Educational Resources

Scientific Research Papers

The Ultimate Guide to Research in the Field of Active Inference AI and Spatial Web Technologies

Research Organized by Year:   2020 - 2025

2025

Agentic rulebooks using active inference: An artificial intelligence application for environmental sustainability

Resources – Scientific Research Papers Agentic rulebooks using active inference: An artificial intelligence application for environmental sustainability Axel Constant, Marco Perin, Hari Thiruvengada, and Karl Friston, April 14, 2025 https://www.frontiersin.org/journals/sustainable-cities/articles/10.3389/frsc.2025.1571613/abstract Abstract: Artificial intelligence (AI) is increasingly proposed as a solution

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Beyond Imitation Games: A Falsifiable Emergent Sentience Framework

The paper by Hipolito, Albarracin, and Hynes presents a framework for minimal sentience based on self-maintenance, adaptability, and agency. It emphasizes observable patterns of organization over computational properties to address cognitive science challenges concerning consciousness, suggesting new perspectives on distinguishing

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Noumenal Labs White Paper: How To Build A Brain

The Noumenal Labs White Paper outlines design principles for artificial intelligence, focusing on resolving the grounding problem. It emphasizes creating machine intelligences that enhance human understanding rather than replace it, by modeling after the scientific method. Key applications include 3D

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Benchmarking Predictive Coding Networks — Made Simple

The paper addresses efficiency and scalability issues in predictive coding networks (PCNs) by introducing a library called PCX. This open-source tool provides performance benchmarks, allowing comprehensive testing of PCNs against existing algorithms. The authors achieve state-of-the-art results, identify limitations, and

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Gradient-free variational learning with conditional mixture networks

The study introduces CAVICMN, a gradient-free variational method for training conditional mixture networks (CMNs), enhancing computational efficiency in supervised learning. By using coordinate ascent variational inference, it maintains robust predictive performance, achieving competitive accuracy compared to traditional methods while efficiently

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2024

Variational Bayes Gaussian Splatting

The paper presents Variational Bayes Gaussian Splatting (VBGS) as an innovative method for 3D scene modeling using Gaussian mixtures. VBGS overcomes the limitations of traditional gradient optimization by implementing variational inference, facilitating efficient sequential updates without replay buffers. Experiments demonstrate

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Predictive Coding with Spiking Neural Networks: a Survey

This article surveys spiking predictive coding, a class of neuro-mimetic computational models. It explores how prediction errors are represented and categorizes them into three approaches. The paper discusses applications in energy-efficient hardware and outlines future challenges, aiming to inspire further

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From pixels to planning: scale-free active inference

The paper introduces a scale-free active inference model that generalizes partially observed Markov decision processes by incorporating latent variables for path modeling. It discusses renormalising generative models, demonstrating their application in image classification, movie and music generation, and learning Atari-like

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Aligning Active Inference Ontology to SUMO

The document outlines a preliminary alignment of Active Inference terminology with the Suggested Upper Merged Ontology (SUMO) entities. Its purpose is to provide a framework for accurately mapping Active Inference concepts to the SUMO formal ontology, thereby enhancing understanding and

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Sustainability under Active Inference

The paper examines the interplay between sustainability, resilience, and well-being through the active inference framework. It defines sustainability as the enduring capacity to meet needs without resource depletion, linking resilience to transformative processes that combat unsustainability. The authors advocate for

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Active Inference as a Model of Agency

The paper discusses active inference as a model of agency beyond mere reward maximization. It combines exploration and exploitation while minimizing risk and ambiguity in behaviors of biological agents. Active inference refines the free energy principle, offering a normative framework

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2023

Shared Protentions in Multi-Agent Active Inference

The paper integrates Husserlian phenomenology, active inference in theoretical biology, and category theory to create a framework for understanding social actions based on shared goals. It emphasizes shared protentions among agents, linking their behaviors to collective goal-directed actions while employing

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Active Inference and Intentional Behaviour

This paper explores how spontaneous learning in neuronal networks and cell cultures exemplifies emergent cognition and behavior. By employing the free energy principle, the authors differentiate reactive, sentient, and intentional behaviors. Simulations illustrate these distinctions through in vitro experiments and

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Supervised structure learning

The paper explores supervised structure learning of discrete generative models by focusing on Bayesian model selection and data ingestion order. It emphasizes placing priors based on expected free energy, demonstrated through image classification on the MNIST dataset and challenges involving

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Relative representations for cognitive graphs

The paper discusses relative representations derived from latent spaces of neural networks, enabling comparison across various models. It explores their application in discrete state-space models through Clone-Structured Cognitive Graphs for spatial navigation. The study introduces a technique for zero-shot model

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Path integrals, particular kinds, and strange things

The paper presents a path integral formulation of the free energy principle, detailing how particles evolve through time. It introduces a variational principle to differentiate internal from external states, suggesting certain particles possess a basic form of inference or sentience.

