scholarly journals Markov blankets, information geometry and stochastic thermodynamics

2019 ◽  
Vol 378 (2164) ◽  
pp. 20190159 ◽  
Author(s):  
Thomas Parr ◽  
Lancelot Da Costa ◽  
Karl Friston
Keyword(s):  
Gradient Flow ◽  
Information Geometry ◽  
Random Dynamical System ◽  
Stochastic Thermodynamics ◽  
Energy Principle ◽  
Markov Blanket ◽  
Autonomous Computing ◽  
Internal States ◽  
Weakly Mixing ◽  
The Relationship

This paper considers the relationship between thermodynamics, information and inference. In particular, it explores the thermodynamic concomitants of belief updating, under a variational (free energy) principle for self-organization. In brief, any (weakly mixing) random dynamical system that possesses a Markov blanket—i.e. a separation of internal and external states—is equipped with an information geometry. This means that internal states parametrize a probability density over external states. Furthermore, at non-equilibrium steady-state, the flow of internal states can be construed as a gradient flow on a quantity known in statistics as Bayesian model evidence. In short, there is a natural Bayesian mechanics for any system that possesses a Markov blanket. Crucially, this means that there is an explicit link between the inference performed by internal states and their energetics—as characterized by their stochastic thermodynamics. This article is part of the theme issue ‘Harmonizing energy-autonomous computing and intelligence’.

scholarly journals Sentience and the Origins of Consciousness: From Cartesian Duality to Markovian Monism

Entropy ◽  
2020 ◽  
Vol 22 (5) ◽  
pp. 516 ◽  
Author(s):  
Karl J. Friston ◽  
Wanja Wiese ◽  
J. Allan Hobson
Keyword(s):  
Probability Distributions ◽  
Information Geometry ◽  
Mental States ◽  
Extrinsic Information ◽  
Physical Sciences ◽  
Markov Blanket ◽  
Internal States ◽  
Mental Properties ◽  
Intentional Systems ◽  
The Mind

This essay addresses Cartesian duality and how its implicit dialectic might be repaired using physics and information theory. Our agenda is to describe a key distinction in the physical sciences that may provide a foundation for the distinction between mind and matter, and between sentient and intentional systems. From this perspective, it becomes tenable to talk about the physics of sentience and ‘forces’ that underwrite our beliefs (in the sense of probability distributions represented by our internal states), which may ground our mental states and consciousness. We will refer to this view as Markovian monism, which entails two claims: (1) fundamentally, there is only one type of thing and only one type of irreducible property (hence monism). (2) All systems possessing a Markov blanket have properties that are relevant for understanding the mind and consciousness: if such systems have mental properties, then they have them partly by virtue of possessing a Markov blanket (hence Markovian). Markovian monism rests upon the information geometry of random dynamic systems. In brief, the information geometry induced in any system—whose internal states can be distinguished from external states—must acquire a dual aspect. This dual aspect concerns the (intrinsic) information geometry of the probabilistic evolution of internal states and a separate (extrinsic) information geometry of probabilistic beliefs about external states that are parameterised by internal states. We call these intrinsic (i.e., mechanical, or state-based) and extrinsic (i.e., Markovian, or belief-based) information geometries, respectively. Although these mathematical notions may sound complicated, they are fairly straightforward to handle, and may offer a means through which to frame the origins of consciousness.

scholarly journals Life as we know it

2013 ◽  
Vol 10 (86) ◽  
pp. 20130475 ◽  
Author(s):  
Karl Friston
Keyword(s):  
Bayesian Inference ◽  
Structural Integrity ◽  
Energy Functional ◽  
Self Organization ◽  
Random Dynamical System ◽  
Markov Blanket ◽  
Free Energy Functional ◽  
Internal States ◽  
Statistical Sense ◽  
Primordial Soup

This paper presents a heuristic proof (and simulations of a primordial soup) suggesting that life—or biological self-organization—is an inevitable and emergent property of any (ergodic) random dynamical system that possesses a Markov blanket. This conclusion is based on the following arguments: if the coupling among an ensemble of dynamical systems is mediated by short-range forces, then the states of remote systems must be conditionally independent. These independencies induce a Markov blanket that separates internal and external states in a statistical sense. 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. Crucially, this is the same quantity that is optimized in Bayesian inference. Therefore, the internal states (and their blanket) will appear to engage in active Bayesian inference. In other words, they will appear to model—and act on—their world to preserve their functional and structural integrity, leading to homoeostasis and a simple form of autopoiesis.

