Active inference is a leading theory of perception, learning and decision making, which can be applied to neuroscience, robotics, psychology, and machine learning. Active inference is based on the expected free energy, which is mostly justified by the intuitive plausibility of its formulations, e.g., the risk plus ambiguity and information gain / pragmatic value formulations. This paper seek to formalize the problem of deriving these formulations from a single root expected free energy definition, i.e., the unification problem. Then, we study two settings, each one having its own root expected free energy definition. In the first setting, no justification for the expected free energy has been proposed to date, but all the formulations can be recovered from it. However, in this setting, the agent cannot have arbitrary prior preferences over observations. Indeed, only a limited class of prior preferences over observations is compatible with the likelihood mapping of the generative model. In the second setting, a justification of the root expected free energy definition is known, but this setting only accounts for two formulations, i.e., the risk over states plus ambiguity and entropy plus expected energy formulations.

Deep learning's immense capabilities are often constrained by the complexity of its models, leading to an increasing demand for effective sparsification techniques. Bayesian sparsification for deep learning emerges as a crucial approach, facilitating the design of models that are both computationally efficient and competitive in terms of performance across various deep learning applications. The state-of-the-art -- in Bayesian sparsification of deep neural networks -- combines structural shrinkage priors on model weights with an approximate inference scheme based on stochastic variational inference. However, model inversion of the full generative model is exceptionally computationally demanding, especially when compared to standard deep learning of point estimates. In this context, we advocate for the use of Bayesian model reduction (BMR) as a more efficient alternative for pruning of model weights. As a generalization of the Savage-Dickey ratio, BMR allows a post-hoc elimination of redundant model weights based on the posterior estimates under a straightforward (non-hierarchical) generative model. Our comparative study highlights the advantages of the BMR method relative to established approaches based on hierarchical horseshoe priors over model weights. We illustrate the potential of BMR across various deep learning architectures, from classical networks like LeNet to modern frameworks such as Vision Transformers and MLP-Mixers.

Interfacing a kinetic action of a person to an action of a machine system is an important research topic in many application areas. One of the key factors for intimate human-machine interaction is the ability of the control algorithm to detect and classify different user commands with shortest possible latency, thus making a highly correlated link between cause and effect. In our research, we focused on the task of mapping user kinematic actions into sound samples. The presented methodology relies on the wireless sensor nodes equipped with inertial measurement units and the real-time algorithm dedicated for early detection and classification of a variety of movements/gestures performed by a user. The core algorithm is based on the approximate Bayesian inference of Vector Autoregressive Hierarchical Hidden Markov Models (VAR-HHMM), where models database is derived from the set of motion gestures. The performance of the algorithm was compared with an online version of the K-nearest neighbours (KNN) algorithm, where we used offline expert based classification as the benchmark. In almost all of the evaluation metrics (e.g. confusion matrix, recall and precision scores) the VAR-HHMM algorithm outperformed KNN. Furthermore, the VAR-HHMM algorithm, in some cases, achieved faster movement onset detection compared with the offline standard. The proposed concept, although envisioned for movement-to-sound application, could be implemented in other human-machine interfaces.