Mobile Manipulation with Active Inference for Long-Horizon Rearrangement Tasks
Discover a groundbreaking approach that brings Active Inference to complex, real-world robotics, enabling long-horizon robotic control with real-time adaptability
Educational Resources
Scientific Research Papers
The Ultimate Guide to Research in the Field of Active Inference AI and Spatial Web Technologies
Discover a groundbreaking approach that brings Active Inference to complex, real-world robotics, enabling long-horizon robotic control with real-time adaptability
Introduces a novel Active Inference architecture that accelerates learning in low-data environments by embedding object-centric priors and modeling sparse object-object interactions. Unlike traditional Active Inference models designed for single domains, AXIOM (Active eXpanding Inference with Object-centric Models) generalizes across tasks
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
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
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
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
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
The paper introduces a novel algorithm, Divide-and-Conquer Predictive Coding (DCPC), which enhances Bayesian inference in structured generative models. DCPC respects correlation structures and efficiently updates parameters while maintaining biological relevance. It outperforms existing algorithms in high-dimensional tasks, and an open
GenRL presents a novel multimodal-foundation world model for developing generalist embodied agents capable of handling diverse tasks. By integrating vision and language prompts without the need for complex reward systems, GenRL advances reinforcement learning. It demonstrates effective multi-task generalization and
This research explores the geometry of the predictive coding (PC) energy landscape and its impact on learning efficiency. It demonstrates that equilibrated energy simplifies the loss landscape, making it easier to escape non-strict saddles. The findings suggest PC inference can
The study presents a hierarchical active inference model illustrating how the hippocampal-prefrontal circuit integrates navigational systems for spatial alternation tasks. The model reveals dual layers for cognitive mapping, addressing how disruptions affect decision-making and adapt to varying alternation rules, emphasizing
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
The research paper introduces novel techniques in active inference for continuous action POMDPs focusing on sparse reward signals. It highlights improvements over existing models in the context of robotic tasks that require inferring unobserved states from sensory data. The study
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
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
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
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
The paper discusses self-esteem as an active inference process, linking it to an individual’s social perceptions and environmental expectations. It highlights how discrepancies between self-perception and social feedback prompt adjustments in behavior and self-view, emphasizing self-esteem’s role in navigating social
The paper explores active inference as a framework for understanding intelligent behavior in decision-making, examining ‘planning’ and ‘learning from experience’ strategies. A mixed model is proposed to balance these approaches, tested in a grid-world scenario to enhance adaptability and provide
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
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
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
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
The article explores the differences between generative models in living organisms and passive generative AI. It argues that while AI learns from data, biological systems are embodied and actively test their models through sensorimotor interactions, leading to genuine understanding. The
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
The paper explores integrating cognitive map learning and active inference for navigation in ambiguous environments. It evaluates a clone-structured cognitive graph model, comparing a naive agent with an active inference-driven agent. Results indicate that while both perform well in simple
The paper discusses a system combining world models and curiosity-driven exploration for autonomous navigation in unknown environments. It showcases effective simulation performance but identifies challenges in real-world applications, particularly in dynamic settings. The authors highlight the need for adaptable world
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.
