Sophisticated Inference

Resilience phenotypes derived from an active inference account of allostasis

Within a theoretical framework of enactive allostasis, we explore active inference strategies for minimizing surprise to achieve resilience in dynamic environments. While individual differences and extrinsic protective factors traditionally account for variability in resilience trajectories following stressor exposure, the enactive model emphasizes the importance of the physical and social environment, specifically the "enactive niche," which is both shaped by and impacts organisms living in it, accounting for variable success in allostatic prediction and accommodation. Enactive allostasis infers or predicts states of the world to minimize surprise and maintain regulation after surprise, i.e., resilience. Action policies are selected in accordance with the inferred state of a dynamic environment; those actions concurrently shape one's environment, buffering against current and potential stressors. Through such inferential construction, multiple potential solutions exist for achieving stability within one's enactive niche. Spanning a range of adaptive resilience strategies, we propose four phenotypes-fragile, durable, resilient, and pro-entropic (PE)-each characterized by a constellation of genetic, epigenetic, developmental, experiential, and environmental factors. Biological regulatory outcomes range from allostatic (over)load in the fragile and durable phenotypes, to allostatic recovery in resilience, and theoretically to increasing allostatic accommodation or "growth" in the proposed PE phenotype. Awareness distinguishes phenotypes by minimizing allostatically demanding surprise and engenders the cognitive and behavioral flexibility empirically associated with resilience. We further propose a role for awareness in proactively shaping one's enactive niche to further minimize surprise. We conclude by exploring the mechanisms of phenotypic plasticity which may bolster individual resilience.

Dynamic planning in hierarchical active inference

By dynamic planning, we refer to the ability of the human brain to infer and impose motor trajectories related to cognitive decisions. A recent paradigm, active inference, brings fundamental insights into the adaptation of biological organisms, constantly striving to minimize prediction errors to restrict themselves to life-compatible states. Over the past years, many studies have shown how human and animal behaviors could be explained in terms of active inference - either as discrete decision-making or continuous motor control - inspiring innovative solutions in robotics and artificial intelligence. Still, the literature lacks a comprehensive outlook on effectively planning realistic actions in changing environments. Setting ourselves the goal of modeling complex tasks such as tool use, we delve into the topic of dynamic planning in active inference, keeping in mind two crucial aspects of biological behavior: the capacity to understand and exploit affordances for object manipulation, and to learn the hierarchical interactions between the self and the environment, including other agents. We start from a simple unit and gradually describe more advanced structures, comparing recently proposed design choices and providing basic examples. This study distances itself from traditional views centered on neural networks and reinforcement learning, and points toward a yet unexplored direction in active inference: hybrid representations in hierarchical models.

Intrinsic Motivation as Constrained Entropy Maximization

"Intrinsic motivation" refers to the capacity for intelligent systems to be motivated endogenously, i.e., by features of agential architecture itself rather than by learned associations between action and reward. This paper views active inference, empowerment, and other formal accounts of intrinsic motivation as variations on the theme of constrained maximum entropy inference, providing a general perspective on intrinsic motivation complementary to existing frameworks. The connection between free energy and empowerment noted in previous literature is further explored, and it is argued that the maximum-occupancy approach in practice incorporates an implicit model-evidence constraint.

Active Inference and Intentional Behavior

Recent advances in theoretical biology suggest that key definitions of basal cognition and sentient behavior may arise as emergent properties of in vitro cell cultures and neuronal networks. Such neuronal networks reorganize activity to demonstrate structured behaviors when embodied in structured information landscapes. In this article, we characterize this kind of self-organization through the lens of the free energy principle, that is, as self-evidencing. We do this by first discussing the definitions of reactive and sentient behavior in the setting of active inference, which describes the behavior of agents that model the consequences of their actions. We then introduce a formal account of intentional behavior that describes agents as driven by a preferred end point or goal in latent state-spaces. We then investigate these forms of (reactive, sentient, and intentional) behavior using simulations. First, we simulate the in vitro experiments, in which neuronal cultures modulated activity to improve gameplay in a simplified version of Pong by implementing nested, free energy minimizing processes. The simulations are then used to deconstruct the ensuing predictive behavior, leading to the distinction between merely reactive, sentient, and intentional behavior with the latter formalized in terms of inductive inference. This distinction is further studied using simple machine learning benchmarks (navigation in a grid world and the Tower of Hanoi problem) that show how quickly and efficiently adaptive behavior emerges under an inductive form of active inference.

On the varieties of conscious experiences: Altered Beliefs Under Psychedelics (ALBUS)

How is it that psychedelics so profoundly impact brain and mind? According to the model of "Relaxed Beliefs Under Psychedelics" (REBUS), 5-HT2a agonism is thought to help relax prior expectations, thus making room for new perspectives and patterns. Here, we introduce an alternative (but largely compatible) perspective, proposing that REBUS effects may primarily correspond to a particular (but potentially pivotal) regime of very high levels of 5-HT2a receptor agonism. Depending on both a variety of contextual factors and the specific neural systems being considered, we suggest opposite effects may also occur in which synchronous neural activity becomes more powerful, with accompanying "Strengthened Beliefs Under Psychedelics" (SEBUS) effects. Such SEBUS effects are consistent with the enhanced meaning-making observed in psychedelic therapy (e.g. psychological insight and the noetic quality of mystical experiences), with the imposition of prior expectations on perception (e.g. hallucinations and pareidolia), and with the delusional thinking that sometimes occurs during psychedelic experiences (e.g. apophenia, paranoia, engendering of inaccurate interpretations of events, and potentially false memories). With "Altered Beliefs Under Psychedelics" (ALBUS), we propose that the manifestation of SEBUS vs. REBUS effects may vary across the dose-response curve of 5-HT2a signaling. While we explore a diverse range of sometimes complex models, our basic idea is fundamentally simple: psychedelic experiences can be understood as kinds of waking dream states of varying degrees of lucidity, with similar underlying mechanisms. We further demonstrate the utility of ALBUS by providing neurophenomenological models of psychedelics focusing on mechanisms of conscious perceptual synthesis, dreaming, and episodic memory and mental simulation.

