Computing integrated information

Integrated information theory (IIT) 4.0: Formulating the properties of phenomenal existence in physical terms

This paper presents Integrated Information Theory (IIT) 4.0. IIT aims to account for the properties of experience in physical (operational) terms. It identifies the essential properties of experience (axioms), infers the necessary and sufficient properties that its substrate must satisfy (postulates), and expresses them in mathematical terms. In principle, the postulates can be applied to any system of units in a state to determine whether it is conscious, to what degree, and in what way. IIT offers a parsimonious explanation of empirical evidence, makes testable predictions concerning both the presence and the quality of experience, and permits inferences and extrapolations. IIT 4.0 incorporates several developments of the past ten years, including a more accurate formulation of the axioms as postulates and mathematical expressions, the introduction of a unique measure of intrinsic information that is consistent with the postulates, and an explicit assessment of causal relations. By fully unfolding a system's irreducible cause-effect power, the distinctions and relations specified by a substrate can account for the quality of experience.

An implementation of integrated information theory in resting-state fMRI

Integrated Information Theory was developed to explain and quantify consciousness, arguing that conscious systems consist of elements that are integrated through their causal properties. This study presents an implementation of Integrated Information Theory 3.0, the latest version of this framework, to functional MRI data. Data were acquired from 17 healthy subjects who underwent sedation with propofol, a short-acting anaesthetic. Using the PyPhi software package, we systematically analyze how Φ^max, a measure of integrated information, is modulated by the sedative in different resting-state networks. We compare Φ^max to other proposed measures of conscious level, including the previous version of integrated information, Granger causality, and correlation-based functional connectivity. Our results indicate that Φ^max presents a variety of sedative-induced behaviours for different networks. Notably, changes to Φ^max closely reflect changes to subjects' conscious level in the frontoparietal and dorsal attention networks, which are responsible for higher-order cognitive functions. In conclusion, our findings present important insight into different measures of conscious level that will be useful in future implementations to functional MRI and other forms of neuroimaging.

On the non-uniqueness problem in integrated information theory

Integrated Information Theory (IIT) 3.0 is among the leading theories of consciousness in contemporary neuroscience. The core of the theory relies on the calculation of a scalar mathematical measure of consciousness, Φ, which is inspired by the phenomenological axioms of the theory. Here, we show that despite its widespread application, Φ is not a well-defined mathematical concept in the sense that the value it specifies is non-unique. To demonstrate this, we introduce an algorithm that calculates all possible Φ values for a given system in strict accordance with the mathematical definition from the theory. We show that, to date, all published Φ values under consideration are selected arbitrarily from a multitude of equally valid alternatives. Crucially, both [Formula: see text] and [Formula: see text] are often predicted simultaneously, rendering any interpretation of these systems as conscious or not, non-decidable in the current formulation of IIT.

Effects of parity, frustration, and stochastic fluctuations on integrated conceptual information for networks with two small-sized loops

This paper presents an evaluation of the system-level integrated conceptual information of a major complex for a small-scale network containing two loops in accordance with the integrated information theory 3.0 framework. We focus on the following parameters characterizing the system model: (1) number of nodes in the loop, (2) frustration of the loop, and (3) temperature controlling the stochastic fluctuation of the state transition. Effects of these parameters on the integrated conceptual information and conditions for major complexes formed by a single loop, rather than the entire network, are investigated. Our first finding is that parity of the number of nodes forming a loop has a strong effect on the integrated conceptual information. For loops with an even number of nodes, the number of concepts tends to decrease, and the integrated conceptual information becomes smaller. Our second finding is that a major complex is more likely to be formed by a small number of nodes under small stochastic fluctuations. On the other hand, the entire network can easily become a major complex under larger stochastic fluctuations, and this tendency can be reinforced by frustration. It is also shown that, although counterintuitive, the integrated conceptual information can be maximized in the presence of stochastic fluctuations. These results suggest that even when several small subnetworks are connected by only a few connections, such as a bridge, the entire network may become a major complex by introducing some stochastic fluctuations and by frustrating loops with an even number of nodes.

