Accuracy

Accuracy is simply the surprise about sensations that are expected under the recognition density

Action

Action A : S × R → ℝ... corresponds to action emitted by an agent and depends on its sensory and internal states.

RECOGNITION models update internal parameters that correspond to external states (including hidden causes of the environment), blanket states, and internal states (meta-modeling). In contrast, GENERATIVE models take those same internal parameter estimates and emit expected or plausible observations.

Action Planning

The requirement for an adaptive organism to predict the consequences in the future of engaging in this or that action. Also called the problem of mere versus adaptive active inference, or planning as inference.

Action prediction

In principle, the recognition of action goals might be implemented in perceptual and associative brain areas, similar to the way other events such as visual scenes are (believed to be) recognized, predicted and understood semantically.

We propose that the brain automatically predicts others’ future actions while perceiving their current actions. The human perceptual system constantly engages in this kind of reflexive prediction.

Active Inference

(??)

Under the free energy principle, systems can be interpreted as engaging in active inference in order to minimize their free energy. A system can be described to engage in active inference in the sense of performing belief updating and acting such as to fulfil prior preferences about observations. Describing a self-organizing system in terms of active inference means that the system acts upon its external milieu to maintain itself in its preferred states (cf. homoeostasis). Active inference provides a mechanism to derive the dynamics of sensory and active states such that they minimize a variational free energy functional. This allows us to describe an agent as engaging in actions that will get them closer to their preferred sensory states. Belief updates, in turn, contribute to the optimization of internal states, which tightens the (free energy) bound on surprisal, thus enabling action to avoid (statistically) “surprising” sensations; and corresponds to perception.

An extension of predictive coding (and part of the free energy principle), which says that agents can suppress prediction errors by performing actions to bring about sensory states in line with predictions.

1. Computational process in which prediction error is minimized by acting on the world ("making the world more similar to the model"), as opposed to minimizing prediction error by changing the internal model, i.e. perceptual inference ("making the model more similar to the world"). 2. Also used as a generic term for the computational processes which underpin both action and perception, and, in the context of FEP, for all computational processes that minimize free energy.

The minimisation of free energy through changing internal states (perception) and sensory states by acting on the world (action).

active inference is a self-organising process of action policy selection.

Active Learning

To reduce the latter type of uncertainty, agents can expose themselves to observations that complete ‘knowledge gaps’ and thereby learn the probabilistic structure of unknown and unexplored (novel) contingencies – hence active learning allowing for ‘model parameter exploration’.

Active States

Active states are a subset of blanket states that mediate the influence of internal states on external states. Conversely, sensory states are a subset of blanket states that mediate the influence of external states on internal states.

Active Vision

Our vision incorporates both the information that falls on the retina and the consequences of eye movement, in particular the consequences of rapid or saccadic eye movements. We refer to this vision as active vision

Affordance

Gibson defined affordances as action possibilities latent in the environment [3], objectively measurable and independent of the ability to recognize them but always in relation to the actor [4].

Agency

a sense of agency as a probabilistic representation of control that is distinct from the action actually emitted

a sense of agency rests upon prior beliefs about how one will behave

Agent

Agents defined under active inference: A) sample their environment and calibrate their internal generative model to best explain sensory observations (i.e., reduce surprise) and B) perform actions under the objective of reducing their uncertainty about the environment.

Ambiguity

expected uncertainty of observations, expected under a policy.Ambiguity can be thought of as the expected inaccuracy, where marginal likelihood is equal to accuracy minus complexity

ambiguity is the uncertainty about outcomes given the state of the world.

Thus, ambiguity is the expectation of the conditional entropy — or uncertainty about outcomes — under the current policy

Ambiguity is the loss of a precise or definitive mapping between external states of the world and observed sensory states (as quantified by entropy, denoted by H).

In this paper, we address
the issue of ambiguity of objective image quality assessment. We propose an approach
to obtain an ambiguity interval of an objective metric, within which the quality score
difference is not perceptually significant. In particular, we use the visual difference
predictor, which can consider viewing conditions that are important for visual quality perception. In order to demonstrate the usefulness of the proposed approach, we
conduct experiments with 33 state-of-the-art image quality metrics in the viewpoint of
their accuracy and ambiguity for three image quality databases. The results show that
the ambiguity intervals can be applied as an additional figure of merit when conventional performance measurement does not determine superiority between the metrics.
The effect of the viewing distance on the ambiguity interval is also shown.

Attention

Inferring the level of uncertainty or precision during hierarchical perception.

