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Pedro A. M. Mediano

Publications and source records attributed to Pedro A. M. Mediano.

At least 55 records · Page 3Linked to original sources

Disentangling high-order mechanisms and high-order behaviours in complex systems

Battiston et al. (arXiv:2110.06023) provide a comprehensive overview of how investigations of complex systems should take into account interactions between more than two elements, which can be modelled by hypergraphs and studied via topological data analysis. Following a separate line of enquiry, a broad literature has developed information-theoretic tools to characterize high-order interdependencies from observed data. While these could seem to be competing approaches aiming to address the same question, in this correspondence we clarify that this is not the case, and that a complete account of higher-order phenomena needs to embrace both.

cs.IT↗

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 summarise, 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.

q-bio.NC↗

Towards an extended taxonomy of information dynamics via Integrated Information Decomposition

Complex systems, from the human brain to the global economy, are made of multiple elements that interact in such ways that the behaviour of the `whole' often seems to be more than what is readily explainable in terms of the `sum of the parts.' Our ability to understand and control these systems remains limited, one reason being that we still don't know how best to describe -- and quantify -- the higher-order dynamical interactions that characterise their complexity. To address this limitation, we combine principles from the theories of Information Decomposition and Integrated Information into what we call Integrated Information Decomposition, or $Φ$ID. $Φ$ID provides a comprehensive framework to reason about, evaluate, and understand the information dynamics of complex multivariate systems. $Φ$ID reveals the existence of previously unreported modes of collective information flow, providing tools to express well-known measures of information transfer and dynamical complexity as aggregates of these modes. Via computational and empirical examples, we demonstrate that $Φ$ID extends our explanatory power beyond traditional causal discovery methods -- with profound implications for the study of complex systems across disciplines.

q-bio.NC↗

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 behaviour 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. Furthermore, by leveraging metrics put forward by the integrated information decomposition ($Φ$ID) 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 towards bridging the gap between informational and dynamical approaches to complex systems.

q-bio.NC↗

Learning, compression, and leakage: Minimising classification error via meta-universal compression principles

Learning and compression are driven by the common aim of identifying and exploiting statistical regularities in data, which opens the door for fertile collaboration between these areas. A promising group of compression techniques for learning scenarios is normalised maximum likelihood (NML) coding, which provides strong guarantees for compression of small datasets - in contrast with more popular estimators whose guarantees hold only in the asymptotic limit. Here we consider a NML-based decision strategy for supervised classification problems, and show that it attains heuristic PAC learning when applied to a wide variety of models. Furthermore, we show that the misclassification rate of our method is upper bounded by the maximal leakage, a recently proposed metric to quantify the potential of data leakage in privacy-sensitive scenarios.

cs.LG↗

Deep active inference agents using Monte-Carlo methods

Active inference is a Bayesian framework for understanding biological intelligence. The underlying theory brings together perception and action under one single imperative: minimizing free energy. However, despite its theoretical utility in explaining intelligence, computational implementations have been restricted to low-dimensional and idealized situations. In this paper, we present a neural architecture for building deep active inference agents operating in complex, continuous state-spaces using multiple forms of Monte-Carlo (MC) sampling. For this, we introduce a number of techniques, novel to active inference. These include: i) selecting free-energy-optimal policies via MC tree search, ii) approximating this optimal policy distribution via a feed-forward `habitual' network, iii) predicting future parameter belief updates using MC dropouts and, finally, iv) optimizing state transition precision (a high-end form of attention). Our approach enables agents to learn environmental dynamics efficiently, while maintaining task performance, in relation to reward-based counterparts. We illustrate this in a new toy environment, based on the dSprites data-set, and demonstrate that active inference agents automatically create disentangled representations that are apt for modeling state transitions. In a more complex Animal-AI environment, our agents (using the same neural architecture) are able to simulate future state transitions and actions (i.e., plan), to evince reward-directed navigation - despite temporary suspension of visual input. These results show that deep active inference - equipped with MC methods - provides a flexible framework to develop biologically-inspired intelligent agents, with applications in both machine learning and cognitive science.

q-bio.NC↗

Causal blankets: Theory and algorithmic framework

We introduce a novel framework to identify perception-action loops (PALOs) directly from data based on the principles of computational mechanics. Our approach is based on the notion of causal blanket, which captures sensory and active variables as dynamical sufficient statistics -- i.e. as the "differences that make a difference." Moreover, our theory provides a broadly applicable procedure to construct PALOs that requires neither a steady-state nor Markovian dynamics. Using our theory, we show that every bipartite stochastic process has a causal blanket, but the extent to which this leads to an effective PALO formulation varies depending on the integrated information of the bipartition.

nlin.AO↗

Decomposing spectral and phasic differences in non-linear features between datasets

When employing non-linear methods to characterise complex systems, it is important to determine to what extent they are capturing genuine non-linear 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 non-linear 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.

stat.ME↗

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 mechanisms 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 emphasise how a systematic investigation of altered states of consciousness via bottom-up modelling may help us better understand the biophysical, informational, and dynamical underpinnings of consciousness.

q-bio.NC↗

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.

