# Learning Hierarchical Relational Representations through Relational Convolutions

arXiv: https://arxiv.org/abs/2310.03240 · HTML: https://mlsanity.com/paper/2310.03240/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 40 references that are in the map.
- First posted on arXiv 5 Oct 2023.

## Builds on (most cited first, 29 of 29)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Visualizing and Understanding Convolutional Networks](https://mlsanity.com/paper/1311.2901/) (2013)
- [Modeling Relational Data with Graph Convolutional Networks](https://mlsanity.com/paper/1703.06103/) (2017)
- [CLEVR: A Diagnostic Dataset for Compositional Language and Elementary Visual Reasoning](https://mlsanity.com/paper/1612.06890/) (2016)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [Object-Centric Learning with Slot Attention](https://mlsanity.com/paper/2006.15055/) (2020)
- [Dynamic Routing Between Capsules](https://mlsanity.com/paper/1710.09829/) (2017)
- [Multi-Object Representation Learning with Iterative Variational Inference](https://mlsanity.com/paper/1903.00450/) (2019)
- [A simple neural network module for relational reasoning](https://mlsanity.com/paper/1706.01427/) (2017)
- [Neural Relational Inference for Interacting Systems](https://mlsanity.com/paper/1802.04687/) (2018)
- [Learning Convolutional Neural Networks for Graphs](https://mlsanity.com/paper/1605.05273/) (2016)
- [Conditional Object-Centric Learning from Video](https://mlsanity.com/paper/2111.12594/) (2021)
- [Relational recurrent neural networks](https://mlsanity.com/paper/1806.01822/) (2018)
- [Entropy-based Attention Regularization Frees Unintended Bias Mitigation from Lists](https://mlsanity.com/paper/2203.09192/) (2022)
- [Emergent Symbols through Binding in External Memory](https://mlsanity.com/paper/2012.14601/) (2020)
- [Sparse and Continuous Attention Mechanisms](https://mlsanity.com/paper/2006.07214/) (2020)
- [A Regularized Framework for Sparse and Structured Neural Attention](https://mlsanity.com/paper/1705.07704/) (2017)
- [Learning Representations that Support Extrapolation](https://mlsanity.com/paper/2007.05059/) (2020)
- [An Explicitly Relational Neural Network Architecture](https://mlsanity.com/paper/1905.10307/) (2019)
- [The Relational Bottleneck as an Inductive Bias for Efficient Abstraction](https://mlsanity.com/paper/2309.06629/) (2023)
- [On Neural Architecture Inductive Biases for Relational Tasks](https://mlsanity.com/paper/2206.05056/) (2022)
- [Abstractors and relational cross-attention: An inductive bias for explicit relational reasoning in Transformers](https://mlsanity.com/paper/2304.00195/) (2023)

## Built on by (most cited first, 2 of 2)

- [Approximation of relation functions and attention mechanisms](https://mlsanity.com/paper/2402.08856/) (2024)
- [Disentangling and Integrating Relational and Sensory Information in Transformer Architectures](https://mlsanity.com/paper/2405.16727/) (2024)

## Abstract (arXiv)

An evolving area of research in deep learning is the study of architectures and inductive biases that support the learning of relational feature representations. In this paper, we address the challenge of learning representations of hierarchical relations--that is, higher-order relational patterns among groups of objects. We introduce "relational convolutional networks", a neural architecture equipped with computational mechanisms that capture progressively more complex relational features through the composition of simple modules. A key component of this framework is a novel operation that captures relational patterns in groups of objects by convolving graphlet filters--learnable templates of relational patterns--against subsets of the input. Composing relational convolutions gives rise to a deep architecture that learns representations of higher-order, hierarchical relations. We present the motivation and details of the architecture, together with a set of experiments to demonstrate how relational convolutional networks can provide an effective framework for modeling relational tasks that have hierarchical structure.