Inference and Learning for Generative Capsule Models

TL;DR

This paper introduces a generative capsule model with variational inference and learning algorithms, demonstrating improved performance over previous methods on geometric and face data.

Contribution

It develops a new generative model for capsule networks and derives variational inference and learning algorithms, outperforming prior autoencoder-based approaches.

Findings

Outperforms stacked capsule autoencoders on constellation data

Provides effective variational inference algorithms for capsule models

Demonstrates applicability to geometric and face data

Abstract

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).