The article presents a hierarchical active inference model that integrates cognitive maps for navigation and task performance, focusing on the hippocampal-prefrontal circuit. It outlines how this model helps solve spatial alternation tasks by merging physical and task-specific codes, demonstrating the
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
The study validates the free-energy principle through in vitro networks of rat cortical neurons, confirming its predictive accuracy regarding self-organization and plasticity. By manipulating excitability, researchers observed changes in inference capabilities, supporting the principle’s role in coding generative model parameters,
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
The article presents a categorical approach to Predictive Processing and Active Inference using string diagrams within a monoidal category. It includes diagrammatic representations of generative models, Bayesian updating, and free energy minimization. The aim is to offer a visual language
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
The paper evaluates the “inner screen model” of consciousness, derived from the free energy principle (FEP), as a potential minimal unifying model (MUM). It integrates various models based on FEP, including Bayesian theories and those addressing time-consciousness, situating them within
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
The paper discusses advancements in unsupervised reinforcement learning (RL) from visual inputs. The authors propose a method using unsupervised model-based RL coupled with a new hybrid planner, Dyna-MPC, to enhance agent adaptation. Their approach achieves a 93.59% performance on the
The paper examines forward-looking multiple-input multiple-output synthetic aperture radar (FL-MIMO-SAR) for enhancing imaging in autonomous mobile robots (AMRs). It addresses challenges such as low angular resolution by proposing FL-sparseMIMO-SAR, which uses large inter-element spacing to suppress grating lobes and improve
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
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
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
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
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
The paper explores the development of explainable AI systems using active inference, emphasizing transparency in decision-making and introspection. It outlines an architecture that creates human-interpretable models, allowing AI to explain its decisions. The implications for future AI research and ethical
This paper continues the exploration of synthetic Active Inference (AIF) agents as detailed in Part I, focusing on variational message updates. It highlights a scalable method using Forney-style Factor Graphs, deriving algorithms for minimizing generalised Free Energy objectives. The study
The paper introduces “embedded normativity” within the Active Inference framework, proposing that social norms emerge through human interaction with the environment. It suggests that norms are not intrinsic to agents but arise from their engagement with surroundings, leading to both
The study introduces a novel SLAM architecture combining event-based cameras and FMCW radar for drone navigation, utilizing bio-inspired Spiking Neural Networks with continual STDP learning. Unlike traditional systems, this approach continuously learns from data without offline training, proving effective in
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
The paper elucidates the free energy principle, linking random dynamical systems to Bayesian mechanics as a framework for understanding sentience. It highlights key aspects including state partitioning, Bayesian inference implications, and state dynamics through variational principles. Ultimately, it conceptualizes self-organization
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
This paper explores using variational auto-encoders to learn low-dimensional representations from FMCW radar data for indoor drone navigation. It introduces a unique dataset of raw radar data collected from a flying drone, demonstrating that the learned representations can perform comparably
This research explores a computational model of consciousness, focusing on associative memory in the hippocampus. It critiques traditional hierarchical predictive models lacking recurrent connections, proposing alternatives that learn covariance implicitly. The study aims to create biologically plausible models for hippocampal
This paper discusses a new computational model for associative memory that integrates recurrent connections, which are crucial for the hippocampus’s function. It addresses limitations of previous predictive coding models by proposing alternatives that implicitly learn covariance information. The authors demonstrate
The volume contains 25 revised papers from the 3rd International Workshop on Active Inference, held in Grenoble, France, on September 19, 2022, alongside ECML/PKDD. These papers were selected from 31 submissions, showcasing research advancements in the field. The collection was
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
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
The paper explores the use of FMCW radar technology for indoor drones, highlighting its ability to provide detailed obstacle information. It discusses recent advancements in deep learning for processing radar data and introduces unsupervised learning methods that generate low-dimensional representations,
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
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
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
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
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
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
The study presents strategies to enhance computational efficiency in image-based reinforcement learning for robotics, addressing limitations of large models on available hardware. By reducing model complexity, downscaling input resolution, and utilizing weight quantization, the authors achieve up to 300 times
The paper explores how digital social platforms manipulate attention and social interactions through the concept of digital affordances. It highlights how these platforms are designed to maximize user engagement by creating rewarding experiences, particularly in the context of the COVID-19
This paper explores active inference in modeling intelligent agents by minimizing free energy. It critiques the entangled state space from deep learning methods, proposing a model that disentangles object shape, pose, and category using the ShapeNet dataset. Results indicate that
