This paper concerns the distributed intelligence or federated inference that emerges under belief-sharing among agents who share a common world-and world model. Imagine, for example, several animals keeping a lookout for predators. Their collective surveillance rests upon being able to communicate their beliefs-about what they see-among themselves. But, how is this possible? Here, we show how all the necessary components arise from minimising free energy. We use numerical studies to simulate the generation, acquisition and emergence of language in synthetic agents. Specifically, we consider inference, learning and selection as minimising the variational free energy of posterior (i.e., Bayesian) beliefs about the states, parameters and structure of generative models, respectively. The common theme-that attends these optimisation processes-is the selection of actions that minimise expected free energy, leading to active inference, learning and model selection (a.k.a., structure learning). We first illustrate the role of communication in resolving uncertainty about the latent states of a partially observed world, on which agents have complementary perspectives. We then consider the acquisition of the requisite language-entailed by a likelihood mapping from an agent's beliefs to their overt expression (e.g., speech)-showing that language can be transmitted across generations by active learning. Finally, we show that language is an emergent property of free energy minimisation, when agents operate within the same econiche. We conclude with a discussion of various perspectives on these phenomena; ranging from cultural niche construction, through federated learning, to the emergence of complexity in ensembles of self-organising systems.

Adaptive agents must act in intrinsically uncertain environments with complex latent structure. Here, we elaborate a model of visual foraging—in a hierarchical context—wherein agents infer a higher-order visual pattern (a “scene”) by sequentially sampling ambiguous cues. Inspired by previous models of scene construction—that cast perception and action as consequences of approximate Bayesian inference—we use active inference to simulate decisions of agents categorizing a scene in a hierarchically-structured setting. Under active inference, agents develop probabilistic beliefs about their environment, while actively sampling it to maximize the evidence for their internal generative model. This approximate evidence maximization (i.e., self-evidencing) comprises drives to both maximize rewards and resolve uncertainty about hidden states. This is realized via minimization of a free energy functional of posterior beliefs about both the world as well as the actions used to sample or perturb it, corresponding to perception and action, respectively. We show that active inference, in the context of hierarchical scene construction, gives rise to many empirical evidence accumulation phenomena, such as noise-sensitive reaction times and epistemic saccades. We explain these behaviors in terms of the principled drives that constitute the expected free energy, the key quantity for evaluating policies under active inference. In addition, we report novel behaviors exhibited by these active inference agents that furnish new predictions for research on evidence accumulation and perceptual decision-making. We discuss the implications of this hierarchical active inference scheme for tasks that require planned sequences of information-gathering actions to infer compositional latent structure (such as visual scene construction and sentence comprehension). This work sets the stage for future experiments to investigate active inference in relation to other formulations of evidence accumulation (e.g., drift-diffusion models) in tasks that require planning in uncertain environments with higher-order structure.

In theoretical biology, we are often interested in random dynamical systems—like the brain—that appear to model their environments. This can be formalized by appealing to the existence of a (possibly non-equilibrium) steady state, whose density preserves a conditional independence between a biological entity and its surroundings. From this perspective, the conditioning set, or Markov blanket, induces a form of vicarious synchrony between creature and world—as if one were modelling the other. However, this results in an apparent paradox. If all conditional dependencies between a system and its surroundings depend upon the blanket, how do we account for the mnemonic capacity of living systems? It might appear that any shared dependence upon past blanket states violates the independence condition, as the variables on either side of the blanket now share information not available from the current blanket state. This paper aims to resolve this paradox, and to demonstrate that conditional independence does not preclude memory. Our argument rests upon drawing a distinction between the dependencies implied by a steady state density, and the density dynamics of the system conditioned upon its configuration at a previous time. The interesting question then becomes: What determines the length of time required for a stochastic system to ‘forget’ its initial conditions? We explore this question for an example system, whose steady state density possesses a Markov blanket, through simple numerical analyses. We conclude with a discussion of the relevance for memory in cognitive systems like us.

Active inference is an account of cognition and behavior in complex systems which brings together action, perception, and learning under the theoretical mantle of Bayesian inference. Active inference has seen growing applications in academic research, especially in fields that seek to model human or animal behavior. While in recent years, some of the code arising from the active inference literature has been written in open source languages like Python and Julia, to-date, the most popular software for simulating active inference agents is the DEM toolbox of SPM, a MATLAB library originally developed for the statistical analysis and modelling of neuroimaging data. Increasing interest in active inference, manifested both in terms of sheer number as well as diversifying applications across scientific disciplines, has thus created a need for generic, widely-available, and user-friendly code for simulating active inference in open-source scientific computing languages like Python. The Python package we present here, pymdp (see https://github.com/infer-actively/pymdp), represents a significant step in this direction: namely, we provide the first open-source package for simulating active inference with partially-observable Markov Decision Processes or POMDPs. We review the package's structure and explain its advantages like modular design and customizability, while providing in-text code blocks along the way to demonstrate how it can be used to build and run active inference processes with ease. We developed pymdp to increase the accessibility and exposure of the active inference framework to researchers, engineers, and developers with diverse disciplinary backgrounds. In the spirit of open-source software, we also hope that it spurs new innovation, development, and collaboration in the growing active inference community.

Adaptive agents must act in intrinsically uncertain environments with complex latent structure. Here, we elaborate a model of visual foraging – in a hierarchical context – wherein agents infer a higher-order visual pattern (a ‘scene’) by sequentially sampling ambiguous cues. Inspired by previous models of scene construction – that cast perception and action as consequences of approximate Bayesian inference – we use active inference to simulate decisions of agents categorizing a scene in a hierarchically-structured setting. Under active inference, agents develop probabilistic beliefs about their environment, while actively sampling it to maximise the evidence for their internal generative model. This approximate evidence maximization (i.e. self-evidencing) comprises drives to both maximise rewards and resolve uncertainty about hidden states. This is realised via minimization of a free energy functional of posterior beliefs about both the world as well as the actions used to sample or perturb it, corresponding to perception and action, respectively. We show that active inference, in the context of hierarchical scene construction, gives rise to many empirical evidence accumulation phenomena, such as noise-sensitive reaction times and epistemic saccades. We explain these behaviours in terms of the principled drives that constitute the expected free energy , the key quantity for evaluating policies under active inference. In addition, we report novel behaviours exhibited by these active inference agents that furnish new predictions for research on evidence accumulation and perceptual decision-making. We discuss the implications of this hierarchical active inference scheme for tasks that require planned sequences of information-gathering actions to infer compositional latent structure (such as visual scene construction and sentence comprehension). Finally, we propose experiments to contextualise active inference in relation to other formulations of evidence accumulation (e.g. drift-diffusion models) in tasks that require planning in uncertain environments with higher-order structure.