Introducing ActiveInference.jl: A Julia Library for Simulation and Parameter Estimation with Active Inference Models

We introduce a new software package for the Julia programming language, the library ActiveInference.jl. To make active inference agents with Partially Observable Markov Decision Process (POMDP) generative models available to the growing research community using Julia, we re-implemented the pymdp library for Python. ActiveInference.jl is compatible with cutting-edge Julia libraries designed for cognitive and behavioural modelling, as it is used in computational psychiatry, cognitive science and neuroscience. This means that POMDP active inference models can now be easily fit to empirically observed behaviour using sampling, as well as variational methods. In this article, we show how ActiveInference.jl makes building POMDP active inference models straightforward, and how it enables researchers to use them for simulation, as well as fitting them to data or performing a model comparison.

Generative models for sequential dynamics in active inference

A central theme of theoretical neurobiology is that most of our cognitive operations require processing of discrete sequences of items. This processing in turn emerges from continuous neuronal dynamics. Notable examples are sequences of words during linguistic communication or sequences of locations during navigation. In this perspective, we address the problem of sequential brain processing from the perspective of active inference, which inherits from a Helmholtzian view of the predictive (Bayesian) brain. Underneath the active inference lies a generative model; namely, a probabilistic description of how (observable) consequences are generated by (unobservable) causes. We show that one can account for many aspects of sequential brain processing by assuming the brain entails a generative model of the sensed world that comprises central pattern generators, narratives, or well-defined sequences. We provide examples in the domains of motor control (e.g., handwriting), perception (e.g., birdsong recognition) through to planning and understanding (e.g., language). The solutions to these problems include the use of sequences of attracting points to direct complex movements-and the move from continuous representations of auditory speech signals to the discrete words that generate those signals.

An Active-Inference Approach to Second-Person Neuroscience

Social neuroscience has often been criticized for approaching the investigation of the neural processes that enable social interaction and cognition from a passive, detached, third-person perspective, without involving any real-time social interaction. With the emergence of second-person neuroscience, investigators have uncovered the unique complexity of neural-activation patterns in actual, real-time interaction. Social cognition that occurs during social interaction is fundamentally different from that unfolding during social observation. However, it remains unclear how the neural correlates of social interaction are to be interpreted. Here, we leverage the active-inference framework to shed light on the mechanisms at play during social interaction in second-person neuroscience studies. Specifically, we show how counterfactually rich mutual predictions, real-time bodily adaptation, and policy selection explain activation in components of the default mode, salience, and frontoparietal networks of the brain, as well as in the basal ganglia. We further argue that these processes constitute the crucial neural processes that underwrite bona fide social interaction. By placing the experimental approach of second-person neuroscience on the theoretical foundation of the active-inference framework, we inform the field of social neuroscience about the mechanisms of real-life interactions. We thereby contribute to the theoretical foundations of empirical second-person neuroscience.

Supervised structure learning

This paper concerns structure learning or discovery of discrete generative models. It focuses on Bayesian model selection and the assimilation of training data or content, with a special emphasis on the order in which data are ingested. A key move-in the ensuing schemes-is to place priors on the selection of models, based upon expected free energy. In this setting, expected free energy reduces to a constrained mutual information, where the constraints inherit from priors over outcomes (i.e., preferred outcomes). The resulting scheme is first used to perform image classification on the MNIST dataset to illustrate the basic idea, and then tested on a more challenging problem of discovering models with dynamics, using a simple sprite-based visual disentanglement paradigm and the Tower of Hanoi (cf., blocks world) problem. In these examples, generative models are constructed autodidactically to recover (i.e., disentangle) the factorial structure of latent states-and their characteristic paths or dynamics.

Active Inference and Reinforcement Learning: A Unified Inference on Continuous State and Action Spaces Under Partial Observability

Reinforcement learning (RL) has garnered significant attention for developing decision-making agents that aim to maximize rewards, specified by an external supervisor, within fully observable environments. However, many real-world problems involve partial or noisy observations, where agents cannot access complete and accurate information about the environment. These problems are commonly formulated as partially observable Markov decision processes (POMDPs). Previous studies have tackled RL in POMDPs by either incorporating the memory of past actions and observations or by inferring the true state of the environment from observed data. Nevertheless, aggregating observations and actions over time becomes impractical in problems with large decision-making time horizons and high-dimensional spaces. Furthermore, inference-based RL approaches often require many environmental samples to perform well, as they focus solely on reward maximization and neglect uncertainty in the inferred state. Active inference (AIF) is a framework naturally formulated in POMDPs and directs agents to select actions by minimizing a function called expected free energy (EFE). This supplies reward-maximizing (or exploitative) behavior, as in RL, with information-seeking (or exploratory) behavior. Despite this exploratory behavior of AIF, its use is limited to problems with small time horizons and discrete spaces due to the computational challenges associated with EFE. In this article, we propose a unified principle that establishes a theoretical connection between AIF and RL, enabling seamless integration of these two approaches and overcoming their limitations in continuous space POMDP settings. We substantiate our findings with rigorous theoretical analysis, providing novel perspectives for using AIF in designing and implementing artificial agents. Experimental results demonstrate the superior learning capabilities of our method compared to other alternative RL approaches in solving partially observable tasks with continuous spaces. Notably, our approach harnesses information-seeking exploration, enabling it to effectively solve reward-free problems and rendering explicit task reward design by an external supervisor optional.

