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Free energy principle

The free energy principle (FEP) is a theoretical framework in neuroscience and theoretical biology that posits self-organizing biological systems, such as the brain, maintain homeostasis and resist entropic disorder by minimizing variational free energy, which serves as an upper bound on the surprise (negative log probability) of sensory inputs relative to internal generative models. This minimization process unifies perception, learning, and action under a single imperative: systems adapt by optimizing approximate posterior beliefs about environmental causes through hierarchical Bayesian inference, effectively suppressing prediction errors to align sensory data with expectations. Proposed by neuroscientist Karl Friston in the mid-2000s, the FEP draws from statistical physics, information theory, and variational methods to explain how living systems occupy low-entropy states in a fluctuating environment, avoiding phase transitions that could lead to disorder or death.^[1] At its core, free energy is formulated as F = \langle \ln q(\mu) - \ln p(\tilde{y}, \mu) \rangle, where q(\mu) is a recognition density approximating the true posterior over hidden causes \mu, and p(\tilde{y}, \mu) is the joint probability under a generative model; minimizing F bounds sensory entropy and enables self-evidencing behaviors. This principle extends beyond the brain to any autopoietic system, encompassing molecular self-assembly, evolutionary adaptation, and even social phenomena, by framing adaptation as active inference—where agents sample the world to fulfill predictions rather than passively react.^[1] Key implications include predictive coding as a neural implementation, where top-down predictions from higher cortical layers meet bottom-up errors, driving synaptic plasticity and attention to resolve uncertainties. The FEP has influenced fields like active inference models in artificial intelligence and robotics, offering a normative account of cognition that contrasts with reward-based reinforcement learning by emphasizing intrinsic model evidence over extrinsic goals. Ongoing research explores its role in psychiatric disorders, such as schizophrenia, where aberrant precision weighting of predictions may underlie symptoms like hallucinations.^[1]

Introduction

Definition and core concepts

The free energy principle (FEP) is a theoretical framework proposing that self-organizing biological systems resist disorder by minimizing variational free energy, which serves as a tractable upper bound on surprise—or self-information—thereby preserving their structural and functional integrity while maintaining homeostasis. This minimization process ensures that systems remain in states they are optimized for, avoiding excessive unpredictability in their sensory exchanges with the environment. The principle frames adaptive behavior as an inevitable consequence of thermodynamic imperatives, where living systems actively model and interact with their surroundings to bound the improbability of their observations. Central to the FEP are concepts like surprise, defined as the negative logarithm of the probability of sensory data under a system's internal generative model, representing the degree of mismatch between expectations and actual inputs. Markov blankets further delineate system boundaries, comprising sensory states that report external influences and active states that influence the environment, while shielding internal states from direct external access and enabling conditional independence. These elements collectively partition a system from its milieu, allowing it to infer hidden causes of sensations and act to fulfill predictions. The FEP provides a normative account of behavior across scales of living systems, from cellular homeostasis to neural processing in brains, positing that all such entities minimize free energy to sustain viability through predictive coding and environmental modulation. For instance, it explains how organisms anticipate and adapt to perturbations, ensuring long-term survival by resolving uncertainties in sensory streams. Originally proposed by Karl Friston in 2006 and elaborated in key publications through 2010, the framework integrates perception, action, and learning as unified processes under free energy minimization.

Historical development

The free energy principle (FEP) traces its conceptual origins to 19th-century physiological psychology, particularly Hermann von Helmholtz's theory of unconscious inference, which posited that perception involves the brain's probabilistic interpretation of sensory data to infer the external world.^[2] This idea laid early groundwork for viewing the brain as an inferential mechanism, a theme echoed in later FEP formulations. In the mid-20th century, cybernetics emerged as a key influence, emphasizing feedback loops and self-regulation in complex systems to maintain stability against environmental perturbations.^[2] W. Ross Ashby's homeostat, developed in the 1940s, exemplified these principles through a device that autonomously adapted to disturbances via ultrastable reconfiguration, prefiguring notions of adaptive minimization in biological agents. Karl Friston formalized the FEP in the mid-2000s, initially applying variational free energy to model cortical responses and dynamic causal modeling in neuroimaging data. His 2006 paper explicitly articulated the FEP as a unifying account of brain function, drawing on variational methods to bound surprise or prediction error. This was expanded in a seminal 2010 review, which positioned the FEP as a comprehensive brain theory integrating perception, action, and learning through free energy minimization.^[2] Throughout the 2010s, the FEP evolved by incorporating predictive coding frameworks, such as Rao and Ballard's 1999 model of hierarchical error minimization in visual cortex, to explain neural implementations of inference.^[3] Active inference, an extension linking perception to action via expected free energy, gained prominence in Friston's 2010 work on behavioral optimization. Key milestones included Friston's 2013 paper broadening the FEP to biological self-organization and evolution, influencing interdisciplinary applications.^[4] Post-2020 refinements have addressed limitations in assuming steady-state conditions, extending the FEP to non-equilibrium dynamics in random dynamical systems for more general applicability to living processes.^[5] These developments build briefly on Bayesian inference traditions while emphasizing variational approximations for practical computation.^[2]

