# Iterative collaborative routing among equivariant capsules for transformation-robust capsule networks

arXiv: https://arxiv.org/abs/2210.11095 · HTML: https://mlsanity.com/paper/2210.11095/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 23 references that are in the map.
- First posted on arXiv 20 Oct 2022.

## Builds on (most cited first, 14 of 14)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Visualizing and Understanding Convolutional Networks](https://mlsanity.com/paper/1311.2901/) (2013)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [Dynamic Routing Between Capsules](https://mlsanity.com/paper/1710.09829/) (2017)
- [Spherical CNNs](https://mlsanity.com/paper/1801.10130/) (2018)
- [General E(2)-Equivariant Steerable CNNs](https://mlsanity.com/paper/1911.08251/) (2019)
- [DeepCaps: Going Deeper with Capsule Networks](https://mlsanity.com/paper/1904.09546/) (2019)
- [Group Equivariant Capsule Networks](https://mlsanity.com/paper/1806.05086/) (2018)
- [DECA: Deep viewpoint-Equivariant human pose estimation using Capsule Autoencoders](https://mlsanity.com/paper/2108.08557/) (2021)
- [Attention routing between capsules](https://mlsanity.com/paper/1907.01750/) (2019)
- [Cross-Domain 3D Equivariant Image Embeddings](https://mlsanity.com/paper/1812.02716/) (2018)
- [Building Deep, Equivariant Capsule Networks](https://mlsanity.com/paper/1908.01300/) (2019)
- [Quaternion Capsule Networks](https://mlsanity.com/paper/2007.04389/) (2020)

## Abstract (arXiv)

Transformation-robustness is an important feature for machine learning models that perform image classification. Many methods aim to bestow this property to models by the use of data augmentation strategies, while more formal guarantees are obtained via the use of equivariant models. We recognise that compositional, or part-whole structure is also an important aspect of images that has to be considered for building transformation-robust models. Thus, we propose a capsule network model that is, at once, equivariant and compositionality-aware. Equivariance of our capsule network model comes from the use of equivariant convolutions in a carefully-chosen novel architecture. The awareness of compositionality comes from the use of our proposed novel, iterative, graph-based routing algorithm, termed Iterative collaborative routing (ICR). ICR, the core of our contribution, weights the predictions made for capsules based on an iteratively averaged score of the degree-centralities of its nearest neighbours. Experiments on transformed image classification on FashionMNIST, CIFAR-10, and CIFAR-100 show that our model that uses ICR outperforms convolutional and capsule baselines to achieve state-of-the-art performance.