Brain-consistent architecture for imagination

Background

Imagination represents a pivotal capability of human intelligence. To develop human-like artificial intelligence, uncovering the computational architecture pertinent to imaginative capabilities through reverse engineering the brain's computational functions is essential. The existing Structure-Constrained Interface Decomposition (SCID) method, leverages the anatomical structure of the brain to extract computational architecture. However, its efficacy is limited to narrow brain regions, making it unsuitable for realizing the function of imagination, which involves diverse brain areas such as the neocortex, basal ganglia, thalamus, and hippocampus.

Objective

In this study, we proposed the Function-Oriented SCID method, an advancement over the existing SCID method, comprising four steps designed for reverse engineering broader brain areas. This method was applied to the brain's imaginative capabilities to design a hypothetical computational architecture. The implementation began with defining the human imaginative ability that we aspire to simulate. Subsequently, six critical requirements necessary for actualizing the defined imagination were identified. Constraints were established considering the unique representational capacity and the singularity of the neocortex's modes, a distributed memory structure responsible for executing imaginative functions. In line with these constraints, we developed five distinct functions to fulfill the requirements. We allocated specific components for each function, followed by an architectural proposal aligning each component with a corresponding brain organ.

Results

In the proposed architecture, the distributed memory component, associated with the neocortex, realizes the representation and execution function; the imaginary zone maker component, associated with the claustrum, accomplishes the dynamic-zone partitioning function; the routing conductor component, linked with the complex of thalamus and basal ganglia, performs the manipulation function; the mode memory component, related to the specific agranular neocortical area executes the mode maintenance function; and the recorder component, affiliated with the hippocampal formation, handles the history management function. Thus, we have provided a fundamental cognitive architecture of the brain that comprehensively covers the brain's imaginative capacities.

Goal-oriented inference of environment from redundant observations

The agent learns to organize decision behavior to achieve a behavioral goal, such as reward maximization, and reinforcement learning is often used for this optimization. Learning an optimal behavioral strategy is difficult under the uncertainty that events necessary for learning are only partially observable, called as Partially Observable Markov Decision Process (POMDP). However, the real-world environment also gives many events irrelevant to reward delivery and an optimal behavioral strategy. The conventional methods in POMDP, which attempt to infer transition rules among the entire observations, including irrelevant states, are ineffective in such an environment. Supposing Redundantly Observable Markov Decision Process (ROMDP), here we propose a method for goal-oriented reinforcement learning to efficiently learn state transition rules among reward-related "core states" from redundant observations. Starting with a small number of initial core states, our model gradually adds new core states to the transition diagram until it achieves an optimal behavioral strategy consistent with the Bellman equation. We demonstrate that the resultant inference model outperforms the conventional method for POMDP. We emphasize that our model only containing the core states has high explainability. Furthermore, the proposed method suits online learning as it suppresses memory consumption and improves learning speed.

On Predictive Planning and Counterfactual Learning in Active Inference

Given the rapid advancement of artificial intelligence, understanding the foundations of intelligent behaviour is increasingly important. Active inference, regarded as a general theory of behaviour, offers a principled approach to probing the basis of sophistication in planning and decision-making. This paper examines two decision-making schemes in active inference based on "planning" and "learning from experience". Furthermore, we also introduce a mixed model that navigates the data complexity trade-off between these strategies, leveraging the strengths of both to facilitate balanced decision-making. We evaluate our proposed model in a challenging grid-world scenario that requires adaptability from the agent. Additionally, our model provides the opportunity to analyse the evolution of various parameters, offering valuable insights and contributing to an explainable framework for intelligent decision-making.

An Overview of the Free Energy Principle and Related Research

The free energy principle and its corollary, the active inference framework, serve as theoretical foundations in the domain of neuroscience, explaining the genesis of intelligent behavior. This principle states that the processes of perception, learning, and decision making-within an agent-are all driven by the objective of "minimizing free energy," evincing the following behaviors: learning and employing a generative model of the environment to interpret observations, thereby achieving perception, and selecting actions to maintain a stable preferred state and minimize the uncertainty about the environment, thereby achieving decision making. This fundamental principle can be used to explain how the brain processes perceptual information, learns about the environment, and selects actions. Two pivotal tenets are that the agent employs a generative model for perception and planning and that interaction with the world (and other agents) enhances the performance of the generative model and augments perception. With the evolution of control theory and deep learning tools, agents based on the FEP have been instantiated in various ways across different domains, guiding the design of a multitude of generative models and decision-making algorithms. This letter first introduces the basic concepts of the FEP, followed by its historical development and connections with other theories of intelligence, and then delves into the specific application of the FEP to perception and decision making, encompassing both low-dimensional simple situations and high-dimensional complex situations. It compares the FEP with model-based reinforcement learning to show that the FEP provides a better objective function. We illustrate this using numerical studies of Dreamer3 by adding expected information gain into the standard objective function. In a complementary fashion, existing reinforcement learning, and deep learning algorithms can also help implement the FEP-based agents. Finally, we discuss the various capabilities that agents need to possess in complex environments and state that the FEP can aid agents in acquiring these capabilities.