Here, we pursue the notion that attention is the optimum weighting of prediction error in the context of action preparation

It is argued here that attention is frequently used to refer to two very different phenomena. One relates to salience, and is fundamentally a property of action plans and epistemic affordance. The other involves the biasing of inference towards sensory channels providing precise information.

Attentional states, s(2), modulate the confidence in sensory observations, and meta-awareness states, s(3), modulate the confidence in higher-order observations.

Bayesian Inference

Minimisation of variational free energy with respect to a probability distribution over (fictive) hidden states causing sensory states (observations). Variational Bayesian inference is approximate because it minimises a (free energy) bound approximation to surprise. When free energy equals surprise, inference is exact.

Updating a model in accordance with Bayes' rule, i.e. computing the posterior distribution: p(c|s) = p(s|c)p(c)/p(s).

Behavior

Here we use the term behavior to mean what a plant or animal does, in the course of an individual's lifetime, in response to some event or change in its environment

Belief

The term ‘belief’ is used in the sense of ‘belief propagation’ and ‘Bayesian belief updating’, which are just ways of talking about probability distributions or densities. ‘Beliefs’ in Bayesian terms are posteriors and priors, corresponding to the probability distributions (a world of possible states) that are shaped by physically realized states (i.e., the internal states that parameterize distributions over external states). In general, although we use the term ‘beliefs’ to describe the probability densities defined over external states, it is generally recognized that these densities are not themselves the same as propositional beliefs.

In short, self-evidencing appears to require perceptual inference, in the sense that a belief is formed that approximates the probability of the causes of sensations. Note that the term “belief” is used here in the technical sense of Bayesian belief updating—not to indicate a conscious, propositional belief.

Technically, these (Bayesian) beliefs are referred to as approximate posteriors, variational densities or recognition densities. The recognition model is the inverse of a likelihood model: it is a statistical mapping from obser?vable consequences to hidden causes. This explains why forming a posterior belief is often referred to as
model inversion, where Q(s) ’ P(sjo)

Belief updating

a parameterization of posterior beliefs about the past and future that makes state estimation

Belief updating mediates inference and learning, where inference means optimising expectations about hidden states (policies and precision), while learning refers to optimising model parameters. This optimisation entails finding the sufficient statistics of posterior beliefs that minimise variational free energy.

Blanket States

Blanket states comprise active states and sensory states. Generally, external states do not influence active states and internal states do not influence sensory states.

If the states of a system, whose dynamics can be described with random or stochastic differential equations (e.g., the Langevin equation), possess a Markov blanket, then... the conditional independence in question means that a set of (internal) states are independent of another (external) set, when conditioned upon blanket states. The internal states can then be cast as representing, in a probabilistic fashion, external states. From this, one can elaborate a physics of sentience or Bayesian mechanics that would be recognised in theoretical neuroscience and biology.

"A Markov blanket is defined in terms of conditional dependencies entailed by the joint density over some states"

Friston: Blanket states comprise active states and sensory states. Generally, external states do not influence active states and internal states do not influence sensory states.

Cognition

Cognition is the updating of hierarchical, probabilistic models of the world.

In active inference, cognition is viewed as an action-inference loop. The beliefs (priors) of an individual, and the expectations that derive from them, lead to action. Action impacts the environment, producing some effects. The individual senses those effects (perhaps imperfectly), and compares sensations to those that were expected based on beliefs. If they differ—if observations are surprising—then learning (updating of the individual’s generative model) might be necessary.

Complexity

complexity is the divergence between posterior and prior beliefs.

complexity is defined in relation to empirical priors based on the approximate posterior expectations of the preceding (forward) and subsequent (backward) states

Cue

In turn, the deontic cue is the probability of an outcome at any given state, which depends upon concentration parameters α that the environment learns as a function of how agents act on the world, which changes the value of the concentration parameters.

Culture

inter-group behavioural and cognitive variations that arise through social learning within members of the same species

Culture is an umbrella term which encompasses the social behavior and norms found in human societies, as well as the knowledge, beliefs, arts, laws, customs, capabilities, and habits of the individuals in these groups.

Data

Data are units of information, often numeric, that are collected through observation.[1] In a more technical sense, data are a set of values of qualitative or quantitative variables about one or more persons or objects,[1] while a datum (singular of data) is a single value of a single variable.[2]

sensory data is given by Bayes rule (1)

Decision-making

This paper considers decision-making and action selection as variational Bayesian inference. It tries to place heuristics in decision theory (in psychology) and expected utility theory (in economics) within the setting of embodied or active inference.

