# Capsule Routing via Variational Bayes

arXiv: https://arxiv.org/abs/1905.11455 · HTML: https://mlsanity.com/paper/1905.11455/

## Key facts

- Cited by 32 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 May 2019.

## Built on by (most cited first, 30 of 32)

- [Efficient-CapsNet: Capsule Network with Self-Attention Routing](https://mlsanity.com/paper/2101.12491/) (2021)
- [DECA: Deep viewpoint-Equivariant human pose estimation using Capsule Autoencoders](https://mlsanity.com/paper/2108.08557/) (2021)
- [Grounded Object Centric Learning](https://mlsanity.com/paper/2307.09437/) (2023)
- [Effective and Efficient Vote Attack on Capsule Networks](https://mlsanity.com/paper/2102.10055/) (2021)
- [Capsule Network is Not More Robust than Convolutional Network](https://mlsanity.com/paper/2103.15459/) (2021)
- [Lie Group Decompositions for Equivariant Neural Networks](https://mlsanity.com/paper/2310.11366/) (2023)
- [Interpretable part-whole hierarchies and conceptual-semantic relationships in neural networks](https://mlsanity.com/paper/2203.03282/) (2022)
- [Learning with Capsules: A Survey](https://mlsanity.com/paper/2206.02664/) (2022)
- [Identifiable Object-Centric Representation Learning via Probabilistic Slot Attention](https://mlsanity.com/paper/2406.07141/) (2024)
- [An Algorithm for Routing Vectors in Sequences](https://mlsanity.com/paper/2211.11754/) (2022)
- [Spiking CapsNet: A Spiking Neural Network With A Biologically Plausible Routing Rule Between Capsules](https://mlsanity.com/paper/2111.07785/) (2021)
- [Why Capsule Neural Networks Do Not Scale: Challenging the Dynamic Parse-Tree Assumption](https://mlsanity.com/paper/2301.01583/) (2023)
- [XnODR and XnIDR: Two Accurate and Fast Fully Connected Layers For Convolutional Neural Networks](https://mlsanity.com/paper/2111.10854/) (2021)
- [Training Deep Capsule Networks with Residual Connections](https://mlsanity.com/paper/2104.07393/) (2021)
- [ProtoCaps: A Fast and Non-Iterative Capsule Network Routing Method](https://mlsanity.com/paper/2307.09944/) (2023)
- [3DConvCaps: 3DUnet with Convolutional Capsule Encoder for Medical Image Segmentation](https://mlsanity.com/paper/2205.09299/) (2022)
- [Vanishing Activations: A Symptom of Deep Capsule Networks](https://mlsanity.com/paper/2305.11178/) (2023)
- [DPR-CAE: Capsule Autoencoder with Dynamic Part Representation for Image Parsing](https://mlsanity.com/paper/2104.14735/) (2021)
- [Distribution Mismatch Correction for Improved Robustness in Deep Neural Networks](https://mlsanity.com/paper/2110.01955/) (2021)
- [Capsule Networks Do Not Need to Model Everything](https://mlsanity.com/paper/2204.01298/) (2022)
- [Inference and Learning for Generative Capsule Models](https://mlsanity.com/paper/2209.03115/) (2022)
- [Capsule Network Projectors are Equivariant and Invariant Learners](https://mlsanity.com/paper/2405.14386/) (2024)
- [β-CapsNet: Learning Disentangled Representation for CapsNet by Information Bottleneck](https://mlsanity.com/paper/2209.05239/) (2022)
- [Masked Capsule Autoencoders](https://mlsanity.com/paper/2403.04724/) (2024)
- [Capsule networks with non-iterative cluster routing](https://mlsanity.com/paper/2109.09213/) (2021)
- [Momentum Capsule Networks](https://mlsanity.com/paper/2201.11091/) (2022)
- [CapsNet for Medical Image Segmentation](https://mlsanity.com/paper/2203.08948/) (2022)
- [Affordance detection with Dynamic-Tree Capsule Networks](https://mlsanity.com/paper/2211.05200/) (2022)
- [Explainability and Robustness of Deep Visual Classification Models](https://mlsanity.com/paper/2301.01343/) (2023)
- [Capsules as viewpoint learners for human pose estimation](https://mlsanity.com/paper/2302.06194/) (2023)

## Abstract (arXiv)

Capsule networks are a recently proposed type of neural network shown to outperform alternatives in challenging shape recognition tasks. In capsule networks, scalar neurons are replaced with capsule vectors or matrices, whose entries represent different properties of objects. The relationships between objects and their parts are learned via trainable viewpoint-invariant transformation matrices, and the presence of a given object is decided by the level of agreement among votes from its parts. This interaction occurs between capsule layers and is a process called routing-by-agreement. In this paper, we propose a new capsule routing algorithm derived from Variational Bayes for fitting a mixture of transforming gaussians, and show it is possible transform our capsule network into a Capsule-VAE. Our Bayesian approach addresses some of the inherent weaknesses of MLE based models such as the variance-collapse by modelling uncertainty over capsule pose parameters. We outperform the state-of-the-art on smallNORB using 50% fewer capsules than previously reported, achieve competitive performances on CIFAR-10, Fashion-MNIST, SVHN, and demonstrate significant improvement in MNIST to affNIST generalisation over previous works.