Order and change in art: towards an active inference account of aesthetic experience

How to account for the power that art holds over us? Why do artworks touch us deeply, consoling, transforming or invigorating us in the process? In this paper, we argue that an answer to this question might emerge from a fecund framework in cognitive science known as predictive processing (a.k.a. active inference). We unpack how this approach connects sense-making and aesthetic experiences through the idea of an 'epistemic arc', consisting of three parts (curiosity, epistemic action and aha experiences), which we cast as aspects of active inference. We then show how epistemic arcs are built and sustained by artworks to provide us with those satisfying experiences that we tend to call 'aesthetic'. Next, we defuse two key objections to this approach; namely, that it places undue emphasis on the cognitive component of our aesthetic encounters-at the expense of affective aspects-and on closure and uncertainty minimization (order)-at the expense of openness and lingering uncertainty (change). We show that the approach offers crucial resources to account for the open-ended, free and playful behaviour inherent in aesthetic experiences. The upshot is a promising but deflationary approach, both philosophically informed and psychologically sound, that opens new empirical avenues for understanding our aesthetic encounters. This article is part of the theme issue 'Art, aesthetics and predictive processing: theoretical and empirical perspectives'.

Spatial and Temporal Hierarchy for Autonomous Navigation Using Active Inference in Minigrid Environment

Robust evidence suggests that humans explore their environment using a combination of topological landmarks and coarse-grained path integration. This approach relies on identifiable environmental features (topological landmarks) in tandem with estimations of distance and direction (coarse-grained path integration) to construct cognitive maps of the surroundings. This cognitive map is believed to exhibit a hierarchical structure, allowing efficient planning when solving complex navigation tasks. Inspired by human behaviour, this paper presents a scalable hierarchical active inference model for autonomous navigation, exploration, and goal-oriented behaviour. The model uses visual observation and motion perception to combine curiosity-driven exploration with goal-oriented behaviour. Motion is planned using different levels of reasoning, i.e., from context to place to motion. This allows for efficient navigation in new spaces and rapid progress toward a target. By incorporating these human navigational strategies and their hierarchical representation of the environment, this model proposes a new solution for autonomous navigation and exploration. The approach is validated through simulations in a mini-grid environment.

Hierarchical network structure as the source of hierarchical dynamics (power-law frequency spectra) in living and non-living systems: How state-trait continua (body plans, personalities) emerge from first principles in biophysics

Living systems are hierarchical control systems that display a small world network structure. In such structures, many smaller clusters are nested within fewer larger ones, producing a fractal-like structure with a 'power-law' cluster size distribution (a mereology). Just like their structure, the dynamics of living systems shows fractal-like qualities: the timeseries of inner message passing and overt behavior contain high frequencies or 'states' (treble) that are nested within lower frequencies or 'traits' (bass), producing a power-law frequency spectrum that is known as a 'state-trait continuum' in the behavioral sciences. Here, we argue that the power-law dynamics of living systems results from their power-law network structure: organisms 'vertically encode' the deep spatiotemporal structure of their (anticipated) environments, to the effect that many small clusters near the base of the hierarchy produce high frequency signal changes and fewer larger clusters at its top produce ultra-low frequencies. Such ultra-low frequencies exert a tonic regulatory pressure that produces morphological as well as behavioral traits (i.e., body plans and personalities). Nested-modular structure causes higher frequencies to be embedded within lower frequencies, producing a power-law state-trait continuum. At the heart of such dynamics lies the need for efficient energy dissipation through networks of coupled oscillators, which also governs the dynamics of non-living systems (e.q., earthquakes, stock market fluctuations). Since hierarchical structure produces hierarchical dynamics, the development and collapse of hierarchical structure (e.g., during maturation and disease) should leave specific traces in system dynamics (shifts in lower frequencies, i.e. morphological and behavioral traits) that may serve as early warning signs to system failure. The applications of this idea range from (bio)physics and phylogenesis to ontogenesis and clinical medicine.

Decisions under uncertainty are more messy than they seem

Conviction Narrative Theory (CNT) is conceptually so multifaceted as to make critical evaluation difficult. It also omits one course of action: Active engagement with the world. Parsing the developmental and mechanistic processes within CNT would allow for a rigorous research programme to put the account under test. I propose a unifying account based on active inference.

