Shared Protentions in Multi-Agent Active Inference.

In this paper, we unite concepts from Husserlian phenomenology, the active inference framework in theoretical biology, and category theory in mathematics to develop a comprehensive framework for understanding social action premised on shared goals. We begin with an overview of Husserlian phenomenology, focusing on aspects of inner time-consciousness, namely, retention, primal impression, and protention. We then review active inference as a formal approach to modeling agent behavior based on variational (approximate Bayesian) inference. Expanding upon Husserl's model of time consciousness, we consider collective goal-directed behavior, emphasizing shared protentions among agents and their connection to the shared generative models of active inference. This integrated framework aims to formalize shared goals in terms of shared protentions, and thereby shed light on the emergence of group intentionality. Building on this foundation, we incorporate mathematical tools from category theory, in particular, sheaf and topos theory, to furnish a mathematical image of individual and group interactions within a stochastic environment. Specifically, we employ morphisms between polynomial representations of individual agent models, allowing predictions not only of their own behaviors but also those of other agents and environmental responses. Sheaf and topos theory facilitates the construction of coherent agent worldviews and provides a way of representing consensus or shared understanding. We explore the emergence of shared protentions, bridging the phenomenology of temporal structure, multi-agent active inference systems, and category theory. Shared protentions are highlighted as pivotal for coordination and achieving common objectives. We conclude by acknowledging the intricacies stemming from stochastic systems and uncertainties in realizing shared goals.

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.

On Bayesian mechanics: a physics of and by beliefs.

The aim of this paper is to introduce a field of study that has emerged over the last decade, called Bayesian mechanics. Bayesian mechanics is a probabilistic mechanics, comprising tools that enable us to model systems endowed with a particular partition (i.e. into particles), where the internal states (or the trajectories of internal states) of a particular system encode the parameters of beliefs about external states (or their trajectories). These tools allow us to write down mechanical theories for systems that look as if they are estimating posterior probability distributions over the causes of their sensory states. This provides a formal language for modelling the constraints, forces, potentials and other quantities determining the dynamics of such systems, especially as they entail dynamics on a space of beliefs (i.e. on a statistical manifold). Here, we will review the state of the art in the literature on the free energy principle, distinguishing between three ways in which Bayesian mechanics has been applied to particular systems (i.e. path-tracking, mode-tracking and mode-matching). We go on to examine a duality between the free energy principle and the constrained maximum entropy principle, both of which lie at the heart of Bayesian mechanics, and discuss its implications.

The empire strikes back: Some responses to Bruineberg and colleagues.

In their target paper, Bruineberg and colleagues provide us with a timely opportunity to discuss the formal constructs and philosophical implications of the free energy principle. I critically discuss their proposed distinction between Pearl and Friston blankets. I then critically assess the distinction between inference with a model and inference within a model in light of instrumentalist approaches to science.

Some minimal notes on notation and minima: A comment on "How particular is the physics of the free energy principle?" by Aguilera, Millidge, Tschantz, and Buckley.

We comment on a technical critique of the free energy principle in linear systems by Aguilera, Millidge, Tschantz, and Buckley, entitled "How Particular is the Physics of the Free Energy Principle?" Aguilera and colleagues identify an ambiguity in the flow of the mode of a system, and we discuss the context for this ambiguity in earlier papers, and their proposal of a more adequate interpretation of these equations. Following that, we discuss a misinterpretation in their treatment of surprisal and variational free energy, especially with respect to their gradients and their minima. In sum, we argue that the results in the target paper are accurate and stand up to rigorous scrutiny; we also highlight that they, nonetheless, do not undermine the FEP.

Applying the Free Energy Principle to Complex Adaptive Systems.

The free energy principle (FEP) is a formulation of the adaptive, belief-driven behaviour of self-organizing systems that gained prominence in the early 2000s as a unified model of the brain [...].

Epistemic Communities under Active Inference.