q-bio.NC↗

Beyond integrated information: A taxonomy of information dynamics phenomena

Most information dynamics and statistical causal analysis frameworks rely on the common intuition that causal interactions are intrinsically pairwise -- every 'cause' variable has an associated 'effect' variable, so that a 'causal arrow' can be drawn between them. However, analyses that depict interdependencies as directed graphs fail to discriminate the rich variety of modes of information flow that can coexist within a system. This, in turn, creates problems with attempts to operationalise the concepts of 'dynamical complexity' or `integrated information.' To address this shortcoming, we combine concepts of partial information decomposition and integrated information, and obtain what we call Integrated Information Decomposition, or $Φ$ID. We show how $Φ$ID paves the way for more detailed analyses of interdependencies in multivariate time series, and sheds light on collective modes of information dynamics that have not been reported before. Additionally, $Φ$ID reveals that what is typically referred to as 'integration' is actually an aggregate of several heterogeneous phenomena. Furthermore, $Φ$ID can be used to formulate new, tailored measures of integrated information, as well as to understand and alleviate the limitations of existing measures.

q-bio.NC↗

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.

nlin.AO↗

Quantifying High-order Interdependencies via Multivariate Extensions of the Mutual Information

This article introduces a model-agnostic approach to study statistical synergy, a form of emergence in which patterns at large scales are not traceable from lower scales. Our framework leverages various multivariate extensions of Shannon's mutual information, and introduces the O-information as a metric capable of characterising synergy- and redundancy-dominated systems. We develop key analytical properties of the O-information, and study how it relates to other metrics of high-order interactions from the statistical mechanics and neuroscience literature. Finally, as a proof of concept, we use the proposed framework to explore the relevance of statistical synergy in Baroque music scores.

cs.IT↗

The Phi measure of integrated information is not well-defined for general physical systems

According to the Integrated Information Theory of Consciousness, consciousness is a fundamental observer-independent property of physical systems, and the measure Phi of integrated information is identical to the quantity or level of consciousness. For this to be plausible, there should be no alternative formulae for Phi consistent with the axioms of IIT, and there should not be cases of Phi being ill-defined. This article presents three ways in which Phi, in its current formulation, fails to meet these standards, and discusses how this problem might be addressed.

q-bio.NC↗

Relational Forward Models for Multi-Agent Learning

The behavioral dynamics of multi-agent systems have a rich and orderly structure, which can be leveraged to understand these systems, and to improve how artificial agents learn to operate in them. Here we introduce Relational Forward Models (RFM) for multi-agent learning, networks that can learn to make accurate predictions of agents' future behavior in multi-agent environments. Because these models operate on the discrete entities and relations present in the environment, they produce interpretable intermediate representations which offer insights into what drives agents' behavior, and what events mediate the intensity and valence of social interactions. Furthermore, we show that embedding RFM modules inside agents results in faster learning systems compared to non-augmented baselines. As more and more of the autonomous systems we develop and interact with become multi-agent in nature, developing richer analysis tools for characterizing how and why agents make decisions is increasingly necessary. Moreover, developing artificial agents that quickly and safely learn to coordinate with one another, and with humans in shared environments, is crucial.

cs.LG↗

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. Further, only a subset of the measures appear to genuinely 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 that may have more general applicability.

q-bio.NC↗

Balanced Information Storage and Transfer in Modular Spiking Neural Networks

While information processing in complex systems can be described in abstract, general terms, there are cases in which the relation between these computations and the physical substrate of the underlying system is itself of interest. Prominently, the brain is one such case. With the aim of relating information and dynamics in biological neural systems, we study a model network of spiking neurons with different coupling configurations, and explore the relation between its informational, dynamical, and topological properties. We find that information transfer and storage peak at two separate points for different values of the coupling parameter, and are balanced at an intermediate point. In this configuration, avalanches in the network follow a long-tailed, power law-like distribution. Furthermore, the avalanche statistics at this point reproduce empirical findings in the biological brain.

q-bio.NC↗

Spectral Modes of Network Dynamics Reveal Increased Informational Complexity Near Criticality

What does the informational complexity of dynamical networked systems tell us about intrinsic mechanisms and functions of these complex systems? Recent complexity measures such as integrated information have sought to operationalize this problem taking a whole-versus-parts perspective, wherein one explicitly computes the amount of information generated by a network as a whole over and above that generated by the sum of its parts during state transitions. While several numerical schemes for estimating network integrated information exist, it is instructive to pursue an analytic approach that computes integrated information as a function of network weights. Our formulation of integrated information uses a Kullback-Leibler divergence between the multi-variate distribution on the set of network states versus the corresponding factorized distribution over its parts. Implementing stochastic Gaussian dynamics, we perform computations for several prototypical network topologies. Our findings show increased informational complexity near criticality, which remains consistent across network topologies. Spectral decomposition of the system's dynamics reveals how informational complexity is governed by eigenmodes of both, the network's covariance and adjacency matrices. We find that as the dynamics of the system approach criticality, high integrated information is exclusively driven by the eigenmode corresponding to the leading eigenvalue of the covariance matrix, while sub-leading modes get suppressed. The implication of this result is that it might be favorable for complex dynamical networked systems such as the human brain or communication systems to operate near criticality so that efficient information integration might be achieved.

cs.NE↗