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Brain-inspired computational intelligence via predictive coding

The paper discusses the limitations of traditional AI methods, particularly deep neural networks. It proposes predictive coding, a neuroscience-inspired theory, as a potential solution for these issues, emphasizing its applications in cognitive control, robotics, and generative models. The authors review

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Hybrid predictive coding: Inferring, fast and slow

The study proposes a hybrid predictive coding model that integrates both amortized and iterative inference to enhance perceptual beliefs through neural activity. It challenges traditional views by showing that rapid perceptual recognition involves an initial feedforward sweep, followed by iterative

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Collective behavior from surprise minimization

The study explores collective motion in animals, proposing a model based on active inference, where behavior aims to minimize surprise. This approach explains various collective phenomena without predefined rules. It highlights how individual beliefs influence group dynamics, decision-making accuracy, and

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Focus: Object-centric world models for robotics manipulation

The research paper introduces FOCUS, a model-based agent that learns an object-centric world model for robotics manipulation. It addresses the challenge of effectively learning structured interactions between objects. FOCUS enhances exploration and task efficiency in robot-object interactions and demonstrates practical

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On efficient computation in active inference

The paper addresses challenges in employing active inference for intelligent behavior due to high computational costs and target distribution specification difficulties. It introduces a novel planning algorithm reducing computational complexity and a simplified method for defining target distributions, enhancing efficiency

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Causal Inference via Predictive Coding

The paper presents a novel approach to causal inference using predictive coding, a method inspired by neuroscience. By modifying the inference process, the authors enable interventional and counterfactual reasoning even with unknown causal graphs. This framework enhances causal discovery and

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Inferring Hierarchical Structure in Multi-Room Maze Environments

The paper presents a hierarchical active inference model that enhances navigation and exploration in multi-room environments using cognitive maps. It describes a three-layer structure integrating curiosity-driven exploration with goal-oriented behavior, facilitating efficient spatial understanding and dynamic decision-making based on pixel-based

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Intra-Active Inference I: Fundamentals

This paper, the first in a series, explores the application of new materialism to the free energy principle (FEP). It highlights the interplay between ontology and epistemology, aiming to transform naturalized thinking. By framing FEP through a neo-materialistic lens, the

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Active Inference in Hebbian Learning Networks

This research explores active inference using brain-inspired Hebbian learning networks to control agents. It describes a dual-network system that learns environmental dynamics and outperforms Q-learning without requiring a replay buffer. Results from experiments in the Mountain Car environment suggest potential

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Computing with Categories in Machine Learning

The paper introduces DisCoPyro, a framework combining category theory with amortized variational inference for machine learning. It bridges the gap between abstract mathematics and practical applications, specifically in program learning for variational autoencoders. The authors discuss mathematical foundations, applications, and

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String Diagrams with Factorized Densities

The work by Eli Sennesh and Jan-Willem van de Meent explores probabilistic programs and causal models, emphasizing compositionally reasoning about model classes beyond directed graphical models. They introduce a category for combining joint densities with deterministic mappings, bridging category-theoretic probability

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Object-Centric Scene Representations using Active Inference

The paper discusses Bayesian mechanics, a probabilistic approach to modeling systems with partitioned states. It reviews literature on the free energy principle and its applications, including path-tracking, mode-tracking, and mode-matching. The authors explore the duality between the free energy principle

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On Bayesian Mechanics: A Physics of and by Beliefs

This paper introduces Bayesian mechanics, a field modeling systems with specific partitions that encode beliefs about external states. It reviews applications of Bayesian mechanics in path-tracking, mode-tracking, and mode-matching, highlighting the duality between the free energy principle and constrained maximum

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2022

Resilience and active inference

The paper by Mark Miller et al. conceptualizes resilience through active inference, a modeling approach for complex adaptive systems. It defines resilience in three ways: inertia (resisting change), elasticity (recovering from disturbances), and plasticity (expanding adaptive states), situating these concepts

