.11179/) (2024)
- [End-to-end Algorithm Synthesis with Recurrent Networks: Logical Extrapolation Without Overthinking](https://mlsanity.com/paper/2202.05826/) (2022)
- [Neural Algorithmic Reasoning with Causal Regularisation](https://mlsanity.com/paper/2302.10258/) (2023)
- [Goal-Aware Neural SAT Solver](https://mlsanity.com/paper/2106.07162/) (2021)
- [Techniques for Symbol Grounding with SATNet](https://mlsanity.com/paper/2106.11072/) (2021)
- [When can transformers reason with abstract symbols?](https://mlsanity.com/paper/2310.09753/) (2023)
- [Learning to Solve Constraint Satisfaction Problems with Recurrent Transformer](https://mlsanity.com/paper/2307.04895/) (2023)
- [Injecting Logical Constraints into Neural Networks via Straight-Through Estimators](https://mlsanity.com/paper/2307.04347/) (2023)
- [SALSA-CLRS: A Sparse and Scalable Benchmark for Algorithmic Reasoning](https://mlsanity.com/paper/2309.12253/) (2023)
- [Neuro-symbolic Learning Yielding Logical Constraints](https://mlsanity.com/paper/2410.20957/) (2024)
- [Graphically Structured Diffusion Models](https://mlsanity.com/paper/2210.11633/) (2022)
- [Assessing SATNet's Ability to Solve the Symbol Grounding Problem](https://mlsanity.com/paper/2312.11522/) (2023)
- [Efficient Rectification of Neuro-Symbolic Reasoning Inconsistencies by Abductive Reflection](https://mlsanity.com/paper/2412.08457/) (2024)
- [Think Shallow, Solve Deep: Controlling Recurrent Dynamics for Reliable Test-Time Depth](https://mlsanity.com/paper/2608.18222/) (2026)
- [Two-stage Rule-induction Visual Reasoning on RPMs with an Application to Video Prediction](https://mlsanity.com/paper/2111.12301/) (2021)
- [Learning Graph Algorithms With Recurrent Graph Neural Networks](https://mlsanity.com/paper/2212.04934/) (2022)
- [Disentangling Extraction and Reasoning in Multi-hop Spatial Reasoning](https://mlsanity.com/paper/2310.16731/) (2023)
- [VFScale: Intrinsic Reasoning through Verifier-Free Test-time Scalable Diffusion Model](https://mlsanity.com/paper/2502.01989/) (2025)
- [Self-Supervised Transformers as Iterative Solution Improvers for Constraint Satisfaction](https://mlsanity.com/paper/2502.15794/) (2025)
- [A Solver-Free Framework for Scalable Learning in Neural ILP Architectures](https://mlsanity.com/paper/2210.09082/) (2022)
- [Recurrent Self-Attention Dynamics: An Energy-Agnostic Perspective from Jacobians](https://mlsanity.com/paper/2505.19458/) (2025)
- [Down and Across: Introducing Crossword-Solving as a New NLP Benchmark](https://mlsanity.com/paper/2205.10442/) (2022)

## Abstract (arXiv)

This paper is concerned with learning to solve tasks that require a chain of interdependent steps of relational inference, like answering complex questions about the relationships between objects, or solving puzzles where the smaller elements of a solution mutually constrain each other. We introduce the recurrent relational network, a general purpose module that operates on a graph representation of objects. As a generalization of Santoro et al. [2017]'s relational network, it can augment any neural network model with the capacity to do many-step relational reasoning. We achieve state of the art results on the bAbI textual question-answering dataset with the recurrent relational network, consistently solving 20/20 tasks. As bAbI is not particularly challenging from a relational reasoning point of view, we introduce Pretty-CLEVR, a new diagnostic dataset for relational reasoning. In the Pretty-CLEVR set-up, we can vary the question to control for the number of relational reasoning steps that are required to obtain the answer. Using Pretty-CLEVR, we probe the limitations of multi-layer perceptrons, relational and recurrent relational networks. Finally, we show how recurrent relational networks can learn to solve Sudoku puzzles from supervised training data, a challenging task requiring upwards of 64 steps of relational reasoning. We achieve state-of-the-art results amongst comparable methods by solving 96.6% of the hardest Sudoku puzzles.