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Expected Float Entropy Minimisation (view source)
Revision as of 19:56, 10 December 2021
, 19:56, 10 December 2021no edit summary
'''Expected Float Entropy Minimisation (EFE)''' is a mathematically formulated model of consciousness that follows naturally from the intuitive idea that consciousness may be some kind of minimum entropy interpretation of system states. It is formulated with following underlying postulate about the aim of explaining (up to relationship isomorphism) how the brain defines the content nature of consciousness at least with respect to all relationships and associations within subjective experience and the structural content comprised of such relationships. For example, one might ask how in which the brain defines word ''interpretation'' means relational model when translated to the perceived geometry of the field of view or the perceived relationships between different colours, or between different audible frequencies. At higher structural levels there are also perceived relationships between different objects and between objects and words for examplemathematical domain.
(The fundamental postulate of EFE minimisation). ''If we suppose that consciousness is given by an interpretation or representation of system states then, notwithstanding the possibility that a system may need to satisfy a number of requirements to be conscious, among the infinitely many possible interpretations, consciousness is given by some form of minimum expected entropy interpretation of system states that yields an experience free of unnecessary discontinuities whilst exhibiting the intrinsic structural regularities of probable system states.'' The theory is formulated with the aim of explaining (up to relationship isomorphism) how the brain defines the content of consciousness at least with respect to all relationships and associations within subjective experience and the structural content comprised of such relationships. For example, one might ask how the brain defines the perceived geometry of the field of view or the perceived relationships between different colours, or between different audible frequencies. At higher structural levels there are also perceived relationships between different objects and between objects and words for example. In 2021 the theory was shown to easily extend to include the concept and mathematical formulation of Model Unity<ref name=Mason2021>Mason, J. W. (2021), Model Unity and the Unity of Consciousness: Developments in Expected Float Entropy Minimisation. Entropy, 23, 11. doi:10.3390/e23111444</ref>, which is closely related to the unity (and disunity) of consciousness and provides a different notion of integration to that of IIT. The intention behind Model Unity is to answer questions such as, why different individuals do not have shared perception, why individual visual perception is unified and why visual perception is phenomenally very different to auditory perception, for example. Due to properties such as learning, the brain is very biased toward certain system states and therefore determines typical system states and, in theory, a probability distribution over the set of all system states. This opens up the possibility of applying [https://en.wikipedia.org/wiki/Information_theory information theory] type approaches and EFE has some similarities with is a form of expected conditional Shannon entropy except where the condition involved is comprised of involves relationship parameters. EFE is a measure of the expected amount of information required to specify the state of a system (such as an artificial or [https://en.wikipedia.org/wiki/Neural_circuit biological neural network]) beyond what is already known about the system from the relationship parameters. For certain non-uniformly random systems, particular choices of the relationship parameters are isolated from other choices in the sense that they give much lower Expected Float Entropy values and, therefore, the system defines relationships. In According to the theory, in the context of these relationships a brain state acquires meaning in the form of the relational content of the corresponding experience. The principle article (Quasi-Conscious Multivariate Systems<ref name=Mason2016>Mason, J. W. (2016), Quasi-conscious multivariate systems. Complexity, 21: 125-147. doi:10.1002/cplx.21720</ref>) on this mathematical theory was published in 2015 and was followed by the article (From Learning to Consciousness: An Example Using Expected Float Entropy Minimisation<ref name=Mason2019>Mason, J. W. (2019), From Learning to Consciousness: An Example Using Expected Float Entropy Minimisation. Entropy, 21, 60. doi:10.3390/e21010060</ref>) in 2019. The extension to Model Unity was introduced in the article (Model Unity and the Unity of Consciousness: Developments in Expected Float Entropy Minimisation<ref name="Mason2021"/>) published in 2021. EFE first appeared in a publication in 2012<ref name=Mason2012>Mason, J. W. (2013), Consciousness and the structuring property of typical data. Complexity, 18: 28-37. doi:10.1002/cplx.21431</ref>.