This work presents a method for selecting policies in active inference by mapping policies to a vector embedding space. It utilizes k-means clustering for efficient sampling of expected free energy, enabling focused searches around promising policies. The approach is applied
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
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
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
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
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
The commentary by Conor Heins critiques the target article on the Free Energy Principle (FEP) by Aguilera et al., focusing on linear diffusion processes. Heins offers insights into the marginal flows of conditional modes, analyzing how these “particular states” influence
The authors respond to Aguilera et al.’s critique of the free energy principle, addressing ambiguities in system dynamics and misinterpretations of surprisal and variational free energy. They argue that despite these critiques, the original findings remain valid and resilient under
The editorial examines the evolution of the affordance concept within the active inference framework, differentiating between Affordance 1.0, 2.0, and the author’s proposed Affordance 3.0. It argues that while active inference deviates from ecological psychology’s foundations, applying this concept in
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
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
Maxwell JD Ramstead critiques Raja et al.’s 2021 paper on the Markov blanket trick, acknowledging the validity of their argument but identifying a flawed premise that weakens their conclusions. He suggests that subsequent research on the free energy principle provides
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
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
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
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
This paper by Dalton AR Sakthivadivel explores high-dimensional random dynamical systems with sparse couplings to external systems, focusing on controlled exchanges. Utilizing the adiabatic theorem, it demonstrates that such coupling structures are common in complex systems, thereby validating K Friston’s
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
This commentary addresses a technical analysis of the Free Energy Principle by Aguilera et al., challenging the claim that sparse coupling ensures Markov blankets in certain stochastic differential equations. It clarifies conditions under which Markov blankets arise, emphasizing the implications
The author critiques a recent paper on the free energy principle (FEP) by Aguilera et al., arguing their points on its limitations are valid but not detrimental to the FEP. A proposed path-based formulation of the FEP is suggested to
The article discusses the Free Energy Principle (FEP) as a unified model for understanding adaptive behaviors in complex systems, extending beyond the human brain to include various biological phenomena. It aims to explore the FEP’s applicability to different organisms and
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
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
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
The paper discusses how stress induces physiological changes that lead to a loss of predictive confidence, resulting in depression. It uses the active inference framework to explain how organisms manage energy resources. The authors identify neuroendocrine and immunological systems as
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
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
This paper introduces a generative modelling approach to neurophenomenology, merging computational neuroscience with phenomenological philosophy. It reviews objections to naturalized phenomenology, outlines generative modelling frameworks, and details the authors’ method for creating a computational model that interprets lived experiences, distinguishing
The paper introduces Action Perception Divergence (APD), a framework for categorizing objective functions in intelligent agents. It distinguishes between narrow, task-specific rewards, and broad objectives maximizing information through interactions with the environment. The authors assert that effective exploration and adaptability
The paper explores why Bayesian inference in the brain contributes to poor performance on explicit probabilistic reasoning tasks. It distinguishes between inferring probability distributions and representing probabilities as hidden states, asserting that effective reasoning relies on a generative model of
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
The post introduces pymdp, a Python library designed for simulating active inference in complex systems using partially-observable Markov Decision Processes (POMDPs). The authors aim to enhance accessibility and user-friendliness of active inference for researchers from diverse backgrounds, promoting innovation and
The paper discusses advancements in unsupervised reinforcement learning (RL), focusing on enhancing data efficiency in high-dimensional environments. The authors propose a method where an agent collects experience through self-supervised exploration to pre-train a world model. This model, combined with a
The paper discusses the construction of spatial maps for navigation, proposing that a unified mechanism underlies the chunking of sensory data in both time and space. By developing a hierarchical generative model of perception and action, the authors relate their
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
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
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.
The paper explores the concept of trust in human-robot collaboration (HRC), emphasizing its necessity for seamless interaction. It reviews existing literature and proposes a model where trust is viewed as an agent’s explanation for sensory exchange and control over robots.
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
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
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
The paper discusses a neural architecture for deep active inference agents that utilizes Monte-Carlo methods within complex, continuous state spaces. It emphasizes minimizing free energy as the core principle for understanding biological intelligence. The authors introduce innovative techniques, including MC
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