Ensemble

Here, we consider simulations of a primordial soup reported in [11] to illustrate the emergence of active inference of a simple and prebiotic sort. This soup comprises an ensemble of dynamical subsystems, each with its own structural and functional states, that are coupled through short-range interactions.

ensembles; groups of neurons that tend to fire in synchrony. Importantly, spontaneously active ensembles are similar to those evoked by sensory stimuli suggesting that ensembles encode features of the sensory environment and that their spontaneous activation reflects an intrinsic capacity of the brain to generate an internal model of the environment

Epistemic value

Epistemic value is the expected information gain under predicted outcomes. In other words, it reports the reduction in uncertainty about hidden states afforded by observations

Interestingly, (35) tells us that maximizing the epistemic value of the policy maximizes opportunity, while at the same time minimizing risk. In the EFE (20), epistemic value is related with the mutual information between states and outcomes. In the CBFE [constrained Bethe Free Energy], the epistemic value of the policy is more inclusive, because it accounts for the information opportunity as well as the risk of the policy.

“epistemic value” (e.g., information gain or the resolution of uncertainty implicit in exploration or curiosity).

Ergodicity

A process is ergodic if its long term time-average converges to its ensemble average. Ergodic processes that evolve for a long time forget their initial states.

Evidence

Bayesian model evidence is effectively simplicity plus accuracy./Negative surprise is the same as log evidence; namely, the logarithm of Bayesian model evidence.

Expected Free Energy

The expected free energy is a functional of posterior beliefs about states.

External States

Statistically, the existence of a Markov blanket means external states are conditionally independent of internal states, and vice versa, given blanket states. Generally, external states only influence themselves and sensory states.

Here, circular causality is induced by separating the states of a random dynamical system into external and internal states, where external states are subject to random fluctuations and internal states are not.

External states correspond to environmental causes that generate sensory samples (also known as sensory input, sensory outcomes, sensory data, or evidence), which affect the system’s internal state.

Free Energy

An information theory measure that bounds (is greater than) the surprise on sampling some data, given a generative model.

In the context of Friston's FEP, free energy is not a thermodynamic quantity, but an information-theoretic quantity that constitutes an upper bound on surprisal. If this bound is tight, the surprisal of sensory signals can therefore be reduced if free energy is minimized by bringing about changes in the world.

Free Energy Principle

https://en.wikipedia.org/wiki/Free_energy_principlehttps://en.wikipedia.org/wiki/Free_energy_principle.

"The brain aims at reducing surprise, where this surprise (or surprisal) is quantified as accuracy (expected log likelihood) minus complexity (informational divergence between the posterior probability and prior probability). This complexity is also known as Bayesian surprise (or salience), and represents the extent to which the new data is 'surprising' to the prior model."

"Systems minimise a free energy function of their internal states, which entail beliefs about hidden states in their environment. The implicit minimisation of free energy is formally related to variational Bayesian methods."

A generalization of predictive coding (PC) according to which organisms minimize an upper bound on the entropy of sensory signals (the free energy). Under specific assumptions, free energy translates to prediction error.

"A self organising system—that entails a generative model— minimises the free energy of its sensory and internal states; where internal states encode a recognition probability distribution over (fictive) hidden states causing sensory states."

Friston Blanket

For this reason, we propose to distinguish between ‘Pearl blankets’ to refer to the standard use of Markov blankets and ‘Friston blankets’3 to refer to the new construct. While Pearl blankets are unambiguously part of the map, Friston blankets are best understood as part of the territory. Since these are different formal constructs with different metaphysical implications, the scientific credibility of Pearl blankets should not automatically be extended to Friston blankets

Generalized Free Energy

Equation 14

Generative model

Generative model or forward model is a probabilistic mapping from causes to observed consequences (data). It is usually specified in terms of the likelihood of getting some data given their causes (parameters of a model) and priors on the parameters.

A probabilistic model that links (hidden) causes and data, usually specified in terms of likelihoods (of observing some data given their causes) and priors (on these causes). Generative models can be used to generate predictions of data , given their causes.

The joint probability distribution of two or more random variables, often given in terms of a prior and a likelihood: p(s,c) = p(s|c)p(c). (Sometimes, only the likelihood p(s|c) is called a "generative model".) The model is generative in the sense that it models how sensory signals s are generated by hidden causes c. Furthermore, it can be used to generate mock sensory signals, given an estimate of hidden causes.