The spread of ideas is a fundamental concern of today's news ecology. Understanding the dynamics of the spread of information and its co-option by interested parties is of critical importance. Research on this topic has shown that individuals tend to cluster in echo-chambers and are driven by confirmation bias. In this paper, we leverage the active inference framework to provide an in silico model of confirmation bias and its effect on echo-chamber formation. We build a model based on active inference, where agents tend to sample information in order to justify their own view of reality, which eventually leads to them to have a high degree of certainty about their own beliefs. We show that, once agents have reached a certain level of certainty about their beliefs, it becomes very difficult to get them to change their views. This system of self-confirming beliefs is upheld and reinforced by the evolving relationship between an agent's beliefs and observations, which over time will continue to provide evidence for their ingrained ideas about the world. The epistemic communities that are consolidated by these shared beliefs, in turn, tend to produce perceptions of reality that reinforce those shared beliefs. We provide an active inference account of this community formation mechanism. We postulate that agents are driven by the epistemic value that they obtain from sampling or observing the behaviours of other agents. Inspired by digital social networks like Twitter, we build a generative model in which agents generate observable social claims or posts (e.g., 'tweets') while reading the socially observable claims of other agents that lend support to one of two mutually exclusive abstract topics. Agents can choose which other agent they pay attention to at each timestep, and crucially who they attend to and what they choose to read influences their beliefs about the world. Agents also assess their local network's perspective, influencing which kinds of posts they expect to see other agents making. The model was built and simulated using the freely available Python package pymdp. The proposed active inference model can reproduce the formation of echo-chambers over social networks, and gives us insight into the cognitive processes that lead to this phenomenon.

From Generative Models to Generative Passages: A Computational Approach to (Neuro) Phenomenology.

This paper presents a version of neurophenomenology based on generative modelling techniques developed in computational neuroscience and biology. Our approach can be described as computational phenomenology because it applies methods originally developed in computational modelling to provide a formal model of the descriptions of lived experience in the phenomenological tradition of philosophy (e.g., the work of Edmund Husserl, Maurice Merleau-Ponty, etc.). The first section presents a brief review of the overall project to naturalize phenomenology. The second section presents and evaluates philosophical objections to that project and situates our version of computational phenomenology with respect to these projects. The third section reviews the generative modelling framework. The final section presents our approach in detail. We conclude by discussing how our approach differs from previous attempts to use generative modelling to help understand consciousness. In summary, we describe a version of computational phenomenology which uses generative modelling to construct a computational model of the inferential or interpretive processes that best explain this or that kind of lived experience.

Stress and its sequelae: An active inference account of the etiological pathway from allostatic overload to depression.

Survival requires the implementation of adaptive changes that demand energy resources. The efficient regulation of energetic resources thus plays a critical role in enabling systems to adapt to the demands of their internal and external environments. The framework of active inference explains how living organisms can build probabilistic models that enable them to predict, track, and regulate energy expenditure in the short and long run. The aim of the paper is to characterize the physiological changes that accompany stress, and the relationship between these changes and the loss of confidence in a system's predictions about its internal and external milieu-ultimately manifesting as depressive symptomatology. We identify the systems that underwrite goal-directed behavior, and the neuroendocrine and immunological systems, as the hierarchical controller that regulates energy resources. In doing so, we establish an etiological pathway from allostatic overload to depression via active inference.

Resilience and active inference.

In this article, we aim to conceptualize and formalize the construct of resilience using the tools of active inference, a new physics-based modeling approach apt for the description and analysis of complex adaptive systems. We intend this as a first step toward a computational model of resilient systems. We begin by offering a conceptual analysis of resilience, to clarify its meaning, as established in the literature. We examine an orthogonal, threefold distinction between meanings of the word "resilience": (i) inertia, or the ability to resist change (ii) elasticity, or the ability to bounce back from a perturbation, and (iii) plasticity, or the ability to flexibly expand the repertoire of adaptive states. We then situate all three senses of resilience within active inference. We map resilience as inertia onto high precision beliefs, resilience as elasticity onto relaxation back to characteristic (i.e., attracting) states, and resilience as plasticity onto functional redundancy and structural degeneracy.

Embodied skillful performance: where the action is.

