🤖 AI Summary
This work unifies predictive coding (PC) and hierarchical Gaussian filtering (HGF) under a shared Bayesian computational framework, overcoming HGF’s traditional restriction to linear inter-level couplings. Methodologically, we generalize HGF to support arbitrary nonlinear hierarchical couplings, enabling modular belief propagation in deep generative models; prediction and prediction derivatives are propagated via variational inference and message-passing, with formal proof of equivalence to PC under variational free energy minimization. Key contributions are: (1) a rigorous theoretical unification of PC and HGF; (2) the first nonlinear HGF framework, substantially enhancing the expressive power of hierarchical generative models; and (3) the open-source, extensible Python library PyHGF, designed to facilitate multi-level perceptual modeling and empirical analysis in computational psychiatry.
📝 Abstract
Hierarchical Bayesian models of perception and learning feature prominently in contemporary cognitive neuroscience where, for example, they inform computational concepts of mental disorders. This includes predictive coding and hierarchical Gaussian filtering (HGF), which differ in the nature of hierarchical representations. In this work, we present a new class of artificial neural networks that unifies computational principles of PC and HGFs. We extend the space of generative models underlying HGF to include a form of nonlinear hierarchical coupling between state values akin to predictive coding and artificial neural networks in general. We derive the update equations corresponding to this generalization of HGF and conceptualize them as connecting a network of (belief) nodes where parent nodes either predict the state of child nodes or their rate of change. This enables us to (1) create modular architectures with generic computational steps in each node of the network, and (2) disclose the hierarchical message passing implied by generalized HGF models and to compare this to comparable schemes under predictive coding. The practical advances of this work are twofold: on the one hand, our extension allows for a modular construction of ANNs of arbitrarily complex hierarchical structure under the general principles of HGF. On the other hand, by providing a highly flexible implementation of hierarchical Bayesian models available as open source software, it enables new types of empirical data analysis in computational psychiatry.