scholarly journals The Mathematical Structure of Integrated Information Theory

Author(s):  
Johannes Kleiner ◽  
Sean Tull

Integrated Information Theory is one of the leading models of consciousness. It aims to describe both the quality and quantity of the conscious experience of a physical system, such as the brain, in a particular state. In this contribution, we propound the mathematical structure of the theory, separating the essentials from auxiliary formal tools. We provide a definition of a generalized IIT which has IIT 3.0 of Tononi et al., as well as the Quantum IIT introduced by Zanardi et al. as special cases. This provides an axiomatic definition of the theory which may serve as the starting point for future formal investigations and as an introduction suitable for researchers with a formal background.

CNS Spectrums ◽  
2010 ◽  
Vol 15 (3) ◽  
pp. 154-156
Author(s):  
Stefano Pallanti

True progress in understanding how experience arises from the brain has been relatively slow when viewed from a historical perspective. Recently, several technologies to study and stimulate the brain have been applied to this field of inquiry. Such progress was made only 2,500 years after the ancient Greek philosopher Parmenides first adopted a technical procedure involving the application of formal logic instruments to explore the perception of experiences.At the phenomenological level, consciousness has been referred to as “what vanishes every night when we fall into dreamless sleep and reappears when we wake up or when we dream. It is also all we are and all we have: lose consciousness and, as far as you are concerned, your own self, and the entire world dissolves into nothingness”. According to the integrated information theory, consciousness is integrated information.The term “consciousness” therefore has two key senses: wakefulness and awareness. Wakefulness is a state of consciousness distinguished from coma or sleep. Having one's eyes open is generally an indication of wakefulness and we usually assume that anyone who is awake will also be aware. Awareness implies not merely being conscious but also being conscious of something. The broad definition of consciousness includes a large range of processes that we normally regard as unconscious (eg, blindsight or priming by neglected or masked stimuli).Both sleep and anesthesia are reversible states of eyes-closed unresponsiveness to environmental stimuli in which the individual lacks both wakefulness and awareness. In contrast to sleep, where sufficient stimulation will return the individual to wakefulness, even the most vigorous exogenous stimulation cannot produce awakening in a patient under an adequate level of general anesthesia.


2021 ◽  
Author(s):  
Jake Hanson ◽  
Sara Imari Walker

Integrated Information Theory is currently the leading mathematical theory of conscious- ness. The core of the theory relies on the calculation of a scalar mathematical measure of consciousness, Φ, which is deduced from the phenomenological axioms of the theory. Here, we show that despite its widespread use, Φ is not a well-defined mathematical concept in the sense that the value it specifies is neither unique nor specific. This problem, occasionally referred to as “undetermined qualia”, is the result of degeneracies in the optimization routine used to calculate Φ, which leads to ambiguities in determining the consciousness of systems under study. As demonstration, we first apply the mathematical definition of Φ to a simple AND+OR logic gate system and show 83 non-unique Φ values result, spanning a substantial portion of the range of possibilities. We then introduce a Python package called PyPhi-Spectrum which, unlike currently available packages, delivers the entire spectrum of possible Φ values for a given system. We apply this to a variety of examples of recently published calculations of Φ and show how virtually all Φ values from the sampled literature are chosen arbitrarily from a set of non-unique possibilities, the full range of which often includes both conscious and unconscious predictions. Lastly, we review proposed solutions to this degeneracy problem, and find none to provide a satisfactory solution, either because they fail to specify a unique Φ value or yield Φ = 0 for systems that are clearly integrated. We conclude with a discussion of requirements moving forward for scientifically valid theories of consciousness that avoid these degeneracy issues.


2021 ◽  
Author(s):  
Romain Brette

Integrated Information Theory postulates that a conscious experience depends on a repertoire of hypothetical experiences (the axiom of information). This makes consciousness depend on the context that constrains the set of possibilities and on the scenarios imagined by the external observer, and not only on the system itself.


Entropy ◽  
2018 ◽  
Vol 20 (3) ◽  
pp. 173 ◽  
Author(s):  
Jun Kitazono ◽  
Ryota Kanai ◽  
Masafumi Oizumi

The ability to integrate information in the brain is considered to be an essential property for cognition and consciousness. Integrated Information Theory (IIT) hypothesizes that the amount of integrated information ( Φ ) in the brain is related to the level of consciousness. IIT proposes that, to quantify information integration in a system as a whole, integrated information should be measured across the partition of the system at which information loss caused by partitioning is minimized, called the Minimum Information Partition (MIP). The computational cost for exhaustively searching for the MIP grows exponentially with system size, making it difficult to apply IIT to real neural data. It has been previously shown that, if a measure of Φ satisfies a mathematical property, submodularity, the MIP can be found in a polynomial order by an optimization algorithm. However, although the first version of Φ is submodular, the later versions are not. In this study, we empirically explore to what extent the algorithm can be applied to the non-submodular measures of Φ by evaluating the accuracy of the algorithm in simulated data and real neural data. We find that the algorithm identifies the MIP in a nearly perfect manner even for the non-submodular measures. Our results show that the algorithm allows us to measure Φ in large systems within a practical amount of time.