A generative model is a probabilistic mapping from causes in the environment to observed consequences (e.g., sensory data);

Generative Process

"a generative process 𝑝𝐺𝑃(𝑦, 𝑥𝐺𝑃) [captures] the actual causal structure of the environment where hidden states 𝑥 generate observations"

Hidden state

Hidden states Ψ : Ψ × A × Ω → ℝ... constitute the dynamics of states of the world that cause sensory states and depend on action.

Hierarchical Model

Predictive Processing posits a hierarchy of estimators, which operate at different spatio-temporal timescales (so they track features at different scales). The hierarchy does not necessarily have a top level (but it might have a center — think of the levels as rings on a disc or a sphere).

Inference

inference means optimising expectations about hidden states (policies and precision),

Inference in the generative model lies in finding posterior p(s|o) — the probability that the fruit is an apple (or orange) if it lies at a specific location.

Information

Information can be thought of as the resolution of uncertainty; it answers the question of "What an entity is" and thus defines both its essence and the nature of its characteristics. The concept of information has different meanings in different contexts.[1] Thus the concept becomes synonymous to notions of constraint, communication, control, data, form, education, knowledge, meaning, understanding, mental stimuli, pattern, perception, proposition, representation, and entropy.

This notion, known as Bayesian surprise, conceptualises a unit of surprise – a “wow” – in terms of the difference between the prior and posterior beliefs about the world. This allows us to formulate epistemic foraging in terms of the mutual information between an observation, and the unobservable (hidden) states of the world that give rise to it.

Information Geometry

The central idea that underwrites information geometry [9] is that we can define a space of parameters (a statistical manifold), where each point in that space corresponds to a probability density (e.g. the expectation and variance of a normal density).

One can take this metric treatment further and equip spaces of the sufficient statistics (i.e., parameters) of a density with an information geometry. In brief, information geometry rests on Riemannian metrics that can be used to measure distances on statistical manifolds (Amari, 1998; Ay, 2015)

Internal States

Internal states R : R × S × Ω → ℝ... constitute the dynamics of states of the agent that cause action and depend on sensory states.

A system has a boundary that separates it from its environmental niche. It has internal processes (its parts interact). A system behaves. As it does so, there are changes to its internal state.

A common rhetoric used to unpack this is that the blanket states of a given internal state are the parents (things that cause it), children (things that it causes), and parents of its children. The parents of internal states are the sensory states that mediate the influence of the outside world, and their children are the active states that mediate their influence on the outside world.

The existence of a Markov blanket means that internal states will appear to minimize a free energy functional of the states of their Markov blanket.

Since the internal states of the Markov blanket are those states that constitute the system, we can think of the extended phenotype of the organism as literally embodying or encoding information that parameterises a recognition density.

Latent cause

The generative model shown in Fig. 2 links exteroceptive,proprioceptive, and interoceptive information by jointly repre-senting their hidden or latent causes (e.g., a cause can embody theprior knowledge that the sight of a burger will produce certainvisual and gustatory sensations, that it affords a grasping action,and ultimately that it increases the level of glucose in the blood).

The simplest encoding corresponds to representing the belief with the expected value, or expectation, of a hidden or latent cause. These causes are referred to as hidden because they have to be inferred from sensory consequence

Living system

free-energy theorists assume that any living system possesses a random dynamical attractor—a set of states towards which a dynamical system tends to evolve for a wide variety of initial conditions of the system’s state.

In this paper we have argued that the autonomous organization of living systems consists of the hierarchical assembly of Markov blankets of Markov blankets through adaptive active inference.

Markov Blanket

A Markov blanket defines the boundary between a system of interest and its environment in a statistical sense. More specifically, it provides a statistical partitioning Into internal and external states that are separated by blanket statesto the system. In this context, a Markov blanket is a set of variables through which states internal and external to a system interact.

Markov blankets were first proposed by Judea Pearl (1988) in the context of graphical models. These models express the statistical dependencies (edges) between different factors or states (nodes). Given a state of the model, its Markov blanket is the set of sufficient states of the network needed to predict that state.

First, a 'thing' is defined stipulatively in terms of a Markov blanket, such that something’s internal states are independent of its external states, when conditioned on its blanket states. Blanket states can be further partitioned into active and sensory states that are not influenced by internal and external states, respectively. This partition is not part of the definition of a Markov blanket but describes a way of characterising the blanket states.

A Markov blanket is a statement of conditional independence between internal and external states given blanket states.