A neural active inference model of perceptual-motor learning

The active inference framework (AIF) is a promising new computational framework grounded in contemporary neuroscience that can produce human-like behavior through reward-based learning. In this study, we test the ability for the AIF to capture the role of anticipation in the visual guidance of action in humans through the systematic investigation of a visual-motor task that has been well-explored-that of intercepting a target moving over a ground plane. Previous research demonstrated that humans performing this task resorted to anticipatory changes in speed intended to compensate for semi-predictable changes in target speed later in the approach. To capture this behavior, our proposed "neural" AIF agent uses artificial neural networks to select actions on the basis of a very short term prediction of the information about the task environment that these actions would reveal along with a long-term estimate of the resulting cumulative expected free energy. Systematic variation revealed that anticipatory behavior emerged only when required by limitations on the agent's movement capabilities, and only when the agent was able to estimate accumulated free energy over sufficiently long durations into the future. In addition, we present a novel formulation of the prior mapping function that maps a multi-dimensional world-state to a uni-dimensional distribution of free-energy/reward. Together, these results demonstrate the use of AIF as a plausible model of anticipatory visually guided behavior in humans.

Generalized Simultaneous Localization and Mapping (G-SLAM) as unification framework for natural and artificial intelligences: towards reverse engineering the hippocampal/entorhinal system and principles of high-level cognition

Simultaneous localization and mapping (SLAM) represents a fundamental problem for autonomous embodied systems, for which the hippocampal/entorhinal system (H/E-S) has been optimized over the course of evolution. We have developed a biologically-inspired SLAM architecture based on latent variable generative modeling within the Free Energy Principle and Active Inference (FEP-AI) framework, which affords flexible navigation and planning in mobile robots. We have primarily focused on attempting to reverse engineer H/E-S "design" properties, but here we consider ways in which SLAM principles from robotics may help us better understand nervous systems and emergent minds. After reviewing LatentSLAM and notable features of this control architecture, we consider how the H/E-S may realize these functional properties not only for physical navigation, but also with respect to high-level cognition understood as generalized simultaneous localization and mapping (G-SLAM). We focus on loop-closure, graph-relaxation, and node duplication as particularly impactful architectural features, suggesting these computational phenomena may contribute to understanding cognitive insight (as proto-causal-inference), accommodation (as integration into existing schemas), and assimilation (as category formation). All these operations can similarly be describable in terms of structure/category learning on multiple levels of abstraction. However, here we adopt an ecological rationality perspective, framing H/E-S functions as orchestrating SLAM processes within both concrete and abstract hypothesis spaces. In this navigation/search process, adaptive cognitive equilibration between assimilation and accommodation involves balancing tradeoffs between exploration and exploitation; this dynamic equilibrium may be near optimally realized in FEP-AI, wherein control systems governed by expected free energy objective functions naturally balance model simplicity and accuracy. With respect to structure learning, such a balance would involve constructing models and categories that are neither too inclusive nor exclusive. We propose these (generalized) SLAM phenomena may represent some of the most impactful sources of variation in cognition both within and between individuals, suggesting that modulators of H/E-S functioning may potentially illuminate their adaptive significances as fundamental cybernetic control parameters. Finally, we discuss how understanding H/E-S contributions to G-SLAM may provide a unifying framework for high-level cognition and its potential realization in artificial intelligences.

Oversampled and undersolved: Depressive rumination from an active inference perspective

Rumination is a widely recognized cognitive deviation in depression. Despite the recognition, researchers have struggled to explain why patients cannot disengage from the process, although it depresses their mood and fails to lead to effective problem-solving. We rethink rumination as repetitive but unsuccessful problem-solving attempts. Appealing to an active inference account, we suggest that adaptive problem-solving is based on the generation, evaluation, and performance of candidate policies that increase an organism's knowledge of its environment. We argue that the problem-solving process is distorted during rumination. Specifically, rumination is understood as engaging in excessive yet unsuccessful oversampling of policy candidates that do not resolve uncertainty. Because candidates are sampled from policies that were selected in states resembling one's current state, "bad" starting points (e.g., depressed mood, physical inactivity) make the problem-solving process vulnerable for generating a ruminative "halting problem". This problem leads to high opportunity costs, learned helplessness and diminished overt behavior. Besides reviewing evidence for the conceptual paths of this model, we discuss its neurophysiological correlates and point towards clinical implications.

Branching Time Active Inference with Bayesian Filtering

Branching time active inference is a framework proposing to look at planning as a form of Bayesian model expansion. Its root can be found in active inference, a neuroscientific framework widely used for brain modeling, as well as in Monte Carlo tree search, a method broadly applied in the reinforcement learning literature. Up to now, the inference of the latent variables was carried out by taking advantage of the flexibility offered by variational message passing, an iterative process that can be understood as sending messages along the edges of a factor graph. In this letter, we harness the efficiency of an alternative method for inference, Bayesian filtering, which does not require the iteration of the update equations until convergence of the variational free energy. Instead, this scheme alternates between two phases: integration of evidence and prediction of future states. Both phases can be performed efficiently, and this provides a forty times speedup over the state of the art.

Reclaiming saliency: Rhythmic precision-modulated action and perception

Computational models of visual attention in artificial intelligence and robotics have been inspired by the concept of a saliency map. These models account for the mutual information between the (current) visual information and its estimated causes. However, they fail to consider the circular causality between perception and action. In other words, they do not consider where to sample next, given current beliefs. Here, we reclaim salience as an active inference process that relies on two basic principles: uncertainty minimization and rhythmic scheduling. For this, we make a distinction between attention and salience. Briefly, we associate attention with precision control, i.e., the confidence with which beliefs can be updated given sampled sensory data, and salience with uncertainty minimization that underwrites the selection of future sensory data. Using this, we propose a new account of attention based on rhythmic precision-modulation and discuss its potential in robotics, providing numerical experiments that showcase its advantages for state and noise estimation, system identification and action selection for informative path planning.