When someone masters a skill, their performance looks to us like second nature: it looks as if their actions are smoothly performed without explicit, knowledge-driven, online monitoring of their performance. Contemporary computational models in motor control theory, however, are instructionist: that is, they cast skillful performance as a knowledge-driven process. Optimal motor control theory (OMCT), as representative par excellence of such approaches, casts skillful performance as an instruction, instantiated in the brain, that needs to be executed-a motor command. This paper aims to show the limitations of such instructionist approaches to skillful performance. We specifically address the question of whether the assumption of control-theoretic models is warranted. The first section of this paper examines the instructionist assumption, according to which skillful performance consists of the execution of theoretical instructions harnessed in motor representations. The second and third sections characterize the implementation of motor representations as motor commands, with a special focus on formulations from OMCT. The final sections of this paper examine predictive coding and active inference-behavioral modeling frameworks that descend, but are distinct, from OMCT-and argue that the instructionist, control-theoretic assumptions are ill-motivated in light of new developments in active inference.

Towards a computational phenomenology of mental action: modelling meta-awareness and attentional control with deep parametric active inference.

Meta-awareness refers to the capacity to explicitly notice the current content of consciousness and has been identified as a key component for the successful control of cognitive states, such as the deliberate direction of attention. This paper proposes a formal model of meta-awareness and attentional control using hierarchical active inference. To do so, we cast mental action as policy selection over higher-level cognitive states and add a further hierarchical level to model meta-awareness states that modulate the expected confidence (precision) in the mapping between observations and hidden cognitive states. We simulate the example of mind-wandering and its regulation during a task involving sustained selective attention on a perceptual object. This provides a computational case study for an inferential architecture that is apt to enable the emergence of these central components of human phenomenology, namely, the ability to access and control cognitive states. We propose that this approach can be generalized to other cognitive states, and hence, this paper provides the first steps towards the development of a computational phenomenology of mental action and more broadly of our ability to monitor and control our own cognitive states. Future steps of this work will focus on fitting the model with qualitative, behavioural, and neural data.

Active Inferants: An Active Inference Framework for Ant Colony Behavior.

In this paper, we introduce an active inference model of ant colony foraging behavior, and implement the model in a series of in silico experiments. Active inference is a multiscale approach to behavioral modeling that is being applied across settings in theoretical biology and ethology. The ant colony is a classic case system in the function of distributed systems in terms of stigmergic decision-making and information sharing. Here we specify and simulate a Markov decision process (MDP) model for ant colony foraging. We investigate a well-known paradigm from laboratory ant colony behavioral experiments, the alternating T-maze paradigm, to illustrate the ability of the model to recover basic colony phenomena such as trail formation after food location discovery. We conclude by outlining how the active inference ant colony foraging behavioral model can be extended and situated within a nested multiscale framework and systems approaches to biology more generally.

Multiscale integration: beyond internalism and externalism.

We present a multiscale integrationist interpretation of the boundaries of cognitive systems, using the Markov blanket formalism of the variational free energy principle. This interpretation is intended as a corrective for the philosophical debate over internalist and externalist interpretations of cognitive boundaries; we stake out a compromise position. We first survey key principles of new radical (extended, enactive, embodied) views of cognition. We then describe an internalist interpretation premised on the Markov blanket formalism. Having reviewed these accounts, we develop our positive multiscale account. We argue that the statistical seclusion of internal from external states of the system-entailed by the existence of a Markov boundary-can coexist happily with the multiscale integration of the system through its dynamics. Our approach does not privilege any given boundary (whether it be that of the brain, body, or world), nor does it argue that all boundaries are equally prescient. We argue that the relevant boundaries of cognition depend on the level being characterised and the explanatory interests that guide investigation. We approach the issue of how and where to draw the boundaries of cognitive systems through a multiscale ontology of cognitive systems, which offers a multidisciplinary research heuristic for cognitive science.

Markov blankets in the brain.

Recent characterisations of self-organising systems depend upon the presence of a 'Markov blanket': a statistical boundary that mediates the interactions between the inside and outside of a system. We leverage this idea to provide an analysis of partitions in neuronal systems. This is applicable to brain architectures at multiple scales, enabling partitions into single neurons, brain regions, and brain-wide networks. This treatment is based upon the canonical micro-circuitry used in empirical studies of effective connectivity, so as to speak directly to practical applications. The notion of effective connectivity depends upon the dynamic coupling between functional units, whose form recapitulates that of a Markov blanket at each level of analysis. The nuance afforded by partitioning neural systems in this way highlights certain limitations of 'modular' perspectives of brain function that only consider a single level of description.

Deeply Felt Affect: The Emergence of Valence in Deep Active Inference.

