HGF-based Active Inference

Here is developed and expanded the implementation of active inference in continuous state space using filtering of sufficient statistics with hierarchical Gaussian filters

Phi Fluctuates with Surprisal

Simulation project relating the Free Energy Principle and Integrated Information Theory. The ZIP file contains all code and data necessary for replicating the analysis

Introducing tomsup: Theory of Mind Simulations using Python

This is a data repository to store the example simulated data from the usage example in the paper of the same name. The data can be recreated using the time-stamped version of the tomsup package

Phi Fluctuates with Surprise: An empirical pre-study for the synthesis of the Free Energy Principle and Integrated Information Theory

The Free Energy Principle (FEP) and Integrated Information Theory (IIT) are two ambitious theoretical approaches. The first aims to make a formal framework for describing self-organizing and life-like systems in general, and the second attempts a mathematical theory of conscious experience based on the intrinsic properties of a system. They are each concerned with complementary aspects of the properties of systems, one with life and behavior, the other with meaning and experience, so combining them has potential for scientific value. In this paper, we take a first step towards such a synthesis by expanding on the results of the evolutionary simulation study by Albantakis et al. (2014), which show a relationship between IIT-measures and fitness in differing complexities of tasks. We relate some basic FEP-related information theoretic measures to this result, finding that the surprisal of simulated agents’ observations is inversely related to the general increase in fitness and integration over evolutionary time. Moreover, surprisal fluctuates together with IIT-based consciousness measures in within-trial time. This suggests that the consciousness measures used in IIT indirectly depend on the relation between the agent and the external world, and that it should therefore be possible to relate them to the theoretical concepts used in the FEP. Lastly, we suggest a future approach for investigating this relationship empirically

The generalized Hierarchical Gaussian Filter

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. Predictive coding assumes that higher levels in a given hierarchy influence the state (value) of lower levels. In HGF, however, higher levels determine the rate of change at lower levels. Here, 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. We find that the algorithmic architecture instantiated by the generalized HGF is largely compatible with that of predictive coding but extends it with some unique predictions which arise from precision and volatility related computations. Our developments enable highly flexible implementations of hierarchical Bayesian models for empirical data analysis and are available as open source software