# Capsule networks with non-iterative cluster routing

arXiv: https://arxiv.org/abs/2109.09213 · HTML: https://mlsanity.com/paper/2109.09213/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 30 of its 48 references that are in the map.
- First posted on arXiv 19 Sep 2021.

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

- [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)
- [Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks](https://mlsanity.com/paper/1506.01497/) (2015)
- [Mask R-CNN](https://mlsanity.com/paper/1703.06870/) (2017)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [You Only Look Once: Unified, Real-Time Object Detection](https://mlsanity.com/paper/1506.02640/) (2015)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Group Normalization](https://mlsanity.com/paper/1803.08494/) (2018)
- [Instance Normalization: The Missing Ingredient for Fast Stylization](https://mlsanity.com/paper/1607.08022/) (2016)
- [Dynamic Routing Between Capsules](https://mlsanity.com/paper/1710.09829/) (2017)
- [Strike (with) a Pose: Neural Networks Are Easily Fooled by Strange Poses of Familiar Objects](https://mlsanity.com/paper/1811.11553/) (2018)
- [Exploring the Landscape of Spatial Robustness](https://mlsanity.com/paper/1712.02779/) (2017)
- [Capsule Routing via Variational Bayes](https://mlsanity.com/paper/1905.11455/) (2019)
- [Group Equivariant Capsule Networks](https://mlsanity.com/paper/1806.05086/) (2018)
- [Capsules for Object Segmentation](https://mlsanity.com/paper/1804.04241/) (2018)
- [VideoCapsuleNet: A Simplified Network for Action Detection](https://mlsanity.com/paper/1805.08162/) (2018)
- [Capsules with Inverted Dot-Product Attention Routing](https://mlsanity.com/paper/2002.04764/) (2020)
- [Attention routing between capsules](https://mlsanity.com/paper/1907.01750/) (2019)
- [Neural Network Encapsulation](https://mlsanity.com/paper/1808.03749/) (2018)
- [Fast Dynamic Routing Based on Weighted Kernel Density Estimation](https://mlsanity.com/paper/1805.10807/) (2018)
- [HitNet: a neural network with capsules embedded in a Hit-or-Miss layer, extended with hybrid data augmentation and ghost capsules](https://mlsanity.com/paper/1806.06519/) (2018)
- [CapsuleGAN: Generative Adversarial Capsule Network](https://mlsanity.com/paper/1802.06167/) (2018)
- [Dense and Diverse Capsule Networks: Making the Capsules Learn Better](https://mlsanity.com/paper/1805.04001/) (2018)
- [Capsule Networks with Max-Min Normalization](https://mlsanity.com/paper/1903.09662/) (2019)
- [Generalized Capsule Networks with Trainable Routing Procedure](https://mlsanity.com/paper/1808.08692/) (2018)
- [Generative Adversarial Network Architectures For Image Synthesis Using Capsule Networks](https://mlsanity.com/paper/1806.03796/) (2018)
- [An Effective Hit-or-Miss Layer Favoring Feature Interpretation as Learned Prototypes Deformations](https://mlsanity.com/paper/1911.05588/) (2019)
- [Pushing the Limits of Capsule Networks](https://mlsanity.com/paper/2103.08074/) (2021)
- [CapsGAN: Using Dynamic Routing for Generative Adversarial Networks](https://mlsanity.com/paper/1806.03968/) (2018)

## Abstract (arXiv)

Capsule networks use routing algorithms to flow information between consecutive layers. In the existing routing procedures, capsules produce predictions (termed votes) for capsules of the next layer. In a nutshell, the next-layer capsule's input is a weighted sum over all the votes it receives. In this paper, we propose non-iterative cluster routing for capsule networks. In the proposed cluster routing, capsules produce vote clusters instead of individual votes for next-layer capsules, and each vote cluster sends its centroid to a next-layer capsule. Generally speaking, the next-layer capsule's input is a weighted sum over the centroid of each vote cluster it receives. The centroid that comes from a cluster with a smaller variance is assigned a larger weight in the weighted sum process. Compared with the state-of-the-art capsule networks, the proposed capsule networks achieve the best accuracy on the Fashion-MNIST and SVHN datasets with fewer parameters, and achieve the best accuracy on the smallNORB and CIFAR-10 datasets with a moderate number of parameters. The proposed capsule networks also produce capsules with disentangled representation and generalize well to images captured at novel viewpoints. The proposed capsule networks also preserve 2D spatial information of an input image in the capsule channels: if the capsule channels are rotated, the object reconstructed from these channels will be rotated by the same transformation. Codes are available at https://github.com/ZHAOZHIHAO/ClusterRouting.