Markov Decision Process

A Markov decision process (MDP) is a form of probabilistic generative model, defined in a discrete state space. The latent variables of an MDP are hidden states sτ, and policies, π

Markovian Monism

Markovian monism holds that Markov blankets are the type of thing/property that constitutes both mind and matter, and in this sense, their metaphysical monism is dubbed Markovian.

Model Inversion

Model inversion uses available experimental observations of the output to determine the set of input parameters that maximize the predictive potential of a model.

Multi-scale system

Multiscale modeling refers to a style of modeling in which multiple models at different scales are used simultaneously to describe a system. The different models usually focus on different scales of resolution.

Narrative (model)

Narratives are reports of real or imagined events, which can be presented in language (verbally or textually) or through sequences of images or other symbols.

Niche

Niche construction refers to any (implicit or explicit) modification by organisms of the (biotic or abiotic) states of the niche that they and others inhabi

niche construction “[…] refers to the activities, choices, and metabolic processes of organisms, through which they define, choose, modify, and partly create their own niches”

In cognitive science, cognitive niche construction can be viewed as a form of instrumental intelligence whereby organisms “create and maintain cause–effect models of the world as guides for prejudging which courses of action will lead to which results”

Non-Equilibrium Steady State

https://www.sciencedirect.com/science/article/pii/S1571064517301409?

Under appropriate conditions, any system possessing a random dynamical attractor can be shown to be formally equivalent to any system at a steady state far from equilibrium, where the system’s “characteristic” variables are within homeostatic bounds (Friston 2012; Ramstead et al. 2018, p. 2).

living systems carve out and inhabit minima in free energy landscapes, precluding the dissipation of their states over phase space. This (nonequilibrium steady-state) behaviour differentiates living states from other states, like decay and death

Novelty

when resolving uncertainty about the contingencies, the corresponding epistemic affordance becomes novelty, i.e. the opportunity to resolve uncertainty about ‘what would happen if I did that?’

hidden contingencies encoded by the param-eters of the agent’s generative model, i.e. novelty

Observation

We assume the agent has sensory states that register observa- tions or outcomes ̃ o , where outcomes are a function of the state of the agent’s environment, or hidden states, ̃ s . These states are called “hidden” because they are “shielded off” from internal states by observation states.

but AI proposes a twist — rewarding observations are assumed to be likely under agent's innate beliefs.

In the free energy principle (FEP), proposed by Friston, it is supposed that agents seek to minimize the “surprise”–the negative log (marginal) likelihood of observations (i.e., sensory stimuli)–given the agents’ current belief.

Particle

each particle is distinguished from other particles, in virtue of possessing a Markov blanket.

Perception

Perception is an inference about the causes of activity in sensory pathways.

Policy

Policy is defined as a sequence of actions at time τ that enable an agent to transition between hidden states. ... From definition, in active inference, a policy is simply a sequence of choices for actions through time (i.e., a sequential policy)

Policy selection

In active inference, policy selection not only requires Bayesian belief updating; it also entails the imperatives for action. In brief, actions are considered more likely if they maximize the evidence expected under the consequences of that action. Mathematically, this means selecting actions that optimize expected free energy. This expected free energy comprises different terms, such that action policy selection depends on: (i) the potential for information gain about future states of the world (i.e., epistemic value or affordance), and (ii) to potential for fulfilling preferred sensory outcomes (i.e., pragmatic value or affordance).

The endpoint of this argument is that action or policy selection becomes a form of Bayesian model selection, where the evidence for a particular policy becomes the free energy expected in the future.

Posterior

After specifying priors, Bayesian inference – also called estimation or inversion – furnishes a posterior probability over the parameters.These posteriors are related to the priors and likelihood by Bayes rule.

We can obtain the answer from the probabilistic model p0 by doing Bayesian inference, yielding the Bayes’ posterior

Pragmatic value

the expected value of a policy defined in terms of outcomes that are preferred a priori, where the equivalent cost corresponds to prior surprise.

our beliefs about states of the world are as close as possible to the true state of affairs, given the sensory evidence at hand. Based on these beliefs, we can then form beliefs about “what to do” by choosing those actions that minimize expected free energy. The important move here is to separate the divergence and evidence parts of free energy and understand what their expected values mean. It turns out that they correspond to epistemic and pragmatic (i.e., motivational) value respectively. This is remarkable because exactly the same separation emerges from the treatment of cognitive consistency, namely, into epistemic and motivational value. Furthermore, these two components appear to underpin nonspecific and specific closure. In other words, the maximization of epistemic value offers a formal description of nonspecific closure, whereas the maximization of motivational (pragmatic) value corresponds to specific closure

Finally, the pragmatic value just is the value of a policy with respect to its potential of fulfilling preferred outcomes (i.e., potential for supplying expected sensory states).