Computing the Integrated Information of a Quantum Mechanism

Originally conceived as a theory of consciousness, integrated information theory (IIT) provides a theoretical framework intended to characterize the compositional causal information that a system, in its current state, specifies about itself. However, it remains to be determined whether IIT as a theory of consciousness is compatible with quantum mechanics as a theory of microphysics. Here, we present an extension of IIT's latest formalism to evaluate the mechanism integrated information (φ) of a system subset to discrete, finite-dimensional quantum systems (e.g., quantum logic gates). To that end, we translate a recently developed, unique measure of intrinsic information into a density matrix formulation and extend the notion of conditional independence to accommodate quantum entanglement. The compositional nature of the IIT analysis might shed some light on the internal structure of composite quantum states and operators that cannot be obtained using standard information-theoretical analysis. Finally, our results should inform theoretical arguments about the link between consciousness, causation, and physics from the classical to the quantum.

Non-Separability of Physical Systems as a Foundation of Consciousness

A hypothesis is presented that non-separability of degrees of freedom is the fundamental property underlying consciousness in physical systems. The amount of consciousness in a system is determined by the extent of non-separability and the number of degrees of freedom involved. Non-interacting and feedforward systems have zero consciousness, whereas most systems of interacting particles appear to have low non-separability and consciousness. By contrast, brain circuits exhibit high complexity and weak but tightly coordinated interactions, which appear to support high non-separability and therefore high amount of consciousness. The hypothesis applies to both classical and quantum cases, and we highlight the formalism employing the Wigner function (which in the classical limit becomes the Liouville density function) as a potentially fruitful framework for characterizing non-separability and, thus, the amount of consciousness in a system. The hypothesis appears to be consistent with both the Integrated Information Theory and the Orchestrated Objective Reduction Theory and may help reconcile the two. It offers a natural explanation for the physical properties underlying the amount of consciousness and points to methods of estimating the amount of non-separability as promising ways of characterizing the amount of consciousness.

The strength of weak integrated information theory

The integrated information theory of consciousness (IIT) is divisive: while some believe it provides an unprecedentedly powerful approach to address the 'hard problem', others dismiss it on grounds that it is untestable. We argue that the appeal and applicability of IIT can be greatly widened if we distinguish two flavours of the theory: strong IIT, which identifies consciousness with specific properties associated with maxima of integrated information; and weak IIT, which tests pragmatic hypotheses relating aspects of consciousness to broader measures of information dynamics. We review challenges for strong IIT, explain how existing empirical findings are well explained by weak IIT without needing to commit to the entirety of strong IIT, and discuss the outlook for both flavours of IIT.

Why Can the Brain (and Not a Computer) Make Sense of the Liar Paradox?

Ordinary computing machines prohibit self-reference because it leads to logical inconsistencies and undecidability. In contrast, the human mind can understand self-referential statements without necessitating physically impossible brain states. Why can the brain make sense of self-reference? Here, we address this question by defining the Strange Loop Model, which features causal feedback between two brain modules, and circumvents the paradoxes of self-reference and negation by unfolding the inconsistency in time. We also argue that the metastable dynamics of the brain inhibit and terminate unhalting inferences. Finally, we show that the representation of logical inconsistencies in the Strange Loop Model leads to causal incongruence between brain subsystems in Integrated Information Theory.

What Is Consciousness? Integrated Information vs. Inference

Any successful naturalistic account of consciousness must state what consciousness is, in terms that are compatible with the rest of our naturalistic descriptions of the world. Integrated Information Theory represents a pioneering attempt to do just this. This theory accounts for the core features of consciousness by holding that there is an equivalence between the phenomenal experience associated with a system and its intrinsic causal power. The proposal, however, fails to provide insight into the qualitative character of consciousness and, as a result of its proposed equivalence between consciousness and purely internal dynamics, into the intentional character of conscious perception. In recent years, an alternate group of theories has been proposed that claims consciousness to be equivalent to certain forms of inference. One such theory is the Living Mirror theory, which holds consciousness to be a form of inference performed by all living systems. The proposal of consciousness as inference overcomes the shortcomings of Integrated Information Theory, particularly in the case of conscious perception. A synthesis of these two perspectives can be reached by appreciating that conscious living systems are self-organising in nature. This mode of organization requires them to have a high level of integration. From this perspective, we can understand consciousness as being dependent on a system possessing non-trivial amounts of integrated information while holding that the process of inference performed by the system is the fact of consciousness itself.

Computing Integrated Information (Φ) in Discrete Dynamical Systems with Multi-Valued Elements

Integrated information theory (IIT) provides a mathematical framework to characterize the cause-effect structure of a physical system and its amount of integrated information (Φ). An accompanying Python software package (“PyPhi”) was recently introduced to implement this framework for the causal analysis of discrete dynamical systems of binary elements. Here, we present an update to PyPhi that extends its applicability to systems constituted of discrete, but multi-valued elements. This allows us to analyze and compare general causal properties of random networks made up of binary, ternary, quaternary, and mixed nodes. Moreover, we apply the developed tools for causal analysis to a simple non-binary regulatory network model (p53-Mdm2) and discuss commonly used binarization methods in light of their capacity to preserve the causal structure of the original system with multi-valued elements.