Theoretical Foundations

Variational free energy

The variational free energy, denoted as F, is defined in the free energy principle as an approximation to the surprise of sensory data, formulated as

F[q(\mu)] = D_{\text{KL}}[q(\mu) \parallel p(\mu \mid s)] - \ln p(s),

where q(\mu) is a variational distribution approximating the true posterior p(\mu \mid s) over hidden states \mu, s represents sensory inputs, D_{\text{KL}} is the Kullback-Leibler divergence, and -\ln p(s) is the surprise or self-information of the sensory data.^[6] This expression arises in variational Bayesian inference applied to generative models, where the system posits a joint distribution p(s, \mu) over observables and their hidden causes. The derivation of F as an upper bound on surprise follows from the non-negativity of the KL divergence and Jensen's inequality applied to the log-evidence lower bound. Specifically, the marginal likelihood satisfies \ln p(s) = \mathbb{E}_{p(\mu \mid s)}[\ln p(s)] \geq \mathbb{E}_{q(\mu)}[\ln p(s, \mu) - \ln q(\mu)], which rearranges to F[q(\mu)] \geq -\ln p(s), with equality when q(\mu) = p(\mu \mid s).^[6] This bound ensures that minimizing F provides a tractable proxy for minimizing surprise, avoiding direct computation of the intractable posterior. The components of F reflect a trade-off between accuracy and complexity: the KL divergence term D_{\text{KL}}[q(\mu) \parallel p(\mu \mid s)] measures complexity, quantifying the information gain or deviation from the true posterior (often decomposed further into divergence from priors), while -\ln p(s) relates to accuracy via the expected log-likelihood under the approximate posterior, \mathbb{E}_{q(\mu)}[\ln p(s \mid \mu)].^[6] In this framework, biological or artificial systems employ hierarchical generative models to infer the causes of sensory inputs, encoding priors over hidden states in a top-down manner to predict s.

Free energy minimization

The free energy principle posits that adaptive systems, whether biological or artificial, minimize variational free energy F through gradient descent on its partial derivatives with respect to internal model parameters \theta, such that \frac{\partial F}{\partial \theta} = 0.^[7] This optimization process underpins both inference, by refining approximate posterior beliefs about hidden causes of sensory inputs, and learning, by updating the generative model to better predict future observations.^[8] As a variational bound on surprise—the negative log probability of sensory data under the true generative model—minimizing F effectively reduces the divergence between predicted and actual sensory states, enabling systems to maintain accurate internal representations of their environment.^[7] Systems achieve this minimization through two primary strategies. The perceptual strategy involves updating internal beliefs or states to align the model's predictions with incoming sensory data, effectively performing approximate Bayesian inference without altering the external world.^[8] In contrast, the active strategy entails selecting actions that modify the environment or sensory inputs to better match the system's expectations, thereby resolving prediction errors through environmental reconfiguration rather than belief revision.^[7] These complementary approaches allow systems to navigate uncertainty dynamically, with the choice between them depending on the relative costs of inference versus action. The implications of free energy minimization extend to the autonomy and persistence of self-organizing systems, as it ensures long-term survival by systematically reducing expected surprise over time.^[9] By bounding surprise, minimization prevents the accumulation of improbable states that could lead to dissipative phase transitions or system dissolution, thereby promoting adaptive behaviors that sustain the system's operational integrity against entropic decay.^[8] This normative imperative frames autonomy not as isolated self-regulation but as a process of resilient exchange with the environment, where minimized free energy corresponds to maximized model evidence and enhanced predictive power.^[9] Underpinning this framework is the assumption that systems operate as ergodic random dynamical processes at non-equilibrium steady states, where trajectories revisit a bounded attractor with a unique stationary density.^[9] Ergodicity ensures that time-averaged behaviors converge to ensemble averages, allowing free energy to serve as a Lyapunov function that drives the system toward low-entropy configurations while maintaining boundary integrity through a Markov blanket separating internal and external states.^[9] This steady-state condition is essential for persistence, as it confines states to a compact set resistant to external perturbations, with minimization actively enforcing the ergodic density to avoid ergodicity-breaking transitions that would undermine adaptation.^[9]

