13 research outputs found
Particular flows and attracting sets: A comment on "How particular is the physics of the Free Energy Principle?" by Aguilera, Millidge, Tschantz and Buckley
In this commentary, I expand on the analysis of the recent article "How
particular is the physics of the Free Energy Principle?" by Aguilera et al. by
studying the flow fields of linear diffusions, and particularly the rotation of
their attracting sets in the presence of different types of solenoidal
coupling. This analysis sheds new light on previous claims made in the FEP
literature (and contested in the target article) that the internal dynamics of
stochastic systems can be cast performing a gradient flow on variational free
energy, and thus endowed with an inferential interpretation, i.e., as if
internal states are performing inference about states external to the system. I
express general agreement with the target article's statement that the marginal
flow of internal states does not point along variational free energy gradients
evaluated at the most likely internal state (i.e., the conditional mode).
However, in this commentary I focus on the flow of particular states (internal
and blanket states) and their variational free energy gradients, and show that
for a wide but restricted class of solenoidal couplings, the average flow of
these systems point along variational free energy gradients. This licenses a
different but perhaps stronger re-description of the flow of particular states
as performing inference, which importantly holds at arbitrary points in state
space, not just at the conditional modes
An analytical model of active inference in the Iterated Prisoner's Dilemma
This paper addresses a mathematically tractable model of the Prisoner's
Dilemma using the framework of active inference. In this work, we design pairs
of Bayesian agents that are tracking the joint game state of their and their
opponent's choices in an Iterated Prisoner's Dilemma game. The specification of
the agents' belief architecture in the form of a partially-observed Markov
decision process allows careful and rigourous investigation into the dynamics
of two-player gameplay, including the derivation of optimal conditions for
phase transitions that are required to achieve certain game-theoretic steady
states. We show that the critical time points governing the phase transition
are linearly related to each other as a function of learning rate and the
reward function. We then investigate the patterns that emerge when varying the
agents' learning rates, as well as the relationship between the stochastic and
deterministic solutions to the two-agent system
Spin glass systems as collective active inference
An open question in the study of emergent behaviour in multi-agent Bayesian
systems is the relationship, if any, between individual and collective
inference. In this paper we explore the correspondence between generative
models that exist at two distinct scales, using spin glass models as a sandbox
system to investigate this question. We show that the collective dynamics of a
specific type of active inference agent is equivalent to sampling from the
stationary distribution of a spin glass system. A collective of
specifically-designed active inference agents can thus be described as
implementing a form of sampling-based inference (namely, from a Boltzmann
machine) at the higher level. However, this equivalence is very fragile,
breaking upon simple modifications to the generative models of the individual
agents or the nature of their interactions. We discuss the implications of this
correspondence and its fragility for the study of multiscale systems composed
of Bayesian agents.Comment: Accepted for publication: 3rd International Workshop on Active
Inferenc
Path integrals, particular kinds, and strange things
This paper describes a path integral formulation of the free energy
principle. The ensuing account expresses the paths or trajectories that a
particle takes as it evolves over time. The main results are a method or
principle of least action that can be used to emulate the behaviour of
particles in open exchange with their external milieu. Particles are defined by
a particular partition, in which internal states are individuated from external
states by active and sensory blanket states. The variational principle at hand
allows one to interpret internal dynamics - of certain kinds of particles - as
inferring external states that are hidden behind blanket states. We consider
different kinds of particles, and to what extent they can be imbued with an
elementary form of inference or sentience. Specifically, we consider the
distinction between dissipative and conservative particles, inert and active
particles and, finally, ordinary and strange particles. Strange particles (look
as if they) infer their own actions, endowing them with apparent autonomy or
agency. In short - of the kinds of particles afforded by a particular partition
- strange kinds may be apt for describing sentient behaviour.Comment: 31 pages (excluding references), 6 figure
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.publishe
Stochastic Chaos and Markov Blankets
In this treatment of random dynamical systems, we consider the existenceâand identificationâof conditional independencies at nonequilibrium steady-state. These independencies underwrite a particular partition of states, in which internal states are statistically secluded from external states by blanket states. The existence of such partitions has interesting implications for the information geometry of internal states. In brief, this geometry can be read as a physics of sentience, where internal states look as if they are inferring external states. However, the existence of such partitionsâand the functional form of the underlying densitiesâhave yet to be established. Here, using the Lorenz system as the basis of stochastic chaos, we leverage the Helmholtz decompositionâand polynomial expansionsâto parameterise the steady-state density in terms of surprisal or self-information. We then show how Markov blankets can be identifiedâusing the accompanying Hessianâto characterise the coupling between internal and external states in terms of a generalised synchrony or synchronisation of chaos. We conclude by suggesting that this kind of synchronisation may provide a mathematical basis for an elemental form of (autonomous or active) sentience in biology.publishe
What Do You Know? ERP Evidence For Immediate Use Of Common Ground During Online Reference Resolution
Recent evidence on the time-course of conversational perspective taking is mixed. Some results suggest that listeners rapidly incorporate an interlocutorâs knowledge during comprehension, while other findings suggest that listeners initially interpret language egocentrically. A key finding in support of the egocentric view comes from visual-world eye-tracking studies â listeners systematically look at potential referents that are known to them but unknown to the speaker. An alternative explanation is that eye movements might be driven by attentional processes that are unrelated to referent identification. To address this question, we assessed the time-course of perspective taking using event-related potentials (ERP). Participants were instructed to select a referent from a display of four animals (e.g., âClick on the brontosaurus with the bootsâ) by a speaker who could only see three of the animals. A competitor (e.g., a brontosaurus with a purse) was either mutually visible, visible only to the listener, or absent from the display. Results showed that only the mutually visible competitor elicited an ERP signature of referential ambiguity. Critically, ERPs exhibited no evidence of referential confusion when the listener had privileged access to the competitor. Contra the egocentric hypothesis, this pattern of results indicates that listeners did not consider privileged competitors to be candidates for reference. These findings are consistent with theories of language processing that allow socio-pragmatic information to rapidly influence online language comprehension. The results also suggest that eye-tracking evidence in studies of online reference resolution may include distraction effects driven by privileged competitors and highlight the importance of using multiple measures to investigate perspective use
Deep active inference and scene construction
Adaptive agents must act in intrinsically uncertain environments with complex latent structure. Here, we elaborate a model of visual foragingâin a hierarchical contextâwherein agents infer a higher-order visual pattern (a âsceneâ) by sequentially sampling ambiguous cues. Inspired by previous models of scene constructionâthat cast perception and action as consequences of approximate Bayesian inferenceâwe 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
pymdp: A Python library for active inference in discrete state spaces
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
Memory and Markov Blankets
In theoretical biology, we are often interested in random dynamical systemsâlike the brainâthat 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 worldâas 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 âforgetâ 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.publishe