The positive-negative axis of emotional valence has long been recognized as fundamental to adaptive behavior, but its origin and underlying function have largely eluded formal theorizing and computational modeling. Using deep active inference, a hierarchical inference scheme that rests on inverting a model of how sensory data are generated, we develop a principled Bayesian model of emotional valence. This formulation asserts that agents infer their valence state based on the expected precision of their action model-an internal estimate of overall model fitness ("subjective fitness"). This index of subjective fitness can be estimated within any environment and exploits the domain generality of second-order beliefs (beliefs about beliefs). We show how maintaining internal valence representations allows the ensuing affective agent to optimize confidence in action selection preemptively. Valence representations can in turn be optimized by leveraging the (Bayes-optimal) updating term for subjective fitness, which we label affective charge (AC). AC tracks changes in fitness estimates and lends a sign to otherwise unsigned divergences between predictions and outcomes. We simulate the resulting affective inference by subjecting an in silico affective agent to a T-maze paradigm requiring context learning, followed by context reversal. This formulation of affective inference offers a principled account of the link between affect, (mental) action, and implicit metacognition. It characterizes how a deep biological system can infer its affective state and reduce uncertainty about such inferences through internal action (i.e., top-down modulation of priors that underwrite confidence). Thus, we demonstrate the potential of active inference to provide a formal and computationally tractable account of affect. Our demonstration of the face validity and potential utility of this formulation represents the first step within a larger research program. Next, this model can be leveraged to test the hypothesized role of valence by fitting the model to behavioral and neuronal responses.

Neural and phenotypic representation under the free-energy principle.

The aim of this paper is to leverage the free-energy principle and its corollary process theory, active inference, to develop a generic, generalizable model of the representational capacities of living creatures; that is, a theory of phenotypic representation. Given their ubiquity, we are concerned with distributed forms of representation (e.g., population codes), whereby patterns of ensemble activity in living tissue come to represent the causes of sensory input or data. The active inference framework rests on the Markov blanket formalism, which allows us to partition systems of interest, such as biological systems, into internal states, external states, and the blanket (active and sensory) states that render internal and external states conditionally independent of each other. In this framework, the representational capacity of living creatures emerges as a consequence of their Markovian structure and nonequilibrium dynamics, which together entail a dual-aspect information geometry. This entails a modest representational capacity: internal states have an intrinsic information geometry that describes their trajectory over time in state space, as well as an extrinsic information geometry that allows internal states to encode (the parameters of) probabilistic beliefs about (fictive) external states. Building on this, we describe here how, in an automatic and emergent manner, information about stimuli can come to be encoded by groups of neurons bound by a Markov blanket; what is known as the neuronal packet hypothesis. As a concrete demonstration of this type of emergent representation, we present numerical simulations showing that self-organizing ensembles of active inference agents sharing the right kind of probabilistic generative model are able to encode recoverable information about a stimulus array.

Is the Free-Energy Principle a Formal Theory of Semantics? From Variational Density Dynamics to Neural and Phenotypic Representations.

The aim of this paper is twofold: (1) to assess whether the construct of neural representations plays an explanatory role under the variational free-energy principle and its corollary process theory, active inference; and (2) if so, to assess which philosophical stance-in relation to the ontological and epistemological status of representations-is most appropriate. We focus on non-realist (deflationary and fictionalist-instrumentalist) approaches. We consider a deflationary account of mental representation, according to which the explanatorily relevant contents of neural representations are mathematical, rather than cognitive, and a fictionalist or instrumentalist account, according to which representations are scientifically useful fictions that serve explanatory (and other) aims. After reviewing the free-energy principle and active inference, we argue that the model of adaptive phenotypes under the free-energy principle can be used to furnish a formal semantics, enabling us to assign semantic content to specific phenotypic states (the internal states of a Markovian system that exists far from equilibrium). We propose a modified fictionalist account-an organism-centered fictionalism or instrumentalism. We argue that, under the free-energy principle, pursuing even a deflationary account of the content of neural representations licenses the appeal to the kind of semantic content involved in the 'aboutness' or intentionality of cognitive systems; our position is thus coherent with, but rests on distinct assumptions from, the realist position. We argue that the free-energy principle thereby explains the aboutness or intentionality in living systems and hence their capacity to parse their sensory stream using an ontology or set of semantic factors.