Theoretical Connections

Bayesian inference

The free energy principle (FEP) implements Bayesian inference by framing perception and learning as the optimization of hierarchical generative models that approximate the posterior distribution over hidden causes of sensory data. Specifically, the FEP employs variational Bayesian methods, where minimizing the variational free energy F provides an approximation to the posterior p(\mu | s) through an approximate distribution q(\mu) = \arg\min_q D_{\text{KL}}[q(\mu) \| p(\mu | s)], with \mu representing the hidden states or causes and s the sensory inputs.^[8] This minimization ensures that q(\mu) closely matches the true posterior by reducing the Kullback-Leibler divergence, effectively bounding the surprise or negative log-evidence of the data under the generative model. The variational free energy F thus serves as a tractable proxy for inference in complex, high-dimensional spaces where exact Bayesian updating is computationally infeasible.^[10] A core mechanism for this inference in the FEP is predictive coding, which operates through hierarchical message passing to propagate and minimize prediction errors across levels of a generative model. In this framework, prediction errors are computed as \delta = s - g(\mu), where g(\mu) is the top-down prediction of sensory input generated from the current estimate of hidden states \mu, and these errors drive iterative updates to the estimates via gradient descent on the free energy: \mu' = \mu - \frac{\partial F}{\partial \mu}.^[11] This process unfolds hierarchically, with bottom-up error signals ascending to higher levels to refine priors and top-down predictions descending to suppress errors at lower levels, enabling the system to iteratively refine its internal model of the world. Predictive coding thus realizes Bayesian inference as a distributed, recurrent algorithm that balances sensory evidence with prior expectations without requiring centralized computation.^[12] The FEP further incorporates empirical Bayes to learn hierarchical priors from data, allowing the construction of generative models that capture the statistical structure of the environment. Under empirical Bayes, higher-level parameters serve as hyperpriors that are themselves inferred from lower-level sensory data, enabling the system to adapt its expectations dynamically rather than relying on fixed priors. This approach supports the development of deep generative models where each level predicts the causes at the level below, fostering a unified representation of the world's causal hierarchies.^[8] Precision weighting plays a crucial role in modulating the influence of prediction errors during inference, where precision is defined as the inverse variance of noise in sensory or prior signals. In the FEP, precision \Pi weights errors such that \delta^\Pi = \Pi \delta, amplifying reliable (high-precision) signals and attenuating noisy (low-precision) ones to optimize the balance between exploration and exploitation in Bayesian updating.^[13] This mechanism ensures that inference prioritizes evidence with low uncertainty, enhancing the accuracy of posterior approximations in hierarchical models.^[14]

Thermodynamics and self-organization

The free energy principle (FEP) provides a unifying framework for understanding how biological systems maintain order in non-equilibrium thermodynamic environments by minimizing variational free energy, which bounds the surprise or entropy associated with sensory inputs. This minimization process aligns with non-equilibrium thermodynamics, where systems resist the second law of thermodynamics' tendency toward disorder by actively dissipating energy to sustain low-entropy steady states. In particular, free energy minimization reduces the production of thermodynamic entropy, enabling systems to self-organize without external specification.^[1] This connection to self-organization echoes Ilya Prigogine's theory of dissipative structures, where open systems far from equilibrium form ordered patterns through irreversible processes that export entropy to their surroundings. Under the FEP, biological agents achieve similar self-organization by encoding generative models of their environment, allowing them to predict and counteract surprising states that would otherwise increase internal entropy. By minimizing free energy, these systems conform to the principle of least action, optimizing energy dissipation while preserving structural integrity against environmental perturbations.^[1] Markov blankets formalize the thermodynamic boundaries of self-organizing systems under the FEP, acting as semi-permeable interfaces that separate internal states from external influences while minimizing flows of free energy across the boundary. These blankets ensure conditional independence between internal and external dynamics, reducing entropy fluxes that could destabilize the system and thereby preserving its identity as a distinct entity in a fluctuating environment.^[4] For instance, in cellular homeostasis, a cell's plasma membrane functions as a Markov blanket, where transmembrane proteins and ion channels regulate solute exchanges to minimize deviations from internal steady states, effectively implementing free energy minimization through metabolic feedback loops that sustain low-entropy configurations without relying on higher-level neural mechanisms.^[4]

Information theory

In the free energy principle (FEP), surprise is defined as the self-information of a sensory state, quantified as the negative logarithm of its probability, -\ln p(s), where s represents the sensory input or state. This measure captures the improbability of an observed state under the system's generative model, with higher surprise indicating greater deviation from expected outcomes. The FEP posits that biological systems resist excessive surprise to maintain their integrity, as sustained high surprise would imply maladaptive states. Variational free energy serves as an upper bound on surprise, ensuring that its minimization approximates the suppression of self-information. More broadly, the expected free energy bounds the Shannon entropy H = -\int p(s) \ln p(s) \, ds, which represents the average surprise over the distribution of sensory states. By minimizing expected free energy, systems effectively reduce uncertainty in their sensory environment, aligning internal models with external realities without directly computing intractable posterior distributions. The minimization of free energy also relates to mutual information I(s; \mu), where \mu denotes the internal states or approximate posterior beliefs about sensory causes. This mutual information quantifies the shared information between sensory states and internal representations, and its maximization occurs equivalently through free energy minimization. In this framework, free energy minimization maximizes the evidence lower bound (ELBO), expressed as

L = \mathbb{E}_q[\ln p(s \mid \mu)] - D_{\text{KL}}[q(\mu) \parallel p(\mu)],

where q(\mu) is the approximate posterior, p(\mu) is the prior, and the first term reflects accuracy in reconstructing sensory data while the second penalizes divergence from priors. This bound provides a tractable surrogate for model evidence, facilitating inference by balancing representation fidelity and prior consistency. The FEP's free energy minimization embodies a trade-off akin to rate-distortion theory, where accuracy (fidelity to sensory data) is balanced against complexity (descriptive cost of the internal model). Free energy can be decomposed as complexity minus accuracy, with complexity measuring the relative entropy between approximate and true posteriors, and accuracy capturing the expected log-likelihood of observations. This optimization compresses sensory information efficiently, minimizing distortion (error in representation) subject to a rate constraint (model simplicity), much like lossy coding in information theory. In autopoietic systems under the FEP, Markov blankets enforce information closure by partitioning internal states from external ones, thereby reducing uncertainty from the outer environment. The blanket—comprising sensory and active states—mediates all interactions, ensuring that internal dynamics evolve to minimize variational free energy and thus external surprise. This closure supports self-maintenance by confining information flows, allowing the system to treat external causes as effectively stationary while adapting to perturbations.