The nomenclature “Float Entropy” comes from the notion of floating a choice of relationship parameters over a state of a system, similar to the idiom “to float an idea”. Optimisation methods are used in order to obtain the relationship parameters that minimise Expected Float Entropy. A process that performs this minimisation is itself a type of learning method.
==Overview==
Relationships are ubiquitous among mathematical structures. In particular, weighted relations (also called weighted graphs and [https://en.wikipedia.org/wiki/Weighted_network weighted networks]) are very general mathematical objects and, in the finite case, are often handled as adjacency matrices. They are a generalisation of graphs and include all [https://en.wikipedia.org/wiki/Function_(mathematics) functions] since functions are a rather constrained type of [https://en.wikipedia.org/wiki/Graph_(discrete_mathematics) graph]. It is also the case that [[consciousness]] is awash with relationships; for example, red has a stronger relationship to orange than to green, relationships between points in our field of view give rise to geometry, some smells are similar whilst others are very different, and there’s an enormity of other relationships involving many senses such as between the sound of someone’s name, their visual appearance and the timbre of their voice. Expected Float Entropy includes weighted relations as parameters and, for certain non-uniformly random systems, certain choices of weighted relations are isolated from other choices in the sense that they give much lower Expected Float Entropy values. Therefore, systems such as the brain define relationships and, according to the theory, in the context of these relationships a brain state acquires meaning in the form of the relational content of the corresponding experience.
The theory involves a hierarchy of relational models and at the lowest level the primary models involve pairs of weighted relations.
Expected Float Entropy minimisation is very general in scope. For example, the theory has been successfully applied in the context to image processing<ref name="Mason2016" /> but also applies to waveform recovery from audio data<ref name="Mason2012" />.
where <math>P</math> is the [https://en.wikipedia.org/wiki/Probability_distribution probability distribution] <math>P:\Omega_{S,V}\to [0,1]</math> determined by the bias of the system due to the long term effect of the system’s inherent learning paradigms in response to external stimulus.
According to the theory, a system (such as a subregion of the brain and its subregions) defines a particular choice of <math>U</math> and <math>R</math> (up to a certain resolution) under the requirement that the EFE is minimized. Therefore, for a given system (i.e., for a fixed <math>P</math>), solutions in <math>U</math> and <math>R</math> to the equation
: <math>efe(R,U,P)=\min_{R'\in\Psi_{S},\,U'\in\Psi_{V}}efe(R',U',P)</math>
are the weighted relations of interest. For example, when the theory is applied to digital photographs, U gives the relationships between colours and R gives the relationships that determine the geometry of the field of view.
===Model Unity and the unity of consciousness===
The theory of EFE minimisation was extended in 2021 to include the definition of Model Unity<ref name=Mason2021>Mason, J. W. (2021), Model Unity and the Unity of Consciousness: Developments in Expected Float Entropy Minimisation. Entropy, 23, 11. doi:10.3390/e23111444</ref>, which is closely related to the unity (and disunity) of consciousness and provides a different notion of integration to that of IIT.
For a given system, let <math>\widehat{S}</math> denote the set of all possible ways to view the system as a collection of subsystems. Let <math>\mathcal{X}\in\widehat{S}</math>, and define
:<math>\mu(\mathcal{X},P):=\left(\sum_{X\in\mathcal{X}}efe(\mathfrak{R}_{X},\mathfrak{U}_{X},P_{X})\right)-efe(\mathfrak{R},\mathfrak{U},P),</math>
where <math>P_{X}</math> is the marginal probability distribution for the subsystem <math>X</math>, each term is individually minimized with respect to the choice of primary models used and the last term is the minimum EFE for the whole system. Furthermore, define
:<math>M(P):=\min_{\mathcal{X}\in\widehat{S}}\mu(\mathcal{X},P).</math>
The definition of Model Unity is then as follows.
A system, with probability distribution <math>P:\Omega_{S,V}\mapsto [0,1] </math> giving the probability of finding the system in any given state, has '''Model Unity''' if and only if <math>M(P)\geq 0</math>.
The intention behind Model Unity is to answer questions such as, why different individuals do not have shared perception, why individual visual perception is unified and why visual perception is phenomenally very different to auditory perception, for example.
===Connection with ideas in topology===