Choosing a Markov blanket

2020 ◽  
Vol 43 ◽  
Author(s):  
Thomas Parr
Keyword(s):  
Markov Blanket ◽  
Target Article ◽  
The Relationship

Abstract This commentary focuses upon the relationship between two themes in the target article: the ways in which a Markov blanket may be defined and the role of precision and salience in mediating the interactions between what is internal and external to a system. These each rest upon the different perspectives we might take while “choosing” a Markov blanket.

scholarly journals How Experts React: The World Health Organization’s Appraisal of COVID-19 via Communication Patterns

2021 ◽  
pp. 0261927X2110263
Author(s):  
David M. Markowitz
Keyword(s):  
World Health Organization ◽  
Cognitive Processing ◽  
Communication Patterns ◽  
World Health ◽  
Working Through ◽  
The World ◽  
Internal States ◽  
Health Organization ◽  
The Relationship ◽  
Health Experts

How do COVID-19 experts psychologically manage the pandemic and its effects? Using a full year of press briefings (January 2020–January 2021) from the World Health Organization ( N = 126), this paper evaluated the relationship between communication patterns and COVID-19 cases and deaths. The data suggest as COVID-19 cases and deaths increased, health experts tended to think about the virus in a more formal and analytic manner. Experts also communicated with fewer cognitive processing terms, which typically indicate people “working through” a crisis. This report offers a lens into the internal states of COVID-19 experts and their organization as they gradually learned about the virus and its daily impact.

scholarly journals Free Energy Principle in Human Postural Control System: Skin Stretch Feedback Reduces the Entropy

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Pilwon Hur ◽  
Yi-Tsen Pan ◽  
Christian DeBuys
Keyword(s):  
Free Energy ◽  
Control System ◽  
Postural Control ◽  
Standing Balance ◽  
Postural Control System ◽  
Energy Principle ◽  
Free Energy Principle ◽  
Sensory Deficits ◽  
Internal States ◽  
Skin Stretch

AbstractHuman upright standing involves an integration of multiple sensory inputs such as vision, vestibular and somatosensory systems. It has been known that sensory deficits worsen the standing balance. However, how the modulation of sensory information contributes to postural stabilization still remains an open question for researchers. The purpose of this work was to formulate the human standing postural control system in the framework of the free-energy principle, and to investigate the efficacy of the skin stretch feedback in enhancing the human standing balance. Previously, we have shown that sensory augmentation by skin stretch feedback at the fingertip could modulate the standing balance of the people with simulated sensory deficits. In this study, subjects underwent ten 30-second trials of quiet standing balance with and without skin stretch feedback. Visual and vestibular sensory deficits were simulated by having each subject close their eyes and tilt their head back. We found that sensory augmentation by velocity-based skin stretch feedback at the fingertip reduced the entropy of the standing postural sway of the people with simulated sensory deficits. This result aligns with the framework of the free energy principle which states that a self-organizing biological system at its equilibrium state tries to minimize its free energy either by updating the internal state or by correcting body movement with appropriate actions. The velocity-based skin stretch feedback at the fingertip may increase the signal-to-noise ratio of the sensory signals, which in turn enhances the accuracy of the internal states in the central nervous system. With more accurate internal states, the human postural control system can further adjust the standing posture to minimize the entropy, and thus the free energy.

Investigating the Relationship Between Turnaround Principal Competencies and Student Achievement

2019 ◽  
Vol 103 (3) ◽  
pp. 189-208
Author(s):  
Dallas Hambrick Hitt ◽  
Coby V. Meyers ◽  
Dennis Woodruff ◽  
Guorong Zhu
Keyword(s):  
Student Achievement ◽  
Selection Criteria ◽  
Additional Data ◽  
Data Sources ◽  
School Turnaround ◽  
Principal Competencies ◽  
Initial Effort ◽  
Internal States ◽  
The Relationship ◽  
Policies And Practices

Building upon the prior development of a model of turnaround principal competencies, we investigated the extent to which the identified principal competencies correlate with student achievement. Participants met rigorous selection criteria for having effectively turned around their schools during their first 2 years as principal. We conducted correlational analyses to examine the strength of relationship between each of the seven competencies and found that the model appears to reflect the internal states of principals who orchestrate school turnaround. We suggest that this initial effort should be further refined as additional data sources become available, but note that this model, given the popularity of principal competencies in districts, can inform current policies and practices.