Perception and Action

Perceptual inference

In the free energy principle, perceptual inference is conceptualized as an online process that minimizes variational free energy by updating internal beliefs about hidden causes of sensory data in real time. This occurs through the optimization of a recognition density, which approximates the true posterior distribution over causes, achieved via gradient descent on prediction errors—discrepancies between predicted and actual sensory inputs. These errors drive recurrent message-passing among neuronal populations, akin to predictive coding schemes, enabling rapid adjustments to perceptual states without altering the underlying generative model.^[15] The hierarchical structure of generative models underpins this inference, where top-down predictions from higher levels provide contextual priors that meet bottom-up sensory signals at lower levels, resolving ambiguities in sensory data. Prediction errors propagate upwards to refine higher-level expectations, while top-down signals suppress errors at successive layers, ensuring a coherent inference across scales. This bidirectional flow, implemented through distinct forward and backward cortical connections, allows the brain to infer complex, temporally extended causes from noisy, continuous inputs.^[15] Categorization emerges from this framework as the formation of discrete perceptual states from continuous sensory streams, facilitated by variational modes in the approximate posterior. Under approximations like the Laplace method, the recognition density becomes unimodal, selecting a single mode that best explains the data and effectively discretizing causes into categorical representations, such as object identities or temporal sequences. This process leverages empirical priors from hierarchical models to group sensory regularities, promoting efficient encoding over exhaustive multimodal distributions.^[15] A illustrative example of perceptual inference failures is the rubber hand illusion, where synchronous visuotactile stimulation leads to the misattribution of a fake hand as one's own, reflecting an inability to resolve competing generative models due to ambiguous multisensory predictions. In this scenario, prediction errors from incongruent proprioceptive and visual cues are minimized by adopting a unified model incorporating the rubber hand, highlighting how variational inference prioritizes surprise reduction over veridicality when model evidence is balanced.^[16]^[15]

Active inference

Active inference formulates the selection of actions within the free energy principle as the choice of policies that minimize expected free energy, thereby enabling agents to balance goal-directed behavior with uncertainty reduction.^[17] A policy \pi is defined as a sequence of actions over time, representing possible trajectories through the environment that an agent might pursue.^[18] The expected free energy G(\pi) under a policy \pi quantifies the anticipated surprise or divergence from the agent's generative model, providing a scalar value for policy evaluation. The expected free energy is expressed as

G(\pi) = \sum_{\tau > t} \mathbb{E}_{Q} [\ln P(o_{\tau}|s_{\tau}) - \ln Q(s_{\tau}|\pi)],

where Q denotes the agent's approximate posterior beliefs, P is the generative model, the sum is over future time steps \tau after current time t, s_{\tau} are environmental states, and o_{\tau} are sensory outcomes.^[19] This functional decomposes into two key terms: the risk (or pragmatic) component, which captures the expected divergence from preferred outcomes and drives exploitation of known goals, and the ambiguity (or epistemic) component, which measures uncertainty in predictions and encourages information gain.^[17] Policies are selected probabilistically via a softmax function over the negative expected free energy, \pi^* = \softmax(-\beta [G](/page/G)(\pi)), where \beta is an inverse temperature parameter controlling the determinism of choice; this mechanism ensures that agents prefer policies minimizing future surprise while incorporating precision weighting.^[18] The epistemic term in particular relates to exploration, as its minimization promotes novelty-seeking behaviors that resolve uncertainty about the environment, effectively driving epistemic foraging.^[20] For instance, in simulated foraging tasks, agents under active inference navigate ambiguous environments by selecting policies that first gather information about resource locations (epistemic value) before exploiting them (pragmatic value), thereby minimizing long-term expected surprise without exhaustive search.^[21] This approach integrates seamlessly with perceptual inference by using updated sensory beliefs to inform policy evaluation.^[18]

Neuroscience Applications

Learning and memory

In the free energy principle (FEP), perceptual learning emerges as a slow process that minimizes variational free energy by updating hyperparameters, which encode prior expectations about the environment's causal structure. These updates occur through mechanisms akin to Hebbian plasticity, where synaptic strengths adjust to reduce prediction errors accumulated over multiple exposures, effectively refining the generative model's parameters to better anticipate sensory data.^[22]^[23] This hierarchical optimization ensures that higher-level priors constrain lower-level inferences, promoting efficient encoding of environmental regularities without rapid fluctuations.^[2] Empirical support for these learning processes comes from in vitro experiments with networks of rat cortical neurons, which demonstrate that neural activity and synaptic plasticity conform to free-energy minimization during causal inference tasks, quantitatively validating FEP predictions as of 2023.^[24] Memory formation under the FEP is conceptualized as the development and maintenance of generative models that simulate sensory trajectories. Episodic memory, in particular, captures sequences of states and transitions in these models, allowing agents to reconstruct past experiences by minimizing free energy associated with temporal predictions.^[25] Working memory, meanwhile, sustains high-precision beliefs about current states during inference, enabling the temporary prioritization of relevant predictions to resolve uncertainty in ongoing tasks.^[26] Synaptic plasticity provides the neurobiological substrate for these processes, with long-term potentiation (LTP) and depression (LTD) driven by prediction errors that act as gradients for free energy minimization. In this framework, error signals modulate synaptic weights such that coincident pre- and postsynaptic activity strengthens connections when predictions align with outcomes, mirroring Hebbian rules but grounded in variational Bayesian updates.^[27] This dependency ensures plasticity adapts the generative model to minimize surprise over time-scales relevant to learning. An illustrative example is habit formation, where repeated actions flatten the expected free energy landscape, reducing epistemic value (information gain) while preserving pragmatic value (goal attainment). Through active inference, agents learn habitual policies by caching low-entropy trajectories that reliably minimize future free energy, transitioning from exploratory to exploitative behavior.^[25]^[28]

