# Graph Routing between Capsules

arXiv: https://arxiv.org/abs/2106.11531 · HTML: https://mlsanity.com/paper/2106.11531/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 32 references that are in the map.
- First posted on arXiv 22 Jun 2021.

## Builds on (most cited first, 16 of 16)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Dynamic Routing Between Capsules](https://mlsanity.com/paper/1710.09829/) (2017)
- [Learning Graph Embedding with Adversarial Training Methods](https://mlsanity.com/paper/1901.01250/) (2019)
- [BiERU: Bidirectional Emotional Recurrent Unit for Conversational Sentiment Analysis](https://mlsanity.com/paper/2006.00492/) (2020)
- [Investigating Capsule Networks with Dynamic Routing for Text Classification](https://mlsanity.com/paper/1804.00538/) (2018)
- [Capsule Network Performance on Complex Data](https://mlsanity.com/paper/1712.03480/) (2017)
- [Attention routing between capsules](https://mlsanity.com/paper/1907.01750/) (2019)
- [Towards Scalable and Reliable Capsule Networks for Challenging NLP Applications](https://mlsanity.com/paper/1906.02829/) (2019)
- [Fast Dynamic Routing Based on Weighted Kernel Density Estimation](https://mlsanity.com/paper/1805.10807/) (2018)
- [Compositional Coding Capsule Network with K-Means Routing for Text Classification](https://mlsanity.com/paper/1810.09177/) (2018)
- [Generalized Capsule Networks with Trainable Routing Procedure](https://mlsanity.com/paper/1808.08692/) (2018)
- [Information Aggregation via Dynamic Routing for Sequence Encoding](https://mlsanity.com/paper/1806.01501/) (2018)

## Built on by (most cited first, 5 of 5)

- [Learning with Capsules: A Survey](https://mlsanity.com/paper/2206.02664/) (2022)
- [Flexible Physical Camouflage Generation Based on a Differential Approach](https://mlsanity.com/paper/2402.13575/) (2024)
- [Deep-Attack over the Deep Reinforcement Learning](https://mlsanity.com/paper/2205.00807/) (2022)
- [DOEPatch: Dynamically Optimized Ensemble Model for Adversarial Patches Generation](https://mlsanity.com/paper/2312.16907/) (2023)
- [PR-CapsNet: Pseudo-Riemannian Capsule Network with Adaptive Curvature Routing for Graph Learning](https://mlsanity.com/paper/2512.08218/) (2025)

## Abstract (arXiv)

Routing methods in capsule networks often learn a hierarchical relationship for capsules in successive layers, but the intra-relation between capsules in the same layer is less studied, while this intra-relation is a key factor for the semantic understanding in text data. Therefore, in this paper, we introduce a new capsule network with graph routing to learn both relationships, where capsules in each layer are treated as the nodes of a graph. We investigate strategies to yield adjacency and degree matrix with three different distances from a layer of capsules, and propose the graph routing mechanism between those capsules. We validate our approach on five text classification datasets, and our findings suggest that the approach combining bottom-up routing and top-down attention performs the best. Such an approach demonstrates generalization capability across datasets. Compared to the state-of-the-art routing methods, the improvements in accuracy in the five datasets we used were 0.82, 0.39, 0.07, 1.01, and 0.02, respectively.