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Learning on arbitrary graph topologies via predictive coding

The paper discusses using predictive coding (PC) for training neural networks on arbitrary graph topologies, addressing limitations of backpropagation (BP) in cyclic structures. It demonstrates how PC can perform flexible tasks by stimulating specific neurons, ultimately examining how graph topology

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Designing Ecosystems of Intelligence from First Principles

The white paper outlines a future vision for artificial intelligence research, proposing a cyber-physical ecosystem of shared intelligence, where humans engage in active inference. It emphasizes self-evidencing through belief updating and highlights the importance of communication protocols and a shared

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Situated models and the modeler: A comment on “The Markov blanket trick: On the scope of the free energy principle and active inference” by Raja, Valluri, Baggs, Chemero and Anderson

Mahault Albarracin and Riddhi J Pitliya provide insights on “The Markov blanket trick” by Raja and colleagues. They acknowledge the critique of the Free Energy Principle (FEP) as interesting yet flawed, highlighting its philosophical nature while appreciating the authors’ technical

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AN ACTIVE INFERENCE APPROACH TO SEMIOTICS

Resources – Scientific Research Papers AN ACTIVE INFERENCE APPROACH TO SEMIOTICS Antoine Milette-Gagnon, Samuel PL Veissière, Karl J Friston, Maxwell JD Ramstead November 14, 2022 https://books.google.com/books?hl=en&lr=&id=hPCKEAAAQBAJ&oi=fnd&pg=PT90&dq=info:4nbBr-hRLywJ:scholar.google.com&ots=swlVMAqd4g&sig=pbcTzDigc55YVsjIYwkCCgSUc4I#v=onepage&q&f=false Abstract: Recent decades have borne witness to the emergence of new frameworks in psychology

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Natural Language Syntax Complies with the Free-Energy Principle

Resources – Scientific Research Papers Natural Language Syntax Complies with the Free-Energy Principle Elliot Murphy, Emma Holmes, Karl Friston October 26, 2022 https://arxiv.org/abs/2210.15098 Abstract: Natural language syntax yields an unbounded array of hierarchically structured expressions. We claim that these are used in

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An active inference approach to second-person neuroscience

The paper critiques traditional social neuroscience for its detached third-person perspective and introduces second-person neuroscience, emphasizing real-time interactions. Utilizing the active inference framework, it explores neural mechanisms during social engagement, highlighting the importance of mutual predictions and bodily adaptation. This

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Spin glass systems as collective active inference

This paper investigates the relationship between individual and collective inference in multi-agent Bayesian systems using spin glass models. It reveals that collective dynamics of active inference agents resemble sampling from a spin glass’s stationary distribution, though this equivalence is delicate

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Capsule Networks as Generative Models

The paper discusses the development of capsule networks as generative models for visual scene recognition, emphasizing their architecture that uses dynamic routing through capsules to extract features and pose information. It presents a new routing algorithm based on iterative inference

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A worked example of the Bayesian mechanics of classical objects

Resources – Scientific Research Papers A worked example of the Bayesian mechanics of classical objects Dalton AR Sakthivadivel September 19, 2022 https://link.springer.com/chapter/10.1007/978-3-031-28719-0_21 Abstract: Bayesian mechanics is a new approach to studying the mathematics and physics of interacting stochastic processes. We

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Mapping Husserlian phenomenology onto active inference

The paper explores the intersection between Husserlian phenomenology and active inference, proposing a mathematical model of perception that incorporates prior knowledge and expectations. It reviews active inference and key aspects of Husserl’s phenomenology, particularly time consciousness, ultimately illustrating how these

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Mapping Husserlian phenomenology onto active inference

The paper explores the relationship between Husserlian phenomenology and active inference, proposing a mathematical framework for understanding perception through prior knowledge and expectations. It aims to enhance computational phenomenology by aligning Husserl’s concepts of consciousness, particularly time consciousness, with active

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On the Map-Territory Fallacy Fallacy

The paper explores the free energy principle (FEP) and addresses the map-territory fallacy in scientific modeling. It asserts that critiques of the FEP based on this fallacy are themselves fallacious. The authors emphasize the FEP’s distinctiveness in modeling interactions within

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The nature of beliefs and believing

The article discusses the nature of beliefs in cognitive science, describing them as propositional attitudes with representational content and assumed veracity. Beliefs shape cognition by influencing perceptions, behaviors, and decision-making, often remaining unconscious. They provide agents with a coherent understanding