Attention and precision

In the free energy principle, attention emerges as a mechanism for optimizing the precision of prediction errors during perceptual inference. Precision, denoted as \psi, is formally defined as the inverse of the variance \sigma^2 of sensory noise or prediction errors (\psi = 1/\sigma^2), which quantifies the reliability of incoming signals.^[22] This precision acts as a gain modulator on error-signaling neurons, amplifying responses from more trustworthy channels while downweighting unreliable ones, thereby refining the hierarchical minimization of variational free energy.^[13] By dynamically adjusting this gain, the brain prioritizes information that best reduces surprise, aligning perceptual processes with environmental demands.^[29] Salience within this framework bifurcates into endogenous and exogenous forms of precision control. Endogenous precision is goal-driven, originating from top-down priors that enhance attention toward task-relevant features, such as voluntarily shifting focus in a search task.^[22] In contrast, exogenous precision is stimulus-driven, triggered by bottom-up surprises like sudden visual onsets that capture attention involuntarily.^[13] This distinction allows the system to balance internal expectations with external perturbations, ensuring efficient resource allocation in predictive coding schemes. Neuromodulatory systems underpin these precision dynamics. Acetylcholine primarily tunes precision by increasing synaptic gain on prediction error units, promoting selective attention through sharpened sensory representations and associated gamma oscillations.^[13] Dopamine, meanwhile, modulates salience in error signaling, particularly by encoding the motivational value of predictions, which influences the weighting of errors in value-sensitive contexts.^[22] A key example of precision overload is the attentional blink, where rapid successive stimuli lead to missed detection of a second target due to insufficient precision allocation in hierarchical inference; the ongoing optimization for the first stimulus temporarily saturates the system's capacity to update precision for subsequent inputs.^[30] This phenomenon highlights how precision constraints in temporal processing can disrupt inference, as the brain struggles to balance error minimization across layers.^[31]

Broader Extensions

Artificial intelligence and robotics

The free energy principle (FEP) has been applied in artificial intelligence and robotics to develop autonomous agents that minimize variational free energy through active inference, enabling adaptive perception-action loops in engineered systems.^[32] In robotics, active inference frameworks leverage the expected free energy (EFE) to balance exploitation and exploration, allowing robots to select actions that reduce uncertainty while pursuing goals in dynamic environments.^[33] Post-2020 implementations have demonstrated active inference on humanoid platforms like the iCub robot, where generative models minimize prediction errors for body perception and reaching tasks, outperforming traditional inverse kinematics methods in noisy sensory conditions.^[34] For instance, multimodal variational autoencoder-based controllers integrated with active inference have enabled the iCub to perform visuomotor tasks, such as object tracking, by optimizing EFE for epistemic foraging in real-world settings.^[35] These advancements highlight FEP's role in creating robust, self-calibrating robotic systems capable of lifelong learning without explicit reward signals.^[32] In AI alignment research, the FEP provides a foundation for safe AGI by framing alignment as surprise minimization, where agents inherently avoid catastrophic states that increase free energy, thus promoting systemic safety in multi-agent interactions. Discussions from 2023 to 2025 emphasize how EFE-driven policies can mitigate risks in agentic systems, ensuring robustness against misalignment by prioritizing predictive coherence over short-term gains.^[36] This approach has been proposed as a metric for evaluating AGI safety, reducing the likelihood of unintended harmful behaviors through variational bounds on risk. The FEP underpins curiosity-driven learning in reinforcement learning (RL) and variational autoencoders (VAEs), where intrinsic rewards are derived from hidden state uncertainty to encourage exploration in sparse-reward environments.^[37] A 2024 framework integrates FEP-based curiosity with deep RL, using KL divergence between predictive distributions as a reward signal to guide agents toward informative states without external supervision.^[37] This has enabled efficient solving of robotic tasks from pixel inputs via active inference, where EFE planning optimizes long-horizon policies by treating action selection as variational inference over generative models. Such methods outperform standard RL baselines in adaptability, as seen in simulations of locomotion and manipulation.^[37] Recent 2025 models explore consciousness in AI through FEP-based attentional control, positing that "inner screens" of predictive processing enable self-referential awareness by minimizing free energy in hierarchical inference.^[38] These architectures simulate attentional shifts as precision-weighted updates, allowing AI systems to model their own "experiences" via EFE, with applications in generative agents that exhibit emergent metacognition.^[38] For example, implementations in neuro-symbolic AI demonstrate how FEP constrains attentional mechanisms to produce coherent, non-hallucinating outputs akin to human-like focus.^[38]