In active inference, behaviour has explorative (epistemic) and exploitative (pragmatic) aspects that are sensitive to ambiguity and risk respectively, where epistemic (ambiguity-resolving) behaviour enables pragmatic (reward-seeking) behaviour and the subsequent emergence of habits.

Prediction

A prediction is a deterministic function of an estimate, which can be compared to another estimate (the predicted estimate). Predictions are not necessarily about the future (note that a variable can be predictive of another variable if the first carries information about the second, i.e., if there is a correlation, cf. Anderson and Chemero 2013, p. 204). Still, many estimates in PP are also predictive in the temporal sense.

Principle

A principle is a proposition or value that is a guide for behavior or evaluation. In law, it is a rule that has to be or usually is to be followed, or can be desirably followed, or is an inevitable consequence of something, such as the laws observed in nature or the way that a system is constructed. The principles of such a system are understood by its users as the essential characteristics of the system, or reflecting system's designed purpose, and the effective operation or use of which would be impossible if any one of the principles was to be ignored

Process Theory

a "process theory or hypothesis [is] about how that principle is realized."

Recognition Models

which harness posterior beliefs that represent the system’s observationally informed ‘best guess’ about the causes of its sensations

Regime of Attention

central kind of patterned cultural practice, and higher level expectations encoded in higher levels of the cortical hierarchy, guide agents’ attentional styles

shared style of allocating attentional resources that characterizes a given cultural group

Representation

internal representations: organizational aspects (e.g., having some variable inside a system that is separated from that which it represents outside that system), structural aspects (e.g., having representational vehicles that are structurally similar to the state of affairs in the world that they stand in for), content-related aspects (e.g., having internal models that either encode environmental contingencies or sensorimotor contingencies; specification or description of how the world is taken to be in turn analysed in terms of correctness or truth conditions) and functional role aspects (e.g., supporting vicarious use before or in the absence of external events) of internal variables of a model.

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

Risk

Risk, in this setting, is simply the difference between predicted and prior beliefs about final states. It can be thought of as the expected complexity, where marginal likelihood is equal to accuracy minus complexity.

risk is the relative entropy or uncertainty about outcomes, in relation to preferences,

Salience

Stimulus salience is the degree to which a stimulus is likely to attract attention based on its low-level properties and independently of the internal mental state of the observer. This is the driving force behind bottom-up or exogenous attentional control.In active inference, it is just the epistemic value or affordance of a particular eye movement or attentional orientation. Note that salience is an attribute of action; i.e., a function of the stimulus that would sampled actively.

Sense States

Sensory states S : Ψ × A × Ω → ℝ... correspond to the agent’s sensations and constitute a probabilistic mapping from action and hidden states.

State

State variables are variables whose values evolve over time in a way that depends on the values they have at any given time and on the externally imposed values of input variables. Output variables’ values depend on the values of the state variables.

[See Active, Blanket, Control, Equilibrium, External, Hidden, Internal, Sense, Steady, World States]

State space

abstract space that allows us to describe the time evolution of a system in terms of all the possible states in which it can find itself.

Surprise

The negative log-probability of an outcome. An improbable outcome is therefore surprising. Also called self-information.

System

A thermodynamic system is a body of matter and/or radiation, confined in space by boundaries that separate it from its surroundings. It comprises an ensemble of (intensive and extensive) state variables.

Thermodynamic & Homeostatic systems. H systems do have T properties. But they are not the same thing. Two poles of the analogy. Media & Message. Memeology. "What is Life" - Schrodinger's question -- Ramstead et al. 2018 -- Informational Aperiodic Quasicrystal & Anti-dissipation

cognitive systems can be described as instantiating a form of Bayesian inference. That is, their physical properties and patterns of behaviour come to match (or infer, in a statistical sense) those of their embedding ecological niche (Bruineberg, Kiverstein, & Rietveld, 2016; Kiefer, 2017).

A random dynamical system has equations of motion with an element of randomness. These systems are characterized by a state space, the set of all possible equations of motion, and a probability distribution on the set.

Temporal Depth

In this sense, counterfactual beliefs pertain to the future consequences of action and necessarily entail temporal depth.

Uncertainty

A measure of unpredictability or expected surprise (cf, entropy). The uncertainly about a variable is often quantified with its variance (inverse precision).

Variational

https://www.sciencedirect.com/science/article/pii/S1053811908002462?