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Extended plastic inevitable

The commentary analyzes the role of the free-energy principle (FEP) in defining cognitive system boundaries within third-wave extended-mind research. It emphasizes that Markov blankets connect internal and external states, highlighting the plasticity of these boundaries and the relevance of niche

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The Free Energy Principle drives neuromorphic development

The authors demonstrate that systems with morphological degrees of freedom and constrained free energy evolve toward neuromorphic structures that facilitate hierarchical computations. This concept is applicable in various biological contexts, linking quantum reference frames and topological quantum field theories to

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Successor representation active inference

The paper by Millidge and Buckley explores the relationship between classical reinforcement learning, Bayesian filtering, and Active Inference, proposing a novel agent architecture using successor representations. This new model shows benefits in planning horizons and computational efficiency, allowing generalization to

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Commentary: The Nature of Beliefs and Believing

The editorial discusses belief in cognitive science, particularly through the lens of computational neuroscience, defining beliefs as representations of reality. It introduces active inference, a theory detailing how organisms update beliefs and minimize uncertainty. The article also explores belief dynamics

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A Probabilistic Generative Model of Free Categories

This paper presents a probabilistic generative model for morphisms in free monoidal categories, linking applied category theory and machine learning. It demonstrates how acyclic directed wiring diagrams can specify morphisms and employs amortized variational inference for parameter learning and latent

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Towards a geometry and analysis for Bayesian mechanics

The paper formulates Bayesian mechanics via axiomatic principles, arguing that constrained dynamical systems infer against these constraints, implying environmental influences. It links classical dynamical systems theory to Bayesian inference, using concepts like Shannon entropy and gauge degrees of freedom. This

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Embodied object representation learning and recognition

The article discusses a novel approach to object recognition and representation learning, emphasizing the importance of interactive learning, akin to human cognition. It introduces a Cortical Column Network (CCN) that predicts object transformations through active inference, enhancing classification accuracy and

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Active inference models do not contradict folk psychology

Active inference presents a cohesive theory of perception, learning, and decision-making. The authors address concerns about its compatibility with folk psychology’s beliefs and desires, demonstrating that active inference includes elements reflecting desires. They explore how this framework can enhance folk-psychological

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Epistemic communities under active inference

The paper explores the dynamics of information spread and confirmation bias within epistemic communities using an active inference model. It reveals how agents create echo chambers by selectively engaging with content that reinforces their beliefs, resulting in entrenched views and

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Canonical neural networks perform active inference

This research explores canonical neural networks, demonstrating that they perform active inference and learning via rate coding models. It reveals that plasticity modulation with delay allows for minimising future risk, aligning with principles of Bayesian belief updating. The findings highlight

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Chunking space and time with information geometry

The paper “Chunking space and time with information geometry” presents a unified approach to how humans and robots process sensory data by forming discrete concepts over continuous input. It proposes a hierarchical generative model for perception and navigation, illustrating the

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2021

A free energy principle for generic quantum systems

The Free Energy Principle (FEP) proposes that random dynamical systems minimize an upper bound on surprisal through weak coupling. This paper reformulates the FEP within quantum information theory, suggesting that quantum systems act as observers and agents, minimizing Bayesian prediction

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Active inference, Bayesian optimal design, and expected utility

The abstract discusses active inference, linked to the free energy principle, as a method for understanding certain random dynamical systems resembling sentience. It merges Bayesian decision theory with optimal Bayesian design to minimize expected free energy, leading to information-seeking behavior.

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Active Inference Tree Search in Large POMDPs

The paper presents a new method called Active Inference Tree Search (AcT) for efficient planning in Partially Observable Markov Decision Processes (POMDPs). It combines principles from neuroscience and artificial intelligence to enhance model-based planning. AcT addresses the exploration-exploitation dilemma and

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2020

Sophisticated Inference

The paper by Friston et al. presents a framework of active inference, which elucidates sentient behavior through a principled lens. By integrating information gain with reward structures, it addresses the exploitation-exploration dilemma. The authors introduce a recursive model of expected

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Markov Blankets in the Brain

The paper explores the concept of Markov blankets in the context of self-organizing systems, particularly focusing on neuronal systems. It discusses how these statistical boundaries can mediate interactions within and outside systems, facilitating analysis at various brain architecture scales including

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