Biological and physical systems

The free energy principle (FEP) has been extended to intracellular processes, where it explains the emergence of compartmentalization as a mechanism to minimize variational free energy by preserving boundary integrity. In 2024 studies, researchers demonstrated that systems governed by the FEP naturally induce the formation of intracellular compartments, such as organelles, through the minimization of surprise at system boundaries, which effectively reduces free energy by constraining internal states against external perturbations.^[39] This process amplifies symmetry breaking at cellular boundaries, leading to self-organized structures that maintain non-equilibrium steady states essential for cellular persistence. For instance, bioelectric signaling within cells acts as a constraint that propagates compartmentalization, aligning with the FEP's prediction that adaptive systems partition states to bound free energy.^[39] In evolutionary biology, the FEP frames natural selection as a process that favors robust phenotypes capable of minimizing free energy over generations, ensuring survival in fluctuating environments. Karl Friston's 2013 work posits that biological systems, including evolving populations, maintain their form through Markov blankets that partition internal and external states, with selection pressures acting to optimize phenotypes that resist entropy and surprise.^[40] This perspective, developed onward from Friston's foundational formulations, views evolution as an implicit free energy minimization, where phenotypes that robustly predict and adapt to environmental contingencies are selected, thereby perpetuating self-organizing traits across scales from molecules to organisms. Subsequent extensions reinforce that evolutionary dynamics align with the FEP by prioritizing variational bounds on phenotypic variability, promoting homeostasis and adaptability without invoking teleological assumptions. The FEP also applies to physical systems, particularly non-equilibrium dissipative structures that minimize free energy fluxes to sustain ordered states far from thermodynamic equilibrium. In such systems, like dissipative particle dynamics, particles exchange energy and matter with their environment, with flows governed by gradient descent on a free energy functional that bounds entropy production. This minimization ensures the persistence of structures, such as self-assembling colloids or reaction-diffusion patterns, by constraining trajectories to low-surprise attractors, akin to biological homeostasis but in purely physical contexts. The principle's formulation for random dynamical systems highlights how these fluxes arise from ergodic partitioning, linking Prigogine's dissipative structures to variational inference without requiring biological specificity. A key example of the FEP in non-neural biology is bacterial chemotaxis, interpreted as active inference where cells minimize expected free energy without cognitive processes. Recent extensions from 2023 to 2025 model bacterial navigation toward nutrients as Bayesian inference under the FEP, with run-and-tumble motility adjusting policies to reduce sensory prediction errors and epistemic value.^[41] In Escherichia coli, for instance, temporal and spatial gradient sensing embodies active inference by updating internal models of attractant concentrations, thereby bounding surprise through directed movement that preserves the cell's non-equilibrium state. This molecular implementation demonstrates how the FEP unifies perception and action at the simplest biological scales, with mutual constraints from exteroceptive (chemical) and interoceptive (metabolic) signals driving adaptive behavior.^[41]

Criticisms and Debates

Falsifiability concerns

Critics have argued that the free energy principle (FEP) lacks falsifiability because it can retrospectively accommodate any observed behavior by framing it as an instance of free energy minimization, rendering it tautological rather than empirically testable. More recent critiques have amplified these concerns, portraying the FEP as a pseudoscientific construct that evades refutation through terminological maneuvers. In a 2025 preprint, Madhur Mangalam described the FEP as an "emperor's new pseudo-theory," arguing that core concepts like "surprise" are redefined so broadly that contradictory evidence—such as systems failing to minimize free energy—can be reinterpreted as successful minimization under alternative model specifications.^[42] Mangalam contended that this adaptability undermines the FEP's scientific status, as it permits proponents to claim universality without genuine vulnerability to empirical disconfirmation.^[42] Proponents of the FEP counter that such criticisms mischaracterize the principle as a descriptive empirical theory when it is fundamentally normative, akin to physical laws like the principle of least action, which guide behavior without being falsifiable in observation.^[5] Karl Friston, the FEP's primary architect, has emphasized that the principle provides a mathematical prescription for optimal inference and control, testable through specific, falsifiable predictions derived from it—such as the modulation of sensory precision weighting in perceptual tasks or the emergence of hierarchical predictive coding in neural responses.^[5] These derivative models, rather than the principle itself, bear the empirical burden, allowing targeted experiments to validate or refute FEP-based hypotheses.^[5] A related point of contention involves the empirical detectability of Markov blankets, which partition systems into internal, external, and boundary states under the FEP and are essential for defining autonomous agents. Critics argue that in complex, real-world biological systems, identifying these blankets is practically infeasible due to entangled interactions and incomplete observational data, potentially rendering the FEP's application unverifiable.^[43] For instance, Vicente Raja and colleagues in 2021 highlighted how the "Markov blanket trick"—imposing such partitions analytically—expands the FEP's scope to non-adaptive systems without clear empirical demarcation, raising questions about whether blankets can be robustly detected beyond idealized simulations.^[43] This debate underscores ongoing philosophical scrutiny over the FEP's boundaries as a scientific construct.^[43]