Organizational Neuroscience of Industrial Adaptive Behavior

Organizational neuroscience is recognized in organizational behavior literature as offering an interpretive framework that can shed new light on existing organizational challenges. In this paper, findings from neuroscience studies concerned with adaptive behavior for ecological fitness are applied to explore industrial adaptive behavior. This is important because many companies are not able to manage dynamics between adaptability and stability. The reported analysis relates business-to-business signaling in competitive environments to three levels of inference. In accordance with neuroscience studies concerned with adaptive behavior, trade-offs between complexity and accuracy in business-to-business signaling and inference are explained. In addition, signaling and inference are related to risks and ambiguities in competitive industrial markets. Overall, the paper provides a comprehensive analysis of industrial adaptive behavior in terms of relevant neuroscience constructs. In doing so, the paper makes a contribution to the field of organizational neuroscience, and to research concerned with industrial adaptive behavior. The reported analysis is relevant to organizational adaptive behavior that involves combining human intelligence and artificial intelligence.

Branching Time Active Inference: The theory and its generality

Over the last 10 to 15 years, active inference has helped to explain various brain mechanisms from habit formation to dopaminergic discharge and even modelling curiosity. However, the current implementations suffer from an exponential (space and time) complexity class when computing the prior over all the possible policies up to the time-horizon. Fountas et al. (2020) used Monte Carlo tree search to address this problem, leading to impressive results in two different tasks. In this paper, we present an alternative framework that aims to unify tree search and active inference by casting planning as a structure learning problem. Two tree search algorithms are then presented. The first propagates the expected free energy forward in time (i.e., towards the leaves), while the second propagates it backward (i.e., towards the root). Then, we demonstrate that forward and backward propagations are related to active inference and sophisticated inference, respectively, thereby clarifying the differences between those two planning strategies.

Active Inference and Epistemic Value in Graphical Models

The Free Energy Principle (FEP) postulates that biological agents perceive and interact with their environment in order to minimize a Variational Free Energy (VFE) with respect to a generative model of their environment. The inference of a policy (future control sequence) according to the FEP is known as Active Inference (AIF). The AIF literature describes multiple VFE objectives for policy planning that lead to epistemic (information-seeking) behavior. However, most objectives have limited modeling flexibility. This paper approaches epistemic behavior from a constrained Bethe Free Energy (CBFE) perspective. Crucially, variational optimization of the CBFE can be expressed in terms of message passing on free-form generative models. The key intuition behind the CBFE is that we impose a point-mass constraint on predicted outcomes, which explicitly encodes the assumption that the agent will make observations in the future. We interpret the CBFE objective in terms of its constituent behavioral drives. We then illustrate resulting behavior of the CBFE by planning and interacting with a simulated T-maze environment. Simulations for the T-maze task illustrate how the CBFE agent exhibits an epistemic drive, and actively plans ahead to account for the impact of predicted outcomes. Compared to an EFE agent, the CBFE agent incurs expected reward in significantly more environmental scenarios. We conclude that CBFE optimization by message passing suggests a general mechanism for epistemic-aware AIF in free-form generative models.

Model Reduction Through Progressive Latent Space Pruning in Deep Active Inference

Although still not fully understood, sleep is known to play an important role in learning and in pruning synaptic connections. From the active inference perspective, this can be cast as learning parameters of a generative model and Bayesian model reduction, respectively. In this article, we show how to reduce dimensionality of the latent space of such a generative model, and hence model complexity, in deep active inference during training through a similar process. While deep active inference uses deep neural networks for state space construction, an issue remains in that the dimensionality of the latent space must be specified beforehand. We investigate two methods that are able to prune the latent space of deep active inference models. The first approach functions similar to sleep and performs model reduction post hoc. The second approach is a novel method which is more similar to reflection, operates during training and displays “aha” moments when the model is able to reduce latent space dimensionality. We show for two well-known simulated environments that model performance is retained in the first approach and only diminishes slightly in the second approach. We also show that reconstructions from a real world example are indistinguishable before and after reduction. We conclude that the most important difference constitutes a trade-off between training time and model performance in terms of accuracy and the ability to generalize, via minimization of model complexity.

How Active Inference Could Help Revolutionise Robotics

Recent advances in neuroscience have characterised brain function using mathematical formalisms and first principles that may be usefully applied elsewhere. In this paper, we explain how active inference-a well-known description of sentient behaviour from neuroscience-can be exploited in robotics. In short, active inference leverages the processes thought to underwrite human behaviour to build effective autonomous systems. These systems show state-of-the-art performance in several robotics settings; we highlight these and explain how this framework may be used to advance robotics.

The Free Energy Principle for Perception and Action: A Deep Learning Perspective

The free energy principle, and its corollary active inference, constitute a bio-inspired theory that assumes biological agents act to remain in a restricted set of preferred states of the world, i.e., they minimize their free energy. Under this principle, biological agents learn a generative model of the world and plan actions in the future that will maintain the agent in an homeostatic state that satisfies its preferences. This framework lends itself to being realized in silico, as it comprehends important aspects that make it computationally affordable, such as variational inference and amortized planning. In this work, we investigate the tool of deep learning to design and realize artificial agents based on active inference, presenting a deep-learning oriented presentation of the free energy principle, surveying works that are relevant in both machine learning and active inference areas, and discussing the design choices that are involved in the implementation process. This manuscript probes newer perspectives for the active inference framework, grounding its theoretical aspects into more pragmatic affairs, offering a practical guide to active inference newcomers and a starting point for deep learning practitioners that would like to investigate implementations of the free energy principle.

