Fast and exact search for the partition with minimal information loss

Partial Information Decomposition: Redundancy as Information Bottleneck

The partial information decomposition (PID) aims to quantify the amount of redundant information that a set of sources provides about a target. Here, we show that this goal can be formulated as a type of information bottleneck (IB) problem, termed the "redundancy bottleneck" (RB). The RB formalizes a tradeoff between prediction and compression: it extracts information from the sources that best predict the target, without revealing which source provided the information. It can be understood as a generalization of "Blackwell redundancy", which we previously proposed as a principled measure of PID redundancy. The "RB curve" quantifies the prediction-compression tradeoff at multiple scales. This curve can also be quantified for individual sources, allowing subsets of redundant sources to be identified without combinatorial optimization. We provide an efficient iterative algorithm for computing the RB curve.

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.

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.

Complex of global functional network as the core of consciousness

Finding the neural basis of consciousness is challenging, and the distribution location of the core of consciousness remains inconclusive. Integrated information theory (IIT) argues that the posterior part of the brain is the hot zone of consciousness, especially phenological consciousness. The IIT has proposed a "main complex", a set of elements determined such that the information loss in a hierarchical partition approach is the largest among those of any other supersets and subsets, as the core of consciousness in a dynamic system. This approach may be applicable not only to phenomenal but also to access-consciousness. This study estimated the main complex of brain dynamics using functional magnetic resonance imaging in Human Connectome Project (HCP) and sleep datasets. The complex analyses revealed the common networks across various tasks and rest-state in HCP, composed of executive control, salience, and dorsal/ventral attention networks. The set of networks of the main complex was maintained during sleep. However, compared with the wakefulness stage, the amount of information of these networks and the default mode network, was reduced for the hypnagogic stage. The global interconnected structure composed of major functional networks can comprise the core of consciousness.

Separating weak integrated information theory into inspired and aspirational approaches

Mediano et al. (The strength of weak integrated information theory. Trends Cogn Sci 2022;26: 646-55.) separate out strong and weak flavours of the integrated information theory (IIT) of consciousness. They describe 'strong IIT' as attempting to derive a universal formula for consciousness and 'weak IIT' as searching for empirically measurable correlates of aspects of consciousness. We put forward that their overall notion of 'weak IIT' may be too weak. Rather, it should be separated out to distinguish 'aspirational-IIT', which aims to empirically test IIT by making trade-offs to its proposed measures, and 'IIT-inspired' approaches, which adopt high-level ideas of IIT while dropping the mathematical framework it reaches through its introspective, first-principles approach to consciousness.

The ambiguous feeling between "mine" and "not-mine" measured by integrated information theory during rubber hand illusion

Human body awareness is adaptive to context changes. The illusory sense of body ownership has been studied since the publication of the rubber hand illusion, where ambiguous body ownership feeling was first defined. Phenomenologically, the ambiguous body ownership is attributed to a conflict between feeling and judgement: it characterises a discrepancy between first- and third-person processes. Although Bayesian inference can explain this malleability of body image, it still fails to relate the subjective feeling to physiological data. This study attempts to explain subjective experience during rubber hand illusions by using integrated information theory (IIT). The integrated information [Formula: see text] in IIT measures the difference between the whole system and its subsystems. By analysing seven different time-series of physiological data representing a small body-brain system, we demonstrate that the integrity of the whole system during the illusion decreases, while the integrity of its subsystems increases. These general tendencies agree with many brain-image analyses and subjective reports; furthermore, we found that subjective ratings as ambiguous body ownership were associated with [Formula: see text]. Our result suggests that IIT can explain the general tendency of the sense of ownership illusions and individual differences in subjective experience during the illusions.