Empirical and conceptual challenges

The free energy principle (FEP) faces empirical gaps in its neuroscience applications, primarily due to reliance on correlational evidence from neuroimaging techniques like fMRI rather than direct causal or behavioral tests. While FEP-inspired models have been fitted to fMRI data to explain perceptual inference and active control, these analyses often highlight predictive alignments without manipulating underlying mechanisms or verifying outcomes through targeted interventions.^[10] Independent empirical verification remains scarce, as the framework's mathematical complexity hinders straightforward testing against alternative hypotheses.^[44] For instance, in vitro neural network experiments provide some quantitative support for FEP predictions on causal inference, but they underscore challenges in identifying generative models at cellular levels and ensuring refutability beyond descriptive fits.^[24] Recent consciousness models grounded in FEP, such as those integrating active inference for minimal phenomenal experience, lack robust behavioral validation as of 2025, though emerging whole-brain simulations have begun incorporating neural data from meditation states to link predictions to observable correlates. These models propose that consciousness emerges from free energy minimization in hierarchical predictive processing, yet they rely on theoretical simulations or phenomenological reports without fully linking to observable behavioral metrics like decision-making under uncertainty or adaptive responses in dynamic tasks.^[45] This gap persists because FEP's abstraction allows flexible interpretations that fit diverse data but evade specific falsification through behavioral paradigms.^[46] Conceptually, the FEP's assumption of ergodicity—positing that systems sample all states over time to reach a non-equilibrium steady state—struggles in non-steady biological contexts like transient neural dynamics during learning or stress. Early formulations required ergodic flows for free energy bounds, but critiques highlight that real brains operate in path-dependent, non-ergodic regimes where historical contingencies disrupt steady-state convergence.^[47] Refinements from 2023 to 2025, including thermodynamic extensions to living systems, address this by relaxing ergodicity for variational inference in fluctuating environments, though full resolution remains ongoing.^[48] Scaling FEP to real brains presents further hurdles, particularly in capturing hierarchical depth beyond simplified models. Computational implementations often limit layers to a few levels for tractability, whereas cortical hierarchies span multiple spatiotemporal scales, complicating precise mapping of precision-weighted predictions across depths.^[49] Integration with game theory for multi-agent interactions, such as social inference, is incomplete, as FEP extensions to bounded-rational agents fail to fully incorporate incomplete information or strategic equilibria without ad hoc approximations.^[50] Looking ahead, 2024–2025 advancements in expected free energy (EFE) for planning emphasize the need for interdisciplinary empirical tests to bridge these gaps, such as combining neural recordings with behavioral assays in ecological settings.^[51] In artificial intelligence, EFE-based planning shows promise but encounters analogous scaling issues in high-dimensional environments.^[51]