The evolution of brain architectures for predictive coding and active inference

This article considers the evolution of brain architectures for predictive processing. We argue that brain mechanisms for predictive perception and action are not late evolutionary additions of advanced creatures like us. Rather, they emerged gradually from simpler predictive loops (e.g. autonomic and motor reflexes) that were a legacy from our earlier evolutionary ancestors-and were key to solving their fundamental problems of adaptive regulation. We characterize simpler-to-more-complex brains formally, in terms of generative models that include predictive loops of increasing hierarchical breadth and depth. These may start from a simple homeostatic motif and be elaborated during evolution in four main ways: these include the multimodal expansion of predictive control into an allostatic loop; its duplication to form multiple sensorimotor loops that expand an animal's behavioural repertoire; and the gradual endowment of generative models with hierarchical depth (to deal with aspects of the world that unfold at different spatial scales) and temporal depth (to select plans in a future-oriented manner). In turn, these elaborations underwrite the solution to biological regulation problems faced by increasingly sophisticated animals. Our proposal aligns neuroscientific theorising-about predictive processing-with evolutionary and comparative data on brain architectures in different animal species. This article is part of the theme issue 'Systems neuroscience through the lens of evolutionary theory'.

Synchronous Generative Development amidst Situated Entropy

The Sustainable Development Goals have been criticized for not providing sufficient balance between human well-being and environmental well-being. By contrast, joint agent-environment systems theory is focused on reciprocal synchronous generative development. The purpose of this paper is to extend this theory towards practical application in sustainable development projects. This purpose is fulfilled through three interrelated contributions. First, a practitioner description of the theory is provided. Then, the theory is extended through reference to research concerned with multilevel pragmatics, competing signals, commitment processes, technological mediation, and psychomotor functioning. In addition, the theory is related to human-driven biosocial-technical innovation through the example of digital twins for agroecological urban farming. Digital twins being digital models that mirror physical processes; that are connected to physical processes through, for example, sensors and actuators; and which carry out analyses of physical processes in order to improve their performance. Together, these contributions extend extant theory towards application for synchronous generative development that balances human well-being and environmental well-being. However, the practical examples in the paper indicate that counterproductive complexity can arise from situated entropy amidst biosocial-technical innovations: even when those innovations are compatible with synchronous generative development.

Permutation Entropy as a Universal Disorder Criterion: How Disorders at Different Scale Levels Are Manifestations of the Same Underlying Principle

What do bacteria, cells, organs, people, and social communities have in common? At first sight, perhaps not much. They involve totally different agents and scale levels of observation. On second thought, however, perhaps they share everything. A growing body of literature suggests that living systems at different scale levels of observation follow the same architectural principles and process information in similar ways. Moreover, such systems appear to respond in similar ways to rising levels of stress, especially when stress levels approach near-lethal levels. To explain such communalities, we argue that all organisms (including humans) can be modeled as hierarchical Bayesian controls systems that are governed by the same biophysical principles. Such systems show generic changes when taxed beyond their ability to correct for environmental disturbances. Without exception, stressed organisms show rising levels of 'disorder' (randomness, unpredictability) in internal message passing and overt behavior. We argue that such changes can be explained by a collapse of allostatic (high-level integrative) control, which normally synchronizes activity of the various components of a living system to produce order. The selective overload and cascading failure of highly connected (hub) nodes flattens hierarchical control, producing maladaptive behavior. Thus, we present a theory according to which organic concepts such as stress, a loss of control, disorder, disease, and death can be operationalized in biophysical terms that apply to all scale levels of organization. Given the presumed universality of this mechanism, 'losing control' appears to involve the same process anywhere, whether involving bacteria succumbing to an antibiotic agent, people suffering from physical or mental disorders, or social systems slipping into warfare. On a practical note, measures of disorder may serve as early warning signs of system failure even when catastrophic failure is still some distance away.

On Epistemics in Expected Free Energy for Linear Gaussian State Space Models

Active Inference (AIF) is a framework that can be used both to describe information processing in naturally intelligent systems, such as the human brain, and to design synthetic intelligent systems (agents). In this paper we show that Expected Free Energy (EFE) minimisation, a core feature of the framework, does not lead to purposeful explorative behaviour in linear Gaussian dynamical systems. We provide a simple proof that, due to the specific construction used for the EFE, the terms responsible for the exploratory (epistemic) drive become constant in the case of linear Gaussian systems. This renders AIF equivalent to KL control. From a theoretical point of view this is an interesting result since it is generally assumed that EFE minimisation will always introduce an exploratory drive in AIF agents. While the full EFE objective does not lead to exploration in linear Gaussian dynamical systems, the principles of its construction can still be used to design objectives that include an epistemic drive. We provide an in-depth analysis of the mechanics behind the epistemic drive of AIF agents and show how to design objectives for linear Gaussian dynamical systems that do include an epistemic drive. Concretely, we show that focusing solely on epistemics and dispensing with goal-directed terms leads to a form of maximum entropy exploration that is heavily dependent on the type of control signals driving the system. Additive controls do not permit such exploration. From a practical point of view this is an important result since linear Gaussian dynamical systems with additive controls are an extensively used model class, encompassing for instance Linear Quadratic Gaussian controllers. On the other hand, linear Gaussian dynamical systems driven by multiplicative controls such as switching transition matrices do permit an exploratory drive.

