Inference and Learning for Generative Capsule Models

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. Here 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). Joint work with Alfredo Nazabal and Nikolaos Tsagkas. If there is time, I will also make some comments on Structured Generative Models for Scene Understanding (arXiv 2302.03531).