Filtering ASVs/OTUs via mutual information-based microbiome network analysis

Microbial communities are widely studied using high-throughput sequencing techniques, such as 16S rRNA gene sequencing. These techniques have attracted biologists as they offer powerful tools to explore microbial communities and investigate their patterns of diversity in biological and biomedical samples at remarkable resolution. However, the accuracy of these methods can negatively affected by the presence of contamination. Several studies have recognized that contamination is a common problem in microbial studies and have offered promising computational and laboratory-based approaches to assess and remove contaminants. Here we propose a novel strategy, MI-based (mutual information based) filtering method, which uses information theoretic functionals and graph theory to identify and remove contaminants. We applied MI-based filtering method to a mock community data set and evaluated the amount of information loss due to filtering taxa. We also compared our method to commonly practice traditional filtering methods. In a mock community data set, MI-based filtering approach maintained the true bacteria in the community without significant loss of information. Our results indicate that MI-based filtering method effectively identifies and removes contaminants in microbial communities and hence it can be beneficial as a filtering method to microbiome studies. We believe our filtering method has two advantages over traditional filtering methods. First, it does not required an arbitrary choice of threshold and second, it is able to detect true taxa with low abundance.

Integrated information structure collapses with anesthetic loss of conscious arousal in Drosophila melanogaster

The 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. Consistent with this conjecture, we found that integrated 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. In stark contrast to a view which assumes feedforward architecture for insect brains, especially fly visual systems, we found rich information structures, which cannot arise from purely feedforward systems, occurred across the fly brain. Further, these information structures collapsed uniformly across the brain during anesthesia. 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.

The 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 arousal in the fruit fly. Our results indicate that this structure can be more informative about the level of arousal in a system than even the single-value summary proposed by the theory itself. These results may push consciousness research towards the notion of multi-dimensional informational structures, instead of traditional scalar summaries.

Estimating integrated information in bidirectional neuron-astrocyte communication

There is growing evidence that suggests the importance of astrocytes as elements for neural information processing through the modulation of synaptic transmission. A key aspect of this problem is understanding the impact of astrocytes in the information carried by compound events in neurons across time. In this paper, we investigate how the astrocytes participate in the information integrated by individual neurons in an ensemble through the measurement of "integrated information." We propose a computational model that considers bidirectional communication between astrocytes and neurons through glutamate-induced calcium signaling. Our model highlights the role of astrocytes in information processing through dynamical coordination. Our findings suggest that the astrocytic feedback promotes synergetic influences in the neural communication, which is maximized when there is a balance between excess correlation and spontaneous spiking activity. The results were further linked with additional measures such as net synergy and mutual information. This result reinforces the idea that astrocytes have integrative properties in communication among neurons.

Efficient search for informational cores in complex systems: Application to brain networks

An important step in understanding the nature of the brain is to identify "cores" in the brain network, where brain areas strongly interact with each other. Cores can be considered as essential sub-networks for brain functions. In the last few decades, an information-theoretic approach to identifying cores has been developed. In this approach, interactions between parts are measured by an information loss function, which quantifies how much information would be lost if interactions between parts were removed. Then, a core called a "complex" is defined as a subsystem wherein the amount of information loss is locally maximal. Although identifying complexes can be a novel and useful approach, its application is practically impossible because computation time grows exponentially with system size. Here we propose a fast and exact algorithm for finding complexes, called Hierarchical Partitioning for Complex search (HPC). HPC hierarchically partitions systems to narrow down candidates for complexes. The computation time of HPC is polynomial, enabling us to find complexes in large systems (up to several hundred) in a practical amount of time. We prove that HPC is exact when an information loss function satisfies a mathematical property, monotonicity. We show that mutual information is one such information loss function. We also show that a broad class of submodular functions can be considered as such information loss functions, indicating the expandability of our framework to the class. We applied HPC to electrocorticogram recordings from a monkey and demonstrated that HPC revealed temporally stable and characteristic complexes.

Mathematics and the Brain: A Category Theoretical Approach to Go Beyond the Neural Correlates of Consciousness

Consciousness is a central issue in neuroscience, however, we still lack a formal framework that can address the nature of the relationship between consciousness and its physical substrates. In this review, we provide a novel mathematical framework of category theory (CT), in which we can define and study the sameness between different domains of phenomena such as consciousness and its neural substrates. CT was designed and developed to deal with the relationships between various domains of phenomena. We introduce three concepts of CT which include (i) category; (ii) inclusion functor and expansion functor; and, most importantly, (iii) natural transformation between the functors. Each of these mathematical concepts is related to specific features in the neural correlates of consciousness (NCC). In this novel framework, we will examine two of the major theories of consciousness, integrated information theory (IIT) of consciousness and temporospatial theory of consciousness (TTC). We conclude that CT, especially the application of the notion of natural transformation, highlights that we need to go beyond NCC and unravels questions that need to be addressed by any future neuroscientific theory of consciousness.