Understanding, Explanation, and Active Inference

While machine learning techniques have been transformative in solving a range of problems, an important challenge is to understand why they arrive at the decisions they output. Some have argued that this necessitates augmenting machine intelligence with understanding such that, when queried, a machine is able to explain its behaviour (i.e., explainable AI). In this article, we address the issue of machine understanding from the perspective of active inference. This paradigm enables decision making based upon a model of how data are generated. The generative model contains those variables required to explain sensory data, and its inversion may be seen as an attempt to explain the causes of these data. Here we are interested in explanations of one's own actions. This implies a deep generative model that includes a model of the world, used to infer policies, and a higher-level model that attempts to predict which policies will be selected based upon a space of hypothetical (i.e., counterfactual) explanations-and which can subsequently be used to provide (retrospective) explanations about the policies pursued. We illustrate the construct validity of this notion of understanding in relation to human understanding by highlighting the similarities in computational architecture and the consequences of its dysfunction.

World model learning and inference

Understanding information processing in the brain-and creating general-purpose artificial intelligence-are long-standing aspirations of scientists and engineers worldwide. The distinctive features of human intelligence are high-level cognition and control in various interactions with the world including the self, which are not defined in advance and are vary over time. The challenge of building human-like intelligent machines, as well as progress in brain science and behavioural analyses, robotics, and their associated theoretical formalisations, speaks to the importance of the world-model learning and inference. In this article, after briefly surveying the history and challenges of internal model learning and probabilistic learning, we introduce the free energy principle, which provides a useful framework within which to consider neuronal computation and probabilistic world models. Next, we showcase examples of human behaviour and cognition explained under that principle. We then describe symbol emergence in the context of probabilistic modelling, as a topic at the frontiers of cognitive robotics. Lastly, we review recent progress in creating human-like intelligence by using novel probabilistic programming languages. The striking consensus that emerges from these studies is that probabilistic descriptions of learning and inference are powerful and effective ways to create human-like artificial intelligent machines and to understand intelligence in the context of how humans interact with their world.

Future-Proofing Startups: Stress Management Principles Based on Adaptive Calibration Model and Active Inference Theory

In this paper, the Adaptive Calibration Model (ACM) and Active Inference Theory (AIT) are related to future-proofing startups. ACM encompasses the allocation of energy by the stress response system to alternative options for action, depending upon individuals’ life histories and changing external contexts. More broadly, within AIT, it is posited that humans survive by taking action to align their internal generative models with sensory inputs from external states. The first contribution of the paper is to address the need for future-proofing methods for startups by providing eight stress management principles based on ACM and AIT. Future-proofing methods are needed because, typically, nine out of ten startups do not survive. A second contribution is to relate ACM and AIT to startup life cycle stages. The third contribution is to provide practical examples that show the broader relevance ACM and AIT to organizational practice. These contributions go beyond previous literature concerned with entrepreneurial stress and organizational stress. In particular, rather than focusing on particular stressors, this paper is focused on the recalibrating/updating of startups’ stress responsivity patterns in relation to changes in the internal state of the startup and/or changes in the external state. Overall, the paper makes a contribution to relating physics of life constructs concerned with energy, action and ecological fitness to human organizations.

Realizing Active Inference in Variational Message Passing: The Outcome-Blind Certainty Seeker

Active inference is a state-of-the-art framework in neuroscience that offers a unified theory of brain function. It is also proposed as a framework for planning in AI. Unfortunately, the complex mathematics required to create new models can impede application of active inference in neuroscience and AI research. This letter addresses this problem by providing a complete mathematical treatment of the active inference framework in discrete time and state spaces and the derivation of the update equations for any new model. We leverage the theoretical connection between active inference and variational message passing as described by John Winn and Christopher M. Bishop in 2005. Since variational message passing is a well-defined methodology for deriving Bayesian belief update equations, this letter opens the door to advanced generative models for active inference. We show that using a fully factorized variational distribution simplifies the expected free energy, which furnishes priors over policies so that agents seek unambiguous states. Finally, we consider future extensions that support deep tree searches for sequential policy optimization based on structure learning and belief propagation.

Neural Dynamics under Active Inference: Plausibility and Efficiency of Information Processing

Active inference is a normative framework for explaining behaviour under the free energy principle-a theory of self-organisation originating in neuroscience. It specifies neuronal dynamics for state-estimation in terms of a descent on (variational) free energy-a measure of the fit between an internal (generative) model and sensory observations. The free energy gradient is a prediction error-plausibly encoded in the average membrane potentials of neuronal populations. Conversely, the expected probability of a state can be expressed in terms of neuronal firing rates. We show that this is consistent with current models of neuronal dynamics and establish face validity by synthesising plausible electrophysiological responses. We then show that these neuronal dynamics approximate natural gradient descent, a well-known optimisation algorithm from information geometry that follows the steepest descent of the objective in information space. We compare the information length of belief updating in both schemes, a measure of the distance travelled in information space that has a direct interpretation in terms of metabolic cost. We show that neural dynamics under active inference are metabolically efficient and suggest that neural representations in biological agents may evolve by approximating steepest descent in information space towards the point of optimal inference.