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None
### Summary of the Free Energy Principle from the Paper
[9]
A Free Energy Principle for Biological Systems - PMC
This paper describes a free energy principle that tries to explain the ability of biological systems to resist a natural tendency to disorder.
[10]
[PDF] The free-energy principle: a unified brain theory?
Jan 13, 2010 · This paper introduces the central role of generative models and variational approaches to hierarchical self-supervised learning and relates this ...
[11]
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### Summary of Predictive Coding under the Free-Energy Principle
[12]
Predictive coding under the free-energy principle - Journals
May 12, 2009 · Predictive coding under the free-energy principle. Karl Friston. Karl Friston. k.friston@fil.ion.ucl.ac.uk · Google Scholar · Find this author ...Missing: Friston | Show results with:Friston
[13]
Attention, Uncertainty, and Free-Energy - PMC - PubMed Central - NIH
These range from ordinary least squares to advanced variational deconvolution schemes (see Friston, 2008). For example, the schemes used to invert ...
[14]
https://doi.org/10.3389/fnhum.2010.00215
[15]
https://doi.org/10.1016/j.tics.2009.04.005
[16]
https://doi.org/10.3389/fnhum.2013.00547
[17]
Generalised free energy and active inference - PMC - PubMed Central
This is variational free energy (Beal 2003; Dayan et al. 1995; Friston 2003) which depends upon specifying a generative model of how data are caused. This ...Introduction · Table 1 · Comparison Of Active...<|control11|><|separator|>
[18]
[PDF] Active Inference: A Process Theory - Free Energy Principle
This article describes a process theory based on active inference and be- lief propagation. Starting from the premise that all neuronal processing.
[19]
[PDF] Generalised free energy and active inference - bioRxiv
Apr 23, 2018 · G π is the expected free energy, conditioned on a policy. It is ... Friston K, Buzsaki G (2016) The Functional Anatomy of Time: What ...
[20]
Scene Construction, Visual Foraging, and Active Inference - Frontiers
Active inference assumes that the only self-consistent prior belief is that our actions will minimize free energy; in other words, we (believe we) will behave ...
[21]
Active Inference, epistemic value, and vicarious trial and error - PMC
This section describes four simulations of VTE behavior using a Bayesian (Active Inference) formulation of choice and foraging (Friston et al. 2013, 2014, 2015) ...
[22]
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### Summary of Perceptual Inference in the Free Energy Principle
[23]
A free energy principle for the brain - ScienceDirect.com
In this paper, we show these perceptual processes are just one aspect of emergent behaviours of systems that conform to a free energy principle.Missing: original | Show results with:original
[24]
Active inference and learning - ScienceDirect.com
This paper offers an active inference account of choice behaviour and learning. It focuses on the distinction between goal-directed and habitual behaviour.
[25]
Working memory, attention, and salience in active inference - Nature
Nov 7, 2017 · We use active inference to demonstrate how attention and salience can be disambiguated in terms of message passing between populations of neurons.
[26]
Bayesian Mechanics of Synaptic Learning Under the Free-Energy ...
The free-energy principle (FEP) advocated by Karl Friston explicates the local, recurrent, and self-supervised cognitive dynamics of the brain's higher-order ...
[27]
Caching mechanisms for habit formation in Active Inference - PMC
In other words, agents can learn habits through minimising their expected free energy – and then select them from an augmented repertoire of policies, in a ...
[28]
The free-energy principle: a rough guide to the brain? - ScienceDirect
A free energy principle for the brain. J. Physiol. Paris. (2006) ; The Bayesian brain: the role of uncertainty in neural coding and computation. Trends Neurosci.
[29]
Predictive coding under the free-energy principle - Journals
May 12, 2009 · ... perceptual inference, eLife, 10.7554/eLife.11476, 5. Maes P (2016) ... Rubber Hand Illusion, Neural Plasticity, 10.1155/2016/8307175 ...
[30]
A key role of the hippocampal P3 in the attentional blink
May 1, 2023 · The attentional blink (AB) refers to an impaired identification of target stimuli (T2), which are presented shortly after a prior target ...
[31]
How Active Inference Could Help Revolutionise Robotics - MDPI
In this paper, we explain how active inference—a well-known description of sentient behaviour from neuroscience—can be exploited in robotics ...Missing: iCub post-
[32]
https://www.mdpi.com/1099-4300/24/3/361
[33]
https://arxiv.org/abs/2112.01871
[34]
https://doi.org/10.1109/TCDS.2021.3049907
[35]
A reply to Byrnes on the Free Energy Principle - AI Alignment Forum
Mar 3, 2023 · And we don't know in what direction the AGI architecture will evolve (whether via self-modification or not). The FEP ontology might be one of ...Missing: minimization | Show results with:minimization
[36]
Intrinsic Rewards for Exploration without Harm from Observational ...
May 13, 2024 · Based on the Free Energy Principle (FEP), this paper proposes hidden state curiosity, which rewards agents by the KL divergence between the ...Missing: variational autoencoders
[37]
How do inner screens enable imaginative experience? Applying the ...
We present a model of imaginative experience that is compliant with the free-energy principle (FEP). ... Depression thus entails altered precision weighting ...
[38]
The Emperor's New Pseudo-Theory: How the Free Energy Principle ...
The Emperor's New Pseudo-Theory: How the Free Energy Principle Ransacked Neuroscience ... Murphy et al. (2024). Natural language syntax. complies with the free-.
[39]
(PDF) The Markov Blanket Trick: On the Scope of the Free Energy ...
Mar 25, 2021 · The free energy principle (FEP) has been presented as a unified ... Markov blankets were first proposed by Judea Pearl (1988) in the c ...Missing: falsifiability | Show results with:falsifiability<|control11|><|separator|>
[40]
Free energy: a user's guide | Biology & Philosophy
Jul 20, 2022 · Second, we describe the historical trajectory of the framework and highlight its novel features (“A brief history of the free energy principle” ...
[41]
Experimental validation of the free-energy principle with in vitro ...
Aug 7, 2023 · ... variational Bayes formation. a Schematics of the experimental setup ... Friston, K. J. The free-energy principle: a unified brain theory?
[42]
https://www.researchgate.net/publication/390546288_The_Emperor%27s_New_Pseudo-Theory_How_the_Free_Energy_Principle_Ransacked_Neuroscience
[43]
[PDF] The Free Energy Principle: A Unifying Framework Connecting ...
May 16, 2025 · Abstract. This paper deeply explores Karl Friston's Free Energy Principle (FEP) as a meta-theory with significant potential for unifying our ...
[44]
How particular is the physics of the free energy principle?
The free energy principle (FEP) states that any dynamical system can be interpreted as performing Bayesian inference upon its surrounding environment.Missing: empirical detectability
[45]
Free energy and inference in living systems | Interface Focus
Apr 14, 2023 · This study presents an FE minimization theory overarching the essential features of both the thermodynamic and neuroscientific FE principles.
[46]
An Overview of the Free Energy Principle and Related Research
Apr 23, 2024 · This principle states that the processes of perception, learning, and decision making—within an agent—are all driven by the objective of “ ...
[47]
[PDF] Toward a Theory of Interactions Between Boundedly-Rational Agents
We propose that free- energy-based models provide a promising framework for studying cooperation and conflict among boundedly-rational players with incomplete ...
[48]
[PDF] Expected Free Energy-based Planning as Variational Inference - arXiv
EFE-based planning, grounded in the Free Energy Principle, minimizes Expected Free Energy (EFE) and is shown to arise from variational inference.