Evaluating Approximations and Heuristic Measures of Integrated Information

Integrated information theory (IIT) proposes a measure of integrated information, termed Phi (Φ), to capture the level of consciousness of a physical system in a given state. Unfortunately, calculating Φ itself is currently possible only for very small model systems and far from computable for the kinds of system typically associated with consciousness (brains). Here, we considered several proposed heuristic measures and computational approximations, some of which can be applied to larger systems, and tested if they correlate well with Φ. While these measures and approximations capture intuitions underlying IIT and some have had success in practical applications, it has not been shown that they actually quantify the type of integrated information specified by the latest version of IIT and, thus, whether they can be used to test the theory. In this study, we evaluated these approximations and heuristic measures considering how well they estimated the Φ values of model systems and not on the basis of practical or clinical considerations. To do this, we simulated networks consisting of 3–6 binary linear threshold nodes randomly connected with excitatory and inhibitory connections. For each system, we then constructed the system’s state transition probability matrix (TPM) and generated observed data over time from all possible initial conditions. We then calculated Φ, approximations to Φ, and measures based on state differentiation, coalition entropy, state uniqueness, and integrated information. Our findings suggest that Φ can be approximated closely in small binary systems by using one or more of the readily available approximations (r > 0.95) but without major reductions in computational demands. Furthermore, the maximum value of Φ across states (a state-independent quantity) correlated strongly with measures of signal complexity (LZ, r_s = 0.722), decoder-based integrated information (Φ*, r_s = 0.816), and state differentiation (D1, r_s = 0.827). These measures could allow for the efficient estimation of a system’s capacity for high Φ or function as accurate predictors of low- (but not high-)Φ systems. While it is uncertain whether the results extend to larger systems or systems with other dynamics, we stress the importance that measures aimed at being practical alternatives to Φ be, at a minimum, rigorously tested in an environment where the ground truth can be established.

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.

Integrated Information as a Measure of Cognitive Processes in Coupled Genetic Repressilators

Intercellular communication and its coordination allow cells to exhibit multistability as a form of adaptation. This conveys information processing from intracellular signaling networks enabling self-organization between other cells, typically involving mechanisms associated with cognitive systems. How information is integrated in a functional manner and its relationship with the different cell fates is still unclear. In parallel, drawn originally from studies on neuroscience, integrated information proposes an approach to quantify the balance between integration and differentiation in the causal dynamics among the elements in any interacting system. In this work, such an approach is considered to study the dynamical complexity in a genetic network of repressilators coupled by quorum sensing. Several attractors under different conditions are identified and related to proposed measures of integrated information to have an insight into the collective interaction and functional differentiation in cells. This research particularly accounts for the open question about the coding and information transmission in genetic systems.

Measuring Integrated Information: Comparison of Candidate Measures in Theory and Simulation

Integrated Information Theory (IIT) is a prominent theory of consciousness that has at its centre measures that quantify the extent to which a system generates more information than the sum of its parts. While several candidate measures of integrated information (" Φ ") now exist, little is known about how they compare, especially in terms of their behaviour on non-trivial network models. In this article, we provide clear and intuitive descriptions of six distinct candidate measures. We then explore the properties of each of these measures in simulation on networks consisting of eight interacting nodes, animated with Gaussian linear autoregressive dynamics. We find a striking diversity in the behaviour of these measures-no two measures show consistent agreement across all analyses. A subset of the measures appears to reflect some form of dynamical complexity, in the sense of simultaneous segregation and integration between system components. Our results help guide the operationalisation of IIT and advance the development of measures of integrated information and dynamical complexity that may have more general applicability.

Efficient Algorithms for Searching the Minimum Information Partition in Integrated Information Theory

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.