Synergistic information supports modality integration and flexible learning in neural networks solving multiple tasks.

Striking progress has been made in understanding cognition by analyzing how the brain is engaged in different modes of information processing. For instance, so-called synergistic information (information encoded by a set of neurons but not by any subset) plays a key role in areas of the human brain linked with complex cognition. However, two questions remain unanswered: (a) how and why a cognitive system can become highly synergistic; and (b) how informational states map onto artificial neural networks in various learning modes. Here we employ an information-decomposition framework to investigate neural networks performing cognitive tasks. Our results show that synergy increases as networks learn multiple diverse tasks, and that in tasks requiring integration of multiple sources, performance critically relies on synergistic neurons. Overall, our results suggest that synergy is used to combine information from multiple modalities-and more generally for flexible and efficient learning. These findings reveal new ways of investigating how and why learning systems employ specific information-processing strategies, and support the principle that the capacity for general-purpose learning critically relies on the system's information dynamics.

Not with a "zap" but with a "beep": Measuring the origins of perinatal experience.

When does the mind begin? Infant psychology is mysterious in part because we cannot remember our first months of life, nor can we directly communicate with infants. Even more speculative is the possibility of mental life prior to birth. The question of when consciousness, or subjective experience, begins in human development thus remains incompletely answered, though boundaries can be set using current knowledge from developmental neurobiology and recent investigations of the perinatal brain. Here, we offer our perspective on how the development of a sensory perturbational complexity index (sPCI) based on auditory ("beep-and-zip"), visual ("flash-and-zip"), or even olfactory ("sniff-and-zip") cortical perturbations in place of electromagnetic perturbations ("zap-and-zip") might be used to address this question. First, we discuss recent studies of perinatal cognition and consciousness using techniques such as functional magnetic resonance imaging (fMRI), electroencephalography (EEG), and, in particular, magnetoencephalography (MEG). While newborn infants are the archetypal subjects for studying early human development, researchers may also benefit from fetal studies, as the womb is, in many respects, a more controlled environment than the cradle. The earliest possible timepoint when subjective experience might begin is likely the establishment of thalamocortical connectivity at 26 weeks gestation, as the thalamocortical system is necessary for consciousness according to most theoretical frameworks. To infer at what age and in which behavioral states consciousness might emerge following the initiation of thalamocortical pathways, we advocate for the development of the sPCI and similar techniques, based on EEG, MEG, and fMRI, to estimate the perinatal brain's state of consciousness.

Reduced emergent character of neural dynamics in patients with a disrupted connectome.

High-level brain functions are widely believed to emerge from the orchestrated activity of multiple neural systems. However, lacking a formal definition and practical quantification of emergence for experimental data, neuroscientists have been unable to empirically test this long-standing conjecture. Here we investigate this fundamental question by leveraging a recently proposed framework known as "Integrated Information Decomposition," which establishes a principled information-theoretic approach to operationalise and quantify emergence in dynamical systems - including the human brain. By analysing functional MRI data, our results show that the emergent and hierarchical character of neural dynamics is significantly diminished in chronically unresponsive patients suffering from severe brain injury. At a functional level, we demonstrate that emergence capacity is positively correlated with the extent of hierarchical organisation in brain activity. Furthermore, by combining computational approaches from network control theory and whole-brain biophysical modelling, we show that the reduced capacity for emergent and hierarchical dynamics in severely brain-injured patients can be mechanistically explained by disruptions in the patients' structural connectome. Overall, our results suggest that chronic unresponsiveness resulting from severe brain injury may be related to structural impairment of the fundamental neural infrastructures required for brain dynamics to support emergence.

Computational modelling in disorders of consciousness: Closing the gap towards personalised models for restoring consciousness.

Disorders of consciousness are complex conditions characterised by persistent loss of responsiveness due to brain injury. They present diagnostic challenges and limited options for treatment, and highlight the urgent need for a more thorough understanding of how human consciousness arises from coordinated neural activity. The increasing availability of multimodal neuroimaging data has given rise to a wide range of clinically- and scientifically-motivated modelling efforts, seeking to improve data-driven stratification of patients, to identify causal mechanisms for patient pathophysiology and loss of consciousness more broadly, and to develop simulations as a means of testing in silico potential treatment avenues to restore consciousness. As a dedicated Working Group of clinicians and neuroscientists of the international Curing Coma Campaign, here we provide our framework and vision to understand the diverse statistical and generative computational modelling approaches that are being employed in this fast-growing field. We identify the gaps that exist between the current state-of-the-art in statistical and biophysical computational modelling in human neuroscience, and the aspirational goal of a mature field of modelling disorders of consciousness; which might drive improved treatments and outcomes in the clinic. Finally, we make several recommendations for how the field as a whole can work together to address these challenges.

Dynamical noise can enhance high-order statistical structure in complex systems.

