# ProtoCaps: A Fast and Non-Iterative Capsule Network Routing Method

arXiv: https://arxiv.org/abs/2307.09944 · HTML: https://mlsanity.com/paper/2307.09944/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 27 references that are in the map.
- First posted on arXiv 19 Jul 2023.

## Builds on (most cited first, 13 of 13)

- [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)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Searching for MobileNetV3](https://mlsanity.com/paper/1905.02244/) (2019)
- [Deep Clustering for Unsupervised Learning of Visual Features](https://mlsanity.com/paper/1807.05520/) (2018)
- [Dynamic Routing Between Capsules](https://mlsanity.com/paper/1710.09829/) (2017)
- [Efficient-CapsNet: Capsule Network with Self-Attention Routing](https://mlsanity.com/paper/2101.12491/) (2021)
- [Capsule Routing via Variational Bayes](https://mlsanity.com/paper/1905.11455/) (2019)
- [Learning with Capsules: A Survey](https://mlsanity.com/paper/2206.02664/) (2022)
- [Why Capsule Neural Networks Do Not Scale: Challenging the Dynamic Parse-Tree Assumption](https://mlsanity.com/paper/2301.01583/) (2023)
- [Routing with Self-Attention for Multimodal Capsule Networks](https://mlsanity.com/paper/2112.00775/) (2021)
- [Vanishing Activations: A Symptom of Deep Capsule Networks](https://mlsanity.com/paper/2305.11178/) (2023)

## Built on by (most cited first, 4 of 4)

- [Capsule Network Projectors are Equivariant and Invariant Learners](https://mlsanity.com/paper/2405.14386/) (2024)
- [Blind Source Separation of Single-Channel Mixtures via Multi-Encoder Autoencoders](https://mlsanity.com/paper/2309.07138/) (2023)
- [Masked Capsule Autoencoders](https://mlsanity.com/paper/2403.04724/) (2024)
- [PR-CapsNet: Pseudo-Riemannian Capsule Network with Adaptive Curvature Routing for Graph Learning](https://mlsanity.com/paper/2512.08218/) (2025)

## Abstract (arXiv)

Capsule Networks have emerged as a powerful class of deep learning architectures, known for robust performance with relatively few parameters compared to Convolutional Neural Networks (CNNs). However, their inherent efficiency is often overshadowed by their slow, iterative routing mechanisms which establish connections between Capsule layers, posing computational challenges resulting in an inability to scale. In this paper, we introduce a novel, non-iterative routing mechanism, inspired by trainable prototype clustering. This innovative approach aims to mitigate computational complexity, while retaining, if not enhancing, performance efficacy. Furthermore, we harness a shared Capsule subspace, negating the need to project each lower-level Capsule to each higher-level Capsule, thereby significantly reducing memory requisites during training. Our approach demonstrates superior results compared to the current best non-iterative Capsule Network and tests on the Imagewoof dataset, which is too computationally demanding to handle efficiently by iterative approaches. Our findings underscore the potential of our proposed methodology in enhancing the operational efficiency and performance of Capsule Networks, paving the way for their application in increasingly complex computational scenarios. Code is available at https://github.com/mileseverett/ProtoCaps.