# Fast Dynamic Routing Based on Weighted Kernel Density Estimation

arXiv: https://arxiv.org/abs/1805.10807 · HTML: https://mlsanity.com/paper/1805.10807/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 May 2018.

## Built on by (most cited first, 8 of 8)

- [Found a Reason for me? Weakly-supervised Grounded Visual Question Answering using Capsules](https://mlsanity.com/paper/2105.04836/) (2021)
- [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)
- [Graph Routing between Capsules](https://mlsanity.com/paper/2106.11531/) (2021)
- [Routing with Self-Attention for Multimodal Capsule Networks](https://mlsanity.com/paper/2112.00775/) (2021)
- [How to Accelerate Capsule Convolutions in Capsule Networks](https://mlsanity.com/paper/2104.02621/) (2021)
- [Capsule networks with non-iterative cluster routing](https://mlsanity.com/paper/2109.09213/) (2021)
- [Capsule network with shortcut routing](https://mlsanity.com/paper/2307.10212/) (2023)

## Abstract (arXiv)

Capsules as well as dynamic routing between them are most recently proposed structures for deep neural networks. A capsule groups data into vectors or matrices as poses rather than conventional scalars to represent specific properties of target instance. Besides of pose, a capsule should be attached with a probability (often denoted as activation) for its presence. The dynamic routing helps capsules achieve more generalization capacity with many fewer model parameters. However, the bottleneck that prevents widespread applications of capsule is the expense of computation during routing. To address this problem, we generalize existing routing methods within the framework of weighted kernel density estimation, and propose two fast routing methods with different optimization strategies. Our methods prompt the time efficiency of routing by nearly 40% with negligible performance degradation. By stacking a hybrid of convolutional layers and capsule layers, we construct a network architecture to handle inputs at a resolution of 64×64 pixels. The proposed models achieve a parallel performance with other leading methods in multiple benchmarks.