Recent research has provided a wealth of evidence highlighting the pivotal role of high-order interdependencies in supporting the information-processing capabilities of distributed complex systems. These findings may suggest that high-order interdependencies constitute a powerful resource that is, however, challenging to harness and can be readily disrupted. In this paper, we contest this perspective by demonstrating that high-order interdependencies can not only exhibit robustness to stochastic perturbations, but can in fact be enhanced by them. Using elementary cellular automata as a general testbed, our results unveil the capacity of dynamical noise to enhance the statistical regularities between agents and, intriguingly, even alter the prevailing character of their interdependencies. Furthermore, our results show that these effects are related to the high-order structure of the local rules, which affect the system's susceptibility to noise and characteristic time scales. These results deepen our understanding of how high-order interdependencies may spontaneously emerge within distributed systems interacting with stochastic environments, thus providing an initial step toward elucidating their origin and function in complex systems like the human brain.

Metastability, fractal scaling, and synergistic information processing: What phase relationships reveal about intrinsic brain activity.

Dynamic functional connectivity (dFC) in resting-state fMRI holds promise to deliver candidate biomarkers for clinical applications. However, the reliability and interpretability of dFC metrics remain contested. Despite a myriad of methodologies and resulting measures, few studies have combined metrics derived from different conceptualizations of brain functioning within the same analysis - perhaps missing an opportunity for improved interpretability. Using a complexity-science approach, we assessed the reliability and interrelationships of a battery of phase-based dFC metrics including tools originating from dynamical systems, stochastic processes, and information dynamics approaches. Our analysis revealed novel relationships between these metrics, which allowed us to build a predictive model for integrated information using metrics from dynamical systems and information theory. Furthermore, global metastability - a metric reflecting simultaneous tendencies for coupling and decoupling - was found to be the most representative and stable metric in brain parcellations that included cerebellar regions. Additionally, spatiotemporal patterns of phase-locking were found to change in a slow, non-random, continuous manner over time. Taken together, our findings show that the majority of characteristics of resting-state fMRI dynamics reflect an interrelated dynamical and informational complexity profile, which is unique to each acquisition. This finding challenges the interpretation of results from cross-sectional designs for brain neuromarker discovery, suggesting that individual life-trajectories may be more informative than sample means.

Psychedelics and schizophrenia: Distinct alterations to Bayesian inference.

Schizophrenia and states induced by certain psychotomimetic drugs may share some physiological and phenomenological properties, but they differ in fundamental ways: one is a crippling chronic mental disease, while the others are temporary, pharmacologically-induced states presently being explored as treatments for mental illnesses. Building towards a deeper understanding of these different alterations of normal consciousness, here we compare the changes in neural dynamics induced by LSD and ketamine (in healthy volunteers) against those associated with schizophrenia, as observed in resting-state M/EEG recordings. While both conditions exhibit increased neural signal diversity, our findings reveal that this is accompanied by an increased transfer entropy from the front to the back of the brain in schizophrenia, versus an overall reduction under the two drugs. Furthermore, we show that these effects can be reproduced via different alterations of standard Bayesian inference applied on a computational model based on the predictive processing framework. In particular, the effects observed under the drugs are modelled as a reduction of the precision of the priors, while the effects of schizophrenia correspond to an increased precision of sensory information. These findings shed new light on the similarities and differences between schizophrenia and two psychotomimetic drug states, and have potential implications for the study of consciousness and future mental health treatments.

Ketamine and sleep modulate neural complexity dynamics in cats.

There is increasing evidence that the level of consciousness can be captured by neural informational complexity: for instance, complexity, as measured by the Lempel Ziv (LZ) compression algorithm, decreases during anaesthesia and non-rapid eye movement (NREM) sleep in humans and rats, when compared with LZ in awake and REM sleep. In contrast, LZ is higher in humans under the effect of psychedelics, including subanaesthetic doses of ketamine. However, it is both unclear how this result would be modulated by varying ketamine doses, and whether it would extend to other species. Here, we studied LZ with and without auditory stimulation during wakefulness and different sleep stages in five cats implanted with intracranial electrodes, as well as under subanaesthetic doses of ketamine (5, 10, and 15 mg/kg i.m.). In line with previous results, LZ was lowest in NREM sleep, but similar in REM and wakefulness. Furthermore, we found an inverted U-shaped curve following different levels of ketamine doses in a subset of electrodes, primarily in prefrontal cortex. However, it is worth noting that the variability in the ketamine dose-response curve across cats and cortices was larger than that in the sleep-stage data, highlighting the differential local dynamics created by two different ways of modulating conscious state. These results replicate previous findings, both in humans and other species, demonstrating that neural complexity is highly sensitive to capture state changes between wake and sleep stages while adding a local cortical description. Finally, this study describes the differential effects of ketamine doses, replicating a rise in complexity for low doses, and further fall as doses approach anaesthetic levels in a differential manner depending on the cortex.