Entropy ◽  
2021 ◽  
Vol 23 (3) ◽  
pp. 362
Author(s):  
Leonardo S. Barbosa ◽  
William Marshall ◽  
Larissa Albantakis ◽  
Giulio Tononi

The Integrated Information Theory (IIT) of consciousness starts from essential phenomenological properties, which are then translated into postulates that any physical system must satisfy in order to specify the physical substrate of consciousness. We recently introduced an information measure (Barbosa et al., 2020) that captures three postulates of IIT—existence, intrinsicality and information—and is unique. Here we show that the new measure also satisfies the remaining postulates of IIT—integration and exclusion— and create the framework that identifies maximally irreducible mechanisms. These mechanisms can then form maximally irreducible systems, which in turn will specify the physical substrate of conscious experience.


2020 ◽  
Author(s):  
Angus Leung ◽  
Dror Cohen ◽  
Bruno van Swinderen ◽  
Naotsugu Tsuchiya

AbstractThe physical basis of consciousness remains one of the most elusive concepts in current science. One influential conjecture is that consciousness is to do with some form of causality, measurable through information. The integrated information theory of consciousness (IIT) proposes that conscious experience, filled with rich and specific content, corresponds directly to a hierarchically organised, irreducible pattern of causal interactions; i.e. an integrated informational structure among elements of a system. Here, we tested this conjecture in a simple biological system (fruit flies), estimating the information structure of the system during wakefulness and general anesthesia. We found that causal interactions among populations of neurons during wakefulness collapsed to isolated clusters of interactions during anesthesia. We used classification analysis to quantify the accuracy of discrimination between wakeful and anesthetised states, and found that informational structures inferred conscious states with greater accuracy than a scalar summary of the structure, a measure which is generally championed as the main measure of IIT. Spatially, we found that the information structures collapsed rather uniformly across the fly brain. Our results speak to the potential utility of the novel concept of an “informational structure” as a measure for level of consciousness, above and beyond simple scalar values.Author summaryThe physical basis of consciousness remains elusive. Efforts to measure consciousness have generally been restricted to simple, scalar quantities which summarise the complexity of a system, inspired by integrated information theory, which links a multi-dimensional, informational structure to the contents of experience in a system. Due to the complexity of the definition of the structure, assessment of its utility as a measure of conscious arousal in a system has largely been ignored. In this manuscript we evaluate the utility of such an information structure in measuring the level of consciousness in the fruit fly. Our results indicate that this structure can be more informative about the level of consciousness in a system than even the scalar summary proposed by the theory itself. These results may push consciousness research towards the notion of multi-dimensional informational structures, instead of traditional summaries.


2021 ◽  
Author(s):  
Siddharth Sharma

This paper is an attempt to give mathematical structure to classical integrated information theory by Masafumi Oizumi, Larissa Albantakis, Giulio Tononi, using the definition provided by Giulio Tononi and making few assumptions like the mechanisms are open subset of set of elements and system is the topology of the set of elements. This would make IIT accessible to a wide audience, with more formal basis who can then apply it to non-biological objects too.


2016 ◽  
Author(s):  
Andrew M. Haun ◽  
Masafumi Oizumi ◽  
Christopher K Kovach ◽  
Hiroto Kawasaki ◽  
Hiroyuki Oya ◽  
...  

Integrated information theory postulates that the particular way stimuli appear when we consciously experience them arises from integrated information relationships across neural populations. We investigated if such equivalence holds by testing if similar/different percepts map onto similar/different information structures. We computed integrated information structure from intracranial EEGs recorded in 6 neurosurgical patients who had electrodes implanted over posterior cortices. During recordings, we dissociated their subjective percepts from physical inputs in three distinct paradigms (passive viewing, continuous flash suppression and backward masking). Unsupervised classification showed that integrated information within stimulus-selective cortical regions classified visual experiences with significant accuracy (peaking on average around 64% classification accuracy). Classification by other relevant information theoretic measures such as mutual information and entropy was consistently poorer (56% and 54% accuracy). The findings argue that concepts from integrated information theory are empirically testable, promising a potential link between conscious experience and informational structures.


2021 ◽  
Author(s):  
Siddharth Sharma

This paper is an attempt to give a Quantum theory of Mathematical integrated information theory which is mathematical version of integrated information theory by Masafumi Oizumi, Larissa Albantakis, Giulio Tononi. Using the definitions of Classical Mathematical Integrated Information Theory. And considering that the Quantum theory is given by the functor which maps from a category whose objects is topology to a linear category whose objects are Hilbert spaces indexed with the objects from previous category. Also we will be using the definition of conditional density matrix to define repertoire.


2021 ◽  
Author(s):  
Niia Emilova Nikolova ◽  
Peter Thestrup Waade ◽  
Karl Friston ◽  
Micah Allen

The mainstream science of consciousness offers a few predominate views of how the brain gives rise to awareness. Chief among these are the Higher Order Thought Theory, Global Neuronal Workspace Theory, Integrated Information Theory, and hybrids thereof. In parallel, rapid development in predictive processing approaches have begun to outline concrete mechanisms by which interoceptive inference shapes selfhood, affect, and exteroceptive perception. Here, we consider these new approaches in terms of what they might offer our empirical, phenomenological, and philosophical understanding of consciousness and its neurobiological roots.


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