scholarly journals Continuous-domain assignment flows

2020 ◽  
pp. 1-28
Author(s):  
F. SAVARINO ◽  
C. SCHNÖRR
Keyword(s):  
Gradient Flow ◽  
Information Geometry ◽  
Learning Problems ◽  
Dynamical Models ◽  
Contextual Data ◽  
Domain Assignment ◽  
Future Work ◽  
Simple Convex ◽  
Dominant Part ◽  
Continuous Domain

Assignment flows denote a class of dynamical models for contextual data labelling (classification) on graphs. We derive a novel parametrisation of assignment flows that reveals how the underlying information geometry induces two processes for assignment regularisation and for gradually enforcing unambiguous decisions, respectively, that seamlessly interact when solving for the flow. Our result enables to characterise the dominant part of the assignment flow as a Riemannian gradient flow with respect to the underlying information geometry. We consider a continuous-domain formulation of the corresponding potential and develop a novel algorithm in terms of solving a sequence of linear elliptic partial differential equations (PDEs) subject to a simple convex constraint. Our result provides a basis for addressing learning problems by controlling such PDEs in future work.

scholarly journals Classical-Quantum Transition as a Disorder-Order Process

Entropy ◽  
2022 ◽  
Vol 24 (1) ◽  
pp. 87
Author(s):  
Andres M. Kowalski ◽  
Angelo Plastino
Keyword(s):  
Uncertainty Principle ◽  
Information Geometry ◽  
Quantum Transition ◽  
Order Process ◽  
Process Mechanism ◽  
Classical Quantum ◽  
The Relationship ◽  
Insight Into

We associate here the relationship between de-coherence to the statistical notion of disequilibrium with regards to the dynamics of a system that reflects the interaction between matter and a given field. The process is described via information geometry. Some of its tools are shown here to appropriately explain the process’ mechanism. In particular we gain some insight into what is the role of the uncertainty principle (UP) in the pertinent proceedings.

scholarly journals Some Interesting Observations on the Free Energy Principle

Entropy ◽  
2021 ◽  
Vol 23 (8) ◽  
pp. 1076
Author(s):  
Karl J. Friston ◽  
Lancelot Da Costa ◽  
Thomas Parr
Keyword(s):  
Free Energy ◽  
Bayesian Inference ◽  
Coupled Systems ◽  
Energy Principle ◽  
Free Energy Principle ◽  
Markov Blanket ◽  
Approximate Bayesian ◽  
Approximate Bayesian Inference ◽  
Early Formulation

Biehl et al. (2021) present some interesting observations on an early formulation of the free energy principle. We use these observations to scaffold a discussion of the technical arguments that underwrite the free energy principle. This discussion focuses on solenoidal coupling between various (subsets of) states in sparsely coupled systems that possess a Markov blanket—and the distinction between exact and approximate Bayesian inference, implied by the ensuing Bayesian mechanics.

scholarly journals Conceptions of Topological Transitivity on Symmetric Products

2021 ◽  
Vol 27_NS1 (1) ◽  
pp. 61-80
Author(s):  
Franco Barragán ◽  
Sergio Macías ◽  
Anahí Rojas
Keyword(s):  
Positive Integer ◽  
Topological Space ◽  
Symmetric Product ◽  
Topological Transitivity ◽  
Symmetric Products ◽  
Weakly Mixing ◽  
The Relationship

Let X be a topological space. For any positive integer n , we consider the n -fold symmetric product of X , ℱ n ( X ), consisting of all nonempty subsets of X with at most n points; and for a given function ƒ : X → X , we consider the induced functions ℱ n ( ƒ ): ℱ n ( X ) → ℱ n ( X ). Let M be one of the following classes of functions: exact, transitive, ℤ-transitive, ℤ + -transitive, mixing, weakly mixing, chaotic, turbulent, strongly transitive, totally transitive, orbit-transitive, strictly orbit-transitive, ω-transitive, minimal, I N, T T ++ , semi-open and irreducible. In this paper we study the relationship between the following statements: ƒ ∈ M and ℱ n ( ƒ ) ∈ M .

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