Variational Bayes or ensemble learning (Feynman, 1972, Hinton and von Cramp, 1993; MacKay, 1995, Attias, 2000) is a generic approach to model inversion that approximates the conditional density p(ϑ|y,m) on some model parameters, ϑ, given a model m and data y. We will call the approximating conditional density, q(ϑ)a variational or ensemble density. Variational Bayes also provides a lower-bound on the evidence (marginal or integrated likelihood) p(y|m) of the model itself. These two quantities are used for inference on parameter and model-space respectively.

Variational free-energy

A statistical measure used in problems of approximate Bayesian inference as an effective upper bound to surprisal, a (usually incomputable) quantity that represents the negative log-probability of an outcome, e.g., the sensory states for an organism. Under Gaussian assumptions, variational free energy reduces to a weighted sum of prediction errors.

A functional of sensory states and a probability distribution over hidden states that cause sensory states. The variational free energy is an upper bound on the surprise (self information) of sensory states, under a (generative) model. Surprise is the negative logarithm of the Bayesian model evidence or marginal likelihood.

Abstract Action

Action A : S × R → ℝ... corresponds to action emitted by an agent and depends on its sensory and internal states.

RECOGNITION models update internal parameters that correspond to external states (including hidden causes of the environment), blanket states, and internal states (meta-modeling). In contrast, GENERATIVE models take those same internal parameter estimates and emit expected or plausible observations.

Abstract action prediction

In principle, the recognition of action goals might be implemented in perceptual and associative brain areas, similar to the way other events such as visual scenes are (believed to be) recognized, predicted and understood semantically.

We propose that the brain automatically predicts others’ future actions while perceiving their current actions. The human perceptual system constantly engages in this kind of reflexive prediction.

Abstract Bayesian Inference

Minimisation of variational free energy with respect to a probability distribution over (fictive) hidden states causing sensory states (observations). Variational Bayesian inference is approximate because it minimises a (free energy) bound approximation to surprise. When free energy equals surprise, inference is exact.

Updating a model in accordance with Bayes' rule, i.e. computing the posterior distribution: p(c|s) = p(s|c)p(c)/p(s).

Abstract epistemic value

Abstract External State

Abstract Generative Model

Abstract Hidden State

Abstract Internal State

Abstract Sensory State

Abstract System

AbstractAccuracy

Accuracy is simply the surprise about sensations that are expected under the recognition density

Action

Action A : S × R → ℝ... corresponds to action emitted by an agent and depends on its sensory and internal states.

RECOGNITION models update internal parameters that correspond to external states (including hidden causes of the environment), blanket states, and internal states (meta-modeling). In contrast, GENERATIVE models take those same internal parameter estimates and emit expected or plausible observations.

Action and Planning as Divergence Minimization

Action and Perception as Divergence Minimization unify perception and action unified under a single framework. This framework proposes that both action and perception can be modelled as an agent trying to mininimize a divergence functional between two distributions an ‘actual’ distribution A(x;o), and a target distribution T(x;o).

Divergence minimization... connects deep reinforcement learning to the free energy principle (Friston, 2010; 2019), while simplifying and overcoming limitations of its active inference implementations.

Action at a distance

Complexity can be thought of as the degrees of freedom used by the plant to anticipate and predict its sensory exchange. This leads naturally to a principle of minimum redundancy (well established in the neurosciences [77]), whereby a good plant will retain just those sparse, frugal structures that are necessary to anticipate the world. This can be evident in the phenotypic form (as unpacked earlier by analogy with robotic gloves) or in terms of conditional dependencies and ‘action at a distance’ mediated in plants by channels and electrochemical waves (very much like axonal connections and electrochemical synaptic transmission in the brain). In short, under the free-energy principle—and the active inference that this entails—one would anticipate that plants would come to distil the essential causal structure in their environment in terms of their physical form and biophysical function. It is this form and functional architecture that constitutes the generative model and underwrites their existence.

Action Integral

Active Inference

Agency based model

A generative model (probability) over hidden states that include control states.

Agency free model

A generative model (probability) over hidden states that preclude control states.

Alignment (of internal states)

Appraisal theories of emotion

A long-standing tradition, dating back to James (but not Lange), according to which emotions depend on cognitive interpretations of physiological changes.

Attenuation of response

The attenuation of responses encoding prediction error, with perceptual learning, explains repetition suppression (e.g. mismatch negativity in electroencephalography).

Augmented reality

A technique in which virtual images can be combined with real-world real-time visual input to create hybrid perceptual scenes that are usually presented to a subject via a head-mounted display.

