Differentiable Generalised Predictive Coding

This paper deals with differentiable dynamical models congruent with neural process theories in neuroscience that cast brain function as hierarchical filtering aiming at the refinement of an internal generative model explaining observations. Our work extends existing implementations of predictive coding with exact gradients and allows integration with deep neural networks for non-linear latent state parameterization. In contrast to Gradient Descent in combination with error backpropagation, such gradient based predictive coding optimises neural networks locally in each layer by optimising precision-weighted prediction errors that propagate from data towards latent states. Predictions flow backwards, from latent states towards lower layers. The model suggested here, GPC, uses exact gradients to learn hierarchical and dynamical predictions of lower latent states. Hierarchical predictions encode the perceived content and its structure. Dynamical predictions address changes in the encoded content. As a result, hierarchical and dynamical predictions address different aspects of the same latent states. Since changes in latent states are influenced by the content they represent and vice versa, both pathways interact and allow to encode representations of content-dynamics dependencies across spatio-temporal scales and even backwards in time. We apply GPC to various perception tasks on sequential data with adaptive sampling rates. We discuss possibilities to relax the assumption of linearly hierarchical model layout in favour of arbitrary graph structure. Finally, we sketch out ideas for efficient perception and planning in nested spatio-temporal hierarchies and discuss the connection to Markov Blankets in the brain.