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We address the problem of planning under uncertainty, where an agent must choose actions that not only achieve desired outcomes but also reduce uncertainty. Traditional methods often treat exploration and exploitation as separate…

The Free Energy Principle (FEP) describes (biological) agents as minimising a variational Free Energy (FE) with respect to a generative model of their environment. Active Inference (AIF) is a corollary of the FEP that describes how agents…

Machine Learning · Statistics 2025-01-03 Thijs van de Laar , Magnus Koudahl , Bert de Vries

Automated decision-making under uncertainty requires balancing exploitation and exploration. Classical methods treat these separately using heuristics, while Active Inference unifies them through Expected Free Energy (EFE) minimization.…

Artificial Intelligence · Computer Science 2025-11-25 Wouter W. L. Nuijten , Mykola Lukashchuk

We present the design of an autoregressive active inference agent in the form of message passing on a factor graph. Expected free energy is derived and distributed across a planning graph. The proposed agent is validated on a robot…

Artificial Intelligence · Computer Science 2026-01-21 Wouter M. Kouw , Tim N. Nisslbeck , Wouter L. N. Nuijten

Variational message passing (VMP), belief propagation (BP) and expectation propagation (EP) have found their wide applications in complex statistical signal processing problems. In addition to viewing them as a class of algorithms operating…

Information Theory · Computer Science 2021-01-20 Dan Zhang , Xiaohang Song , Wenjin Wang , Gerhard Fettweis , Xiqi Gao

The Free Energy Principle (FEP) postulates that biological agents perceive and interact with their environment in order to minimize a Variational Free Energy (VFE) with respect to a generative model of their environment. The inference of a…

Machine Learning · Statistics 2022-04-07 Thijs van de Laar , Magnus Koudahl , Bart van Erp , Bert de Vries

The Free Energy Principle (FEP) is a theoretical framework for describing how (intelligent) systems self-organise into coherent, stable structures by minimising a free energy functional. Active Inference (AIF) is a corollary of the FEP that…

Artificial Intelligence · Computer Science 2023-10-17 Magnus Koudahl , Thijs van de Laar , Bert de Vries

Physical AI agents, such as robots and other embodied systems operating under tight and fluctuating resource constraints, remain far less capable than biological agents in open-ended real-world environments. This paper argues that Active…

Machine Learning · Statistics 2026-03-24 Bert de Vries

The Expected Free Energy (EFE) is a central quantity in the theory of active inference. It is the quantity that all active inference agents are mandated to minimize through action, and its decomposition into extrinsic and intrinsic value…

Artificial Intelligence · Computer Science 2020-09-30 Beren Millidge , Alexander Tschantz , Christopher L Buckley

Micro-gestures are subtle and transient movements triggered by unconscious neural and emotional activities, holding great potential for human-computer interaction and clinical monitoring. However, their low amplitude, short duration, and…

Computer Vision and Pattern Recognition · Computer Science 2026-03-10 Weijia Feng , Jingyu Yang , Ruojia Zhang , Fengtao Sun , Qian Gao , Chenyang Wang , Tongtong Su , Jia Guo , Xiaobai Li , Minglai Shao

It is shown how expectation maximization (EM) may be viewed as a message passing algorithm in factor graphs. In particular, a general EM message computation rule is identified. As a factor graph tool, EM may be used to break cycles in a…

Information Theory · Computer Science 2009-10-16 Justin Dauwels , Andrew Eckford , Sascha Korl , Hans-Andrea Loeliger

Recent efforts on combining deep models with probabilistic graphical models are promising in providing flexible models that are also easy to interpret. We propose a variational message-passing algorithm for variational inference in such…

Machine Learning · Statistics 2018-06-15 Wu Lin , Nicolas Hubacher , Mohammad Emtiyaz Khan

Expected free energy (EFE) is a central quantity in active inference which has recently gained popularity due to its intuitive decomposition of the expected value of control into a pragmatic and an epistemic component. While numerous…

Artificial Intelligence · Computer Science 2024-08-14 Ran Wei

Based on a generative model (GM) and beliefs over hidden states, the free energy principle (FEP) enables an agent to sense and act by minimizing a free energy bound on Bayesian surprise. Inclusion of prior beliefs in the GM about desired…

Systems and Control · Electrical Eng. & Systems 2021-07-28 Thijs van de Laar , Ayça Özçelikkale , Henk Wymeersch

Research on the so-called "free-energy principle'' (FEP) in cognitive neuroscience is becoming increasingly high-profile. To date, introductions to this theory have proved difficult for many readers to follow, but it depends mainly upon two…

Artificial Intelligence · Computer Science 2015-03-16 Simon McGregor , Manuel Baltieri , Christopher L. Buckley

Message passing on factor graphs is a powerful framework for probabilistic inference, which finds important applications in various scientific domains. The most wide-spread message passing scheme is the sum-product algorithm (SPA) which…

Machine Learning · Computer Science 2023-06-06 Luca Schmid , Joshua Brenk , Laurent Schmalen

In the context of signal detection in the presence of an unknown time-varying channel parameter, receivers based on the Expectation Propagation (EP) framework appear to be very promising. EP is a message-passing algorithm based on factor…

Signal Processing · Electrical Eng. & Systems 2024-04-09 Elisa Conti , Armando Vannucci , Amina Piemontese , Giulio Colavolpe

Matrix factorization is a popular approach to solving matrix estimation problems based on partial observations. Existing matrix factorization is based on least squares and aims to yield a low-rank matrix to interpret the conditional sample…

Machine Learning · Statistics 2017-03-06 Rui Zhu , Di Niu , Linglong Kong , Zongpeng Li

We show how the notion of message passing can be used to streamline the algebra and computer coding for fast approximate inference in large Bayesian semiparametric regression models. In particular, this approach is amenable to handling…

Methodology · Statistics 2016-04-07 M. P. Wand

Autonomous robotic navigation in real-world environments requires exploration to acquire environmental information as well as goal-directed navigation in order to reach specified targets. Active inference (AIF) based on the free-energy…

Robotics · Computer Science 2025-10-28 Riko Yokozawa , Kentaro Fujii , Yuta Nomura , Shingo Murata
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