Integrated information in the thermodynamic limit

A measure centrality index for systematic empirical comparison of consciousness theories

Consciousness science is marred by disparate constructs and methodologies, making it challenging to systematically compare theories. This foundational crisis casts doubts on the scientific character of the field itself. Addressing it, we propose a framework for systematically comparing consciousness theories by introducing a novel inter-theory classification interface, the Measure Centrality Index (MCI). Recognizing its gradient distribution, the MCI assesses the degree of importance a specific empirical measure has for a given consciousness theory. We apply the MCI to probe how the empirical measures of the Global Neuronal Workspace Theory (GNW), Integrated Information Theory (IIT), and Temporospatial Theory of Consciousness (TTC) would fare within the context of the other two. We demonstrate that direct comparison of IIT, GNW, and TTC is meaningful and valid for some measures like Lempel-Ziv Complexity (LZC), Autocorrelation Window (ACW), and possibly Mutual Information (MI). In contrast, it is problematic for others like the anatomical and physiological neural correlates of consciousness (NCC) due to their MCI-based differential weightings within the structure of the theories. In sum, we introduce and provide proof-of-principle of a novel systematic method for direct inter-theory empirical comparisons, thereby addressing isolated evolution of theories and confirmatory bias issues in the state-of-the-art neuroscience of consciousness.

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.

From Brain-Body Function to Conscious Interactions

In this review, we discuss empirical results inspiring the introduction of a formal mathematical multilayer model for the biological neuroscience of conscious experience. First, we motivate the discussion through evidence regarding the dynamic brain. Second, we review different brain-body couplings associated with conscious experience and its potential role in driving brain dynamics. Third, we introduce the machinery of multilayer networks to account for several types of interactions in brain-body systems. Then, a multilayer structure consists of two main generalizations: a formal semantic to study biological systems, and an integrative account for several signatures and models of consciousness. Finally, under this framework, we define composition of layers to account for entangled features of brain-body systems related to conscious experience. As such, a multilayer mathematical framework is highly integrative and thus may be more complete than other models. In this short review, we discuss a variety of empirical results inspiring the introduction of a formal mathematical multilayer model for the biological neuroscience of conscious experience.

Critical integration in neural and cognitive systems: Beyond power-law scaling as the hallmark of soft assembly

Inspired by models of self-organized criticality, a family of measures quantifies long-range correlations in neural and behavioral activity in the form of self-similar (e.g., power-law scaled) patterns across a range of scales. Long-range correlations are often taken as evidence that a system is near a critical transition, suggesting interaction-dominant, softly assembled relations between its parts. Psychologists and neuroscientists frequently use power-law scaling as evidence of critical regimes and soft assembly in neural and cognitive activity. Critics, however, argue that this methodology operates at most at the level of an analogy between cognitive and other natural phenomena. This is because power-laws do not provide information about a particular system's organization or what makes it specifically cognitive. We respond to this criticism using recent work in Integrated Information Theory. We propose a more principled understanding of criticality as a system's susceptibility to changes in its own integration, a property cognitive agents are expected to manifest. We contrast critical integration with power-law measures and find the former more informative about the underlying processes.

Picturing Organisms and Their Environments: Interaction, Transaction, and Constitution Loops

Changing conceptions of the relation between organisms and their environments make up a crucial chapter in the history of psychology. This may be approached by a comparative study of how schematic diagrams portray this relation. Diagrams drive the communication and the teaching of ideas, the sedimentation of epistemic norms and methods of analysis, and in some cases the articulation of novel concepts through pictographic variants. Through a sampling of schematic representations, I offer a concise comparison of how different authors, with different interests and motivations, have portrayed important aspects of the organism–environment relation. I compare example diagrams according to the features they underscore (or omit) and group them into classes that emphasize interaction, transaction, and constitution loops.

Finding continuity and discontinuity in fish schools via integrated information theory

Collective behaviours are known to be the result of diverse dynamics and are sometimes likened to living systems. Although many studies have revealed the dynamics of various collective behaviours, their main focus has been on the information processing performed by the collective, not on interactions within the collective. For example, the qualitative difference between three and four elements in a system has rarely been investigated. Tononi et al. proposed integrated information theory (IIT) to measure the degree of consciousness Φ. IIT postulates that the amount of information loss caused by the minimum information partition is equivalent to the degree of information integration in the system. This measure is not only useful for estimating the degree of consciousness but can also be applied to more general network systems. Here, we obtained two main results from the application of IIT (in particular, IIT 3.0) to the analysis of real fish schools (Plecoglossus altivelis). First, we observed that the discontinuity on 〈Φ(N)〉 distributions emerges for a school of four or more fish. This transition was not observed by measuring the mutual information or the sum of the transfer entropy. We also analysed the IIT on Boids simulations with respect to different coupling strengths; however, the results of the Boids model were found to be quite different from those of real fish. Second, we found a correlation between this discontinuity and the emergence of leadership. We discriminate leadership in this paper from its traditional meaning (e.g. defined by transfer entropy) because IIT-induced leadership refers not to group behaviour, as in other methods, but the degree of autonomy (i.e. group integrity). These results suggest that integrated information Φ can reveal the emergence of a new type of leadership which cannot be observed using other measures.

Scaling Behaviour and Critical Phase Transitions in Integrated Information Theory

Integrated Information Theory proposes a measure of conscious activity (Φ), characterised as the irreducibility of a dynamical system to the sum of its components. Due to its computational cost, current versions of the theory (IIT 3.0) are difficult to apply to systems larger than a dozen units, and, in general, it is not well known how integrated information scales as systems grow larger in size. In this article, we propose to study the scaling behaviour of integrated information in a simple model of a critical phase transition: an infinite-range kinetic Ising model. In this model, we assume a homogeneous distribution of couplings to simplify the computation of integrated information. This simplified model allows us to critically review some of the design assumptions behind the measure and connect its properties with well-known phenomena in phase transitions in statistical mechanics. As a result, we point to some aspects of the mathematical definitions of IIT that 3.0 fail to capture critical phase transitions and propose a reformulation of the assumptions made by integrated information measures.