Greater than the parts: a review of the information decomposition approach to causal emergence.

Emergence is a profound subject that straddles many scientific disciplines, including the formation of galaxies and how consciousness arises from the collective activity of neurons. Despite the broad interest that exists on this concept, the study of emergence has suffered from a lack of formalisms that could be used to guide discussions and advance theories. Here, we summarize, elaborate on, and extend a recent formal theory of causal emergence based on information decomposition, which is quantifiable and amenable to empirical testing. This theory relates emergence with information about a system's temporal evolution that cannot be obtained from the parts of the system separately. This article provides an accessible but rigorous introduction to the framework, discussing the merits of the approach in various scenarios of interest. We also discuss several interpretation issues and potential misunderstandings, while highlighting the distinctive benefits of this formalism. This article is part of the theme issue 'Emergent phenomena in complex physical and socio-technical systems: from cells to societies'.

Integrated information as a common signature of dynamical and information-processing complexity.

The apparent dichotomy between information-processing and dynamical approaches to complexity science forces researchers to choose between two diverging sets of tools and explanations, creating conflict and often hindering scientific progress. Nonetheless, given the shared theoretical goals between both approaches, it is reasonable to conjecture the existence of underlying common signatures that capture interesting behavior in both dynamical and information-processing systems. Here, we argue that a pragmatic use of integrated information theory (IIT), originally conceived in theoretical neuroscience, can provide a potential unifying framework to study complexity in general multivariate systems. By leveraging metrics put forward by the integrated information decomposition framework, our results reveal that integrated information can effectively capture surprisingly heterogeneous signatures of complexity-including metastability and criticality in networks of coupled oscillators as well as distributed computation and emergent stable particles in cellular automata-without relying on idiosyncratic, ad hoc criteria. These results show how an agnostic use of IIT can provide important steps toward bridging the gap between informational and dynamical approaches to complex systems.

Decomposing Spectral and Phasic Differences in Nonlinear Features between Datasets.

When employing nonlinear methods to characterize complex systems, it is important to determine to what extent they are capturing genuine nonlinear phenomena that could not be assessed by simpler spectral methods. Specifically, we are concerned with the problem of quantifying spectral and phasic effects on an observed difference in a nonlinear feature between two systems (or two states of the same system). Here we derive, from a sequence of null models, a decomposition of the difference in an observable into spectral, phasic, and spectrum-phase interaction components. Our approach makes no assumptions about the structure of the data and adds nuance to a wide range of time series analyses.

Reconciling emergences: An information-theoretic approach to identify causal emergence in multivariate data.

The broad concept of emergence is instrumental in various of the most challenging open scientific questions-yet, few quantitative theories of what constitutes emergent phenomena have been proposed. This article introduces a formal theory of causal emergence in multivariate systems, which studies the relationship between the dynamics of parts of a system and macroscopic features of interest. Our theory provides a quantitative definition of downward causation, and introduces a complementary modality of emergent behaviour-which we refer to as causal decoupling. Moreover, the theory allows practical criteria that can be efficiently calculated in large systems, making our framework applicable in a range of scenarios of practical interest. We illustrate our findings in a number of case studies, including Conway's Game of Life, Reynolds' flocking model, and neural activity as measured by electrocorticography.

An Information-Theoretic Approach to Self-Organisation: Emergence of Complex Interdependencies in Coupled Dynamical Systems.

Self-organisation lies at the core of fundamental but still unresolved scientific questions, and holds the promise of de-centralised paradigms crucial for future technological developments. While self-organising processes have been traditionally explained by the tendency of dynamical systems to evolve towards specific configurations, or attractors, we see self-organisation as a consequence of the interdependencies that those attractors induce. Building on this intuition, in this work we develop a theoretical framework for understanding and quantifying self-organisation based on coupled dynamical systems and multivariate information theory. We propose a metric of global structural strength that identifies when self-organisation appears, and a multi-layered decomposition that explains the emergent structure in terms of redundant and synergistic interdependencies. We illustrate our framework on elementary cellular automata, showing how it can detect and characterise the emergence of complex structures.

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.

Bayesian at heart: Towards autonomic outflow estimation via generative state-space modelling of heart rate dynamics.