NREM sleep stages specifically alter dynamical integration of large-scale brain networks

Functional dissociations in the brain observed during non-rapid eye movement (NREM) sleep have been associated with reduced information integration and impaired consciousness that accompany increasing sleep depth. Here, we explored the dynamical properties of large-scale functional brain networks derived from transient brain activity using functional magnetic resonance imaging. Spatial brain maps generally display significant modifications in terms of their tendency to occur across wakefulness and NREM sleep. Unexpectedly, almost all networks predominated in activity during NREM stage 2 before an abrupt loss of activity is observed in NREM stage 3. Yet, functional connectivity and mutual dependencies between these networks progressively broke down with increasing sleep depth. Thus, the efficiency of information transfer during NREM stage 2 is low despite the high attempt to communicate. Critically, our approach provides relevant data for evaluating functional brain network integrity and our findings robustly support a significant advance in our neural models of human sleep and consciousness.

Whole-Brain Models to Explore Altered States of Consciousness from the Bottom Up

The scope of human consciousness includes states departing from what most of us experience as ordinary wakefulness. These altered states of consciousness constitute a prime opportunity to study how global changes in brain activity relate to different varieties of subjective experience. We consider the problem of explaining how global signatures of altered consciousness arise from the interplay between large-scale connectivity and local dynamical rules that can be traced to known properties of neural tissue. For this purpose, we advocate a research program aimed at bridging the gap between bottom-up generative models of whole-brain activity and the top-down signatures proposed by theories of consciousness. Throughout this paper, we define altered states of consciousness, discuss relevant signatures of consciousness observed in brain activity, and introduce whole-brain models to explore the biophysics of altered consciousness from the bottom-up. We discuss the potential of our proposal in view of the current state of the art, give specific examples of how this research agenda might play out, and emphasize how a systematic investigation of altered states of consciousness via bottom-up modeling may help us better understand the biophysical, informational, and dynamical underpinnings of consciousness.

Exclusion and Underdetermined Qualia

Integrated information theory (IIT) asserts that both the level and the quality of consciousness can be explained by the ability of physical systems to integrate information. Although the scientific content and empirical prospects of IIT have attracted interest, this paper focuses on another aspect of IIT, its unique theoretical structure, which relates the phenomenological axioms with the ontological postulates. In particular, the relationship between the exclusion axiom and the exclusion postulate is unclear. Moreover, the exclusion postulate leads to a serious problem in IIT: the quale underdetermination problem. Therefore, in this paper, I will explore answers to the following three questions: (1) how does the exclusion axiom lead to the exclusion postulate? (2) How does the exclusion postulate cause the qualia underdetermination problem? (3) Is there a solution to this problem? I will provide proposals and arguments for each question. If successful, IIT can be confirmed with respect to, not only its theoretical foundation, but also its practical application.

Estimating the Integrated Information Measure Phi from High-Density Electroencephalography during States of Consciousness in Humans

The integrated information theory (IIT) proposes a quantitative measure, denoted as Φ, of the amount of integrated information in a physical system, which is postulated to have an identity relationship with consciousness. IIT predicts that the value of Φ estimated from brain activities represents the level of consciousness across phylogeny and functional states. Practical limitations, such as the explosive computational demands required to estimate Φ for real systems, have hindered its application to the brain and raised questions about the utility of IIT in general. To achieve practical relevance for studying the human brain, it will be beneficial to establish the reliable estimation of Φ from multichannel electroencephalogram (EEG) and define the relationship of Φ to EEG properties conventionally used to define states of consciousness. In this study, we introduce a practical method to estimate Φ from high-density (128-channel) EEG and determine the contribution of each channel to Φ. We examine the correlation of power, frequency, functional connectivity, and modularity of EEG with regional Φ in various states of consciousness as modulated by diverse anesthetics. We find that our approximation of Φ alone is insufficient to discriminate certain states of anesthesia. However, a multi-dimensional parameter space extended by four parameters related to Φ and EEG connectivity is able to differentiate all states of consciousness. The association of Φ with EEG connectivity during clinically defined anesthetic states represents a new practical approach to the application of IIT, which may be used to characterize various physiological (sleep), pharmacological (anesthesia), and pathological (coma) states of consciousness in the human brain.