Bayes-optimal control

Acting to minimise the free energy bound on the (negative logarithm) of Bayesian model evidence – with or without agency.

Bayesian surprise

A measure of unpredictability or expected surprise (cf, entropy). The uncertainly about a variable is often quantified with its variance (inverse precision).

Belief updating

a parameterization of posterior beliefs about the past and future that makes state estimation

Belief updating mediates inference and learning, where inference means optimising expectations about hidden states (policies and precision), while learning refers to optimising model parameters. This optimisation entails finding the sufficient statistics of posterior beliefs that minimise variational free energy.

Bottom-up attentional control

Attentional control that is driven by factors external to the observer, such as stimulus salience (e.g., 'pop-out' stimuli that contrast strongly with surrounding items based on a simple feature value, sudden flashes of light, or loud noises in an otherwise quiet environment). Awh, Belopolsky and Theeuwes view this as the same concept as 'exogenous attentional control'.

Cognitive Science

Cognitive System

cognitive systems can be described as instantiating a form of Bayesian inference. That is, their physical properties and patterns of behaviour come to match (or infer, in a statistical sense) those of their embedding ecological niche (Bruineberg, Kiverstein, & Rietveld, 2016; Kiefer, 2017).

A random dynamical system has equations of motion with an element of randomness. These systems are characterized by a state space, the set of all possible equations of motion, and a probability distribution on the set.

Collective behavior

Conditional density

Conditional density q(˜ψ) := q(˜ψ| ˜μ) [is] an arbitrary probability density function over hidden states ˜ψ ∈ Ψ that is parameterized by internal states ˜μ ∈ R.

Conditional Probability

One of the basic ProbabilityRelations. ConditionalProbability is used to state the numeric value of a conditional probability. (conditionalProbability ?FORMULA1 ?FORMULA2 ?NUMBER) means that the probability of ?FORMULA2 being true given that ?FORMULA1 is true is ?NUMBER.

Control (states)

(Fictive) hidden states that are used to explain the consequences of action. Control states are inferred or represented in the generative model.

Counterfactual

A counterfactual model is a conditional probability distribution that relates possible actions to possible future states (at least following Friston).

Development

Example of regulative development: the two normal bodies resulting when an early embryo is cut in half. Deep evolutionary conservation of ion channel and neurotransmitter mechanisms highlights a fundamental isomorphism between developmental and behavioral processes. At the dawn of developmental biology, Roux wrote of the struggle of the parts in an embryo.

Divergence (Kullback–Leibler)

Information divergence, information gain or relative entropy is a non-commutative measure of the difference between two probability distributions.

A measure of the distance or difference between two probability densities.

Domain-generality

Domain-specificity

Dynamic causal modelling

Dynamic expectation maximization

Ecology, Evolution, Development

Embedded Embodied Encultured Enactive Inference

Embodied Cybernetic Complexity

complexity is the divergence between posterior and prior beliefs.

complexity is defined in relation to empirical priors based on the approximate posterior expectations of the preceding (forward) and subsequent (backward) states

Emotion

An affective state with psychological, experiential, behavioral, and visceral components. Emotional awareness refers to conscious awareness of an emotional state.

Empirical prior

Priors that are induced by hierarchical models; they provide constraints on the recognition density is the usual way but depend on the data.

Enactivism

Friston Symposium, 6/22/2021 (Pt 1, 22:06-23:30)

[The] enactive perspective... is inference about the consequences of action.

Entropy

The average surprise of outcomes sampled from a probability distribution or density. A density with low entropy means, on average, the outcome is relatively predictable (certain).

Estimator

A statistical estimator is a function of random variables that are conceived as samples; so an estimator specifies how to compute an estimate from observed data. An estimate is a particular value of an estimator (which is computed when particular samples, i.e., realizations of random variables, have been obtained).

Event-related potential (ERP)

Expectation maximization

An iterative scheme that estimates conditional expectations and maximum likelihoods of model parameters, in an E- and M-step, respectively.

Expected Utility Theory

Experience of body ownership (EBO)

The experience of certain parts of the world as belonging to one’s body. EBO can be distinguished into that related to body parts (e.g., a hand) and a global sense of identification with a whole body.

Explaining Away

The notion of "explaining away" is ambiguous. 1. Some authors write that sensory signals are explained away by top-down predictions. 2. Another sense in which the term is used is that competing hypotheses or models are explained away. 3. A third sense is as in explaining prediction error away.

Extended Cognition

Far-from-equilibrium

Fokker-Planck Equation