Recent research is revealing how cognitive processes are supported by a complex interplay between the brain and the rest of the body, which can be investigated by the analysis of physiological features such as breathing rhythms, heart rate, and skin conductance. Heart rate dynamics are of particular interest as they provide a way to track the sympathetic and parasympathetic outflow from the autonomic nervous system, which is known to play a key role in modulating attention, memory, decision-making, and emotional processing. However, extracting useful information from heartbeats about the autonomic outflow is still challenging due to the noisy estimates that result from standard signal-processing methods. To advance this state of affairs, we propose a novel approach in how to conceptualise and model heart rate: instead of being a mere summary of the observed inter-beat intervals, we introduce a modelling framework that views heart rate as a hidden stochastic process that drives the observed heartbeats. Moreover, by leveraging the rich literature of state-space modelling and Bayesian inference, our proposed framework delivers a description of heart rate dynamics that is not a point estimate but a posterior distribution of a generative model. We illustrate the capabilities of our method by showing that it recapitulates linear properties of conventional heart rate estimators, while exhibiting a better discriminative power for metrics of dynamical complexity compared across different physiological states.

Information decomposition and the informational architecture of the brain.

To explain how the brain orchestrates information-processing for cognition, we must understand information itself. Importantly, information is not a monolithic entity. Information decomposition techniques provide a way to split information into its constituent elements: unique, redundant, and synergistic information. We review how disentangling synergistic and redundant interactions is redefining our understanding of integrative brain function and its neural organisation. To explain how the brain navigates the trade-offs between redundancy and synergy, we review converging evidence integrating the structural, molecular, and functional underpinnings of synergy and redundancy; their roles in cognition and computation; and how they might arise over evolution and development. Overall, disentangling synergistic and redundant information provides a guiding principle for understanding the informational architecture of the brain and cognition.

Quantifying synergy and redundancy between networks.

Understanding how different networks relate to each other is key for understanding complex systems. We introduce an intuitive yet powerful framework to disentangle different ways in which networks can be (dis)similar and complementary to each other. We decompose the shortest paths between nodes as uniquely contributed by one source network, or redundantly by either, or synergistically by both together. Our approach considers the networks' full topology, providing insights at multiple levels of resolution: from global statistics to individual paths. Our framework is widely applicable across scientific domains, from public transport to brain networks. In humans and 124 other species, we demonstrate the prevalence of unique contributions by long-range white-matter fibers in structural brain networks. Across species, efficient communication also relies on significantly greater synergy between long-range and short-range fibers than expected by chance. Our framework could find applications for designing network systems or evaluating existing ones.

Unravelling consciousness and brain function through the lens of time, space, and information.

Disentangling how cognitive functions emerge from the interplay of brain dynamics and network architecture is among the major challenges that neuroscientists face. Pharmacological and pathological perturbations of consciousness provide a lens to investigate these complex challenges. Here, we review how recent advances about consciousness and the brain's functional organisation have been driven by a common denominator: decomposing brain function into fundamental constituents of time, space, and information. Whereas unconsciousness increases structure-function coupling across scales, psychedelics may decouple brain function from structure. Convergent effects also emerge: anaesthetics, psychedelics, and disorders of consciousness can exhibit similar reconfigurations of the brain's unimodal-transmodal functional axis. Decomposition approaches reveal the potential to translate discoveries across species, with computational modelling providing a path towards mechanistic integration.

Effects of External Stimulation on Psychedelic State Neurodynamics.

Recent findings have shown that psychedelics reliably enhance brain entropy (understood as neural signal diversity), and this effect has been associated with both acute and long-term psychological outcomes, such as personality changes. These findings are particularly intriguing, given that a decrease of brain entropy is a robust indicator of loss of consciousness (e.g., from wakefulness to sleep). However, little is known about how context impacts the entropy-enhancing effect of psychedelics, which carries important implications for how it can be exploited in, for example, psychedelic psychotherapy. This article investigates how brain entropy is modulated by stimulus manipulation during a psychedelic experience by studying participants under the effects of lysergic acid diethylamide (LSD) or placebo, either with gross state changes (eyes closed vs open) or different stimuli (no stimulus vs music vs video). Results show that while brain entropy increases with LSD under all of the experimental conditions, it exhibits the largest changes when subjects have their eyes closed. Furthermore, brain entropy changes are consistently associated with subjective ratings of the psychedelic experience, but this relationship is disrupted when participants are viewing a video─potentially due to a "competition" between external stimuli and endogenous LSD-induced imagery. Taken together, our findings provide strong quantitative evidence of the role of context in modulating neural dynamics during a psychedelic experience, underlining the importance of performing psychedelic psychotherapy in a suitable environment.

Paradoxical pharmacological dissociations result from drugs that enhance delta oscillations but preserve consciousness.

Low-frequency (<4 Hz) neural activity, particularly in the delta band, is generally indicative of loss of consciousness and cortical down states, particularly when it is diffuse and high amplitude. Remarkably, however, drug challenge studies of several diverse classes of pharmacological agents-including drugs which treat epilepsy, activate GABAB receptors, block acetylcholine receptors, or produce psychedelic effects-demonstrate neural activity resembling cortical down states even as the participants remain conscious. Of those substances that are safe to use in healthy volunteers, some may be highly valuable research tools for investigating which neural activity patterns are sufficient for consciousness or its absence.