# Inference and Learning for Generative Capsule Models

arXiv: https://arxiv.org/abs/2209.03115 · HTML: https://mlsanity.com/paper/2209.03115/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 39 references that are in the map.
- First posted on arXiv 7 Sep 2022.

## Builds on (most cited first, 7 of 7)

- [Dynamic Routing Between Capsules](https://mlsanity.com/paper/1710.09829/) (2017)
- [Iterative Amortized Inference](https://mlsanity.com/paper/1807.09356/) (2018)
- [Stacked Capsule Autoencoders](https://mlsanity.com/paper/1906.06818/) (2019)
- [Capsule Routing via Variational Bayes](https://mlsanity.com/paper/1905.11455/) (2019)
- [Learning with Capsules: A Survey](https://mlsanity.com/paper/2206.02664/) (2022)
- [Autoencoders and Probabilistic Inference with Missing Data: An Exact Solution for The Factor Analysis Case](https://mlsanity.com/paper/1801.03851/) (2018)
- [Inference for Generative Capsule Models](https://mlsanity.com/paper/2103.06676/) (2021)

## Built on by (most cited first, 2 of 2)

- [Structured Generative Models for Scene Understanding](https://mlsanity.com/paper/2302.03531/) (2023)
- [Of Mice and Mates: Automated Classification and Modelling of Mouse Behaviour in Groups using a Single Model across Cages](https://mlsanity.com/paper/2306.03066/) (2023)

## Abstract (arXiv)

Capsule networks (see e.g. Hinton et al., 2018) aim to encode knowledge of and reason about the relationship between an object and its parts. In this paper we specify a generative model for such data, and derive a variational algorithm for inferring the transformation of each model object in a scene, and the assignments of observed parts to the objects. We derive a learning algorithm for the object models, based on variational expectation maximization (Jordan et al., 1999). We also study an alternative inference algorithm based on the RANSAC method of Fischler and Bolles (1981). We apply these inference methods to (i) data generated from multiple geometric objects like squares and triangles ("constellations"), and (ii) data from a parts-based model of faces. Recent work by Kosiorek et al. (2019) has used amortized inference via stacked capsule autoencoders (SCAEs) to tackle this problem -- our results show that we significantly outperform them where we can make comparisons (on the constellations data).