Renormalising generative models

Karl Friston ^1,2* Conor Heins ² Tim Verbelen ² Lancelot Da Costa ² Tommaso Salvatori ² Dimitrije Marković ³ Alexander Tschantz ² Magnus Koudahl ² Christopher Buckley ^2,4 Thomas Parr ⁵

• ¹ University College London, London, United Kingdom
• ² VERSES Research Lab, Los Angeles, United States
• ³ Technical University Dresden, Dresden, Lower Saxony, Germany
• ⁴ University of Sussex, Brighton, West Sussex, United Kingdom
• ⁵ Nuffield Department of Clinical Neurosciences, Medical Sciences Division, University of Oxford, Oxford, England, United Kingdom

This paper describes a discrete state-space model-and accompanying methods-for generative modelling. This model generalises partially observed Markov decision processes to include paths as latent variables, rendering it suitable for active inference and learning in a dynamic setting. Specifically, we consider deep or hierarchical forms using the renormalisation group. The ensuing renormalising generative models (RGM) can be regarded as discrete homologues of deep convolutional neural networks or continuous state-space models in generalised coordinates of motion. By construction, these scale-invariant models can be used to learn compositionality over space and time, furnishing models of paths or orbits; i.e., events of increasing temporal depth and itinerancy. This technical note illustrates the automatic discovery, learning and deployment of RGMs using a series of applications. We start with image classification and then consider the compression and generation of movies and music. Finally, we apply the same variational principles to the learning of Atari-like games.