arXiv subjects

Fernando E. Rosas

Publications and source records attributed to Fernando E. Rosas.

At least 37 records · Page 2Linked to original sources

arXiv2024

Characterising high-order interdependence via entropic conjugation

High-order phenomena play crucial roles in many systems of interest, but their analysis is often highly nontrivial. There is a rich literature providing a number of alternative information-theoretic quantities capturing high-order phenomena, but their interpretation and relationship with each other is not well understood. The lack of principles unifying these quantities obscures the choice of tools for enabling specific type of analyses. Here we show how an entropic conjugation provides a theoretically grounded principle to investigate the space of possible high-order quantities, clarifying the nature of the existent metrics while revealing gaps in the literature. This leads to identify novel notions of symmetry and skew-symmetry as key properties for guaranteeing a balanced account of high-order interdependencies and enabling broadly applicable analyses across physical systems.

cs.IT↗

arXiv2024

The Fast Möbius Transform: An algebraic approach to information decomposition

The partial information decomposition (PID) and its extension integrated information decomposition ($Φ$ID) are promising frameworks to investigate information phenomena involving multiple variables. An important limitation of these approaches is the high computational cost involved in their calculation. Here we leverage fundamental algebraic properties of these decompositions to enable a computationally-efficient method to estimate them, which we call the fast Möbius transform. Our approach is based on a novel formula for estimating the Möbius function that circumvents important computational bottlenecks. We showcase the capabilities of this approach by presenting two analyses that would be unfeasible without this method: decomposing the information that neural activity at different frequency bands yield about the brain's macroscopic functional organisation, and identifying distinctive dynamical properties of the interactions between multiple voices in baroque music. Overall, our proposed approach illuminates the value of algebraic facets of information decomposition and opens the way to a wide range of future analyses.

cs.IT↗

arXiv2024

Biological arrow of time: Emergence of tangled information hierarchies and self-modelling dynamics

We study open-ended evolution by focusing on computational and information-processing dynamics underlying major evolutionary transitions. In doing so, we consider biological organisms as hierarchical dynamical systems that generate regularities in their phase-spaces through interactions with their environment. These emergent information patterns can then be encoded within the organism's components, leading to self-modelling "tangled hierarchies". Our main conjecture is that when macro-scale patterns are encoded within micro-scale components, it creates fundamental tensions (computational inconsistencies) between what is encodable at a particular evolutionary stage and what is potentially realisable in the environment. A resolution of these tensions triggers an evolutionary transition which expands the problem-space, at the cost of generating new tensions in the expanded space, in a continual process. We argue that biological complexification can be interpreted computation-theoretically, within the Gödel--Turing--Post recursion-theoretic framework, as open-ended generation of computational novelty. In general, this process can be viewed as a meta-simulation performed by higher-order systems that successively simulate the computation carried out by lower-order systems. This computation-theoretic argument provides a basis for hypothesising the biological arrow of time.

q-bio.PE↗

arXiv2024

Software in the natural world: A computational approach to hierarchical emergence

Understanding the functional architecture of complex systems is crucial to illuminate their inner workings and enable effective methods for their prediction and control. Recent advances have introduced tools to characterise emergent macroscopic levels; however, while these approaches are successful in identifying when emergence takes place, they are limited in the extent they can determine how it does. Here we address this limitation by developing a computational approach to emergence, which characterises macroscopic processes in terms of their computational capabilities. Concretely, we articulate a view on emergence based on how software works, which is rooted on a mathematical formalism that articulates how macroscopic processes can express self-contained informational, interventional, and computational properties. This framework establishes a hierarchy of nested self-contained processes that determines what computations take place at what level, which in turn delineates the functional architecture of a complex system. This approach is illustrated on paradigmatic models from the statistical physics and computational neuroscience literature, which are shown to exhibit macroscopic processes that are akin to software in human-engineered systems. Overall, this framework enables a deeper understanding of the multi-level structure of complex systems, revealing specific ways in which they can be efficiently simulated, predicted, and controlled.

nlin.AO↗

arXiv2024

Characterising directed and undirected metrics of high-order interdependence

Systems of interest for theoretical or experimental work often exhibit high-order interactions, corresponding to statistical interdependencies in groups of variables that cannot be reduced to dependencies in subsets of them. While still under active development, the framework of partial information decomposition (PID) has emerged as the dominant approach to conceptualise and calculate high-order interdependencies. PID approaches can be grouped in two types: directed approaches that divide variables into sources and targets, and undirected approaches that treat all variables equally. Directed and undirected approaches are usually employed to investigate different scenarios, and hence little is known about how these two types of approaches may relate to each other, or if their corresponding quantities are linked in some way. In this paper we investigate the relationship between the redundancy-synergy index (RSI) and the O-information, which are practical metrics of directed and undirected high-order interdependencies, respectively. Our results reveal tight links between these two quantities, and provide interpretations of them in terms of likelihood ratios in a hypothesis testing setting, as well as in terms of projections in information geometry.

cs.IT↗

arXiv2023

Quantifying Hierarchical Selection

At what level does selective pressure effectively act? When considering the reproductive dynamics of interacting and mutating agents, it has long been debated whether selection is better understood by focusing on the individual or if hierarchical selection emerges as a consequence of joint adaptation. Despite longstanding efforts in theoretical ecology there is still no consensus on this fundamental issue, most likely due to the difficulty in obtaining adequate data spanning sufficient number of generations and the lack of adequate tools to quantify the effect of hierarchical selection. Here we capitalise on recent advances in information-theoretic data analysis to advance this state of affairs by investigating the emergence of high-order structures -- such as groups of species -- in the collective dynamics of the Tangled Nature model of evolutionary ecology. Our results show that evolutionary dynamics can lead to clusters of species that act as a selective group, that acquire information-theoretic agency. Overall, our findings provide quantitative evidence supporting the relevance of high-order structures in evolutionary ecology, which can emerge even from relatively simple processes of adaptation and selection.

q-bio.PE↗

arXiv2023

Quantifying High-Order Interdependencies in Entangled Quantum States

Here, we leverage recent advances in information theory to develop a novel method to characterise the dominant character of the high-order dependencies of quantum systems. To this end, we introduce the Q-information: an information-theoretic measure capable of distinguishing quantum states dominated by synergy or redundancy. We illustrate the measure by investigating the properties of paradigmatic entangled Qubit states and find that -- in contrast to classical systems -- quantum systems need at least four variables to exhibit high-order properties. Furthermore, our results reveal that unitary evolution can radically affect the internal information organisation in a way that strongly depends on the corresponding Hamiltonian. Overall, the Q-information sheds light on novel aspects of the internal organisation of quantum systems and their time evolution, opening new avenues for studying several quantum phenomena and related technologies.

quant-ph↗

arXiv2023

Information decomposition reveals hidden high-order contributions to temporal irreversibility

Temporal irreversibility, often referred to as the arrow of time, is a fundamental concept in statistical mechanics. Markers of irreversibility also provide a powerful characterisation of information processing in biological systems. However, current approaches tend to describe temporal irreversibility in terms of a single scalar quantity, without disentangling the underlying dynamics that contribute to irreversibility. Here we propose a broadly applicable information-theoretic framework to characterise the arrow of time in multivariate time series, which yields qualitatively different types of irreversible information dynamics. This multidimensional characterisation reveals previously unreported high-order modes of irreversibility, and establishes a formal connection between recent heuristic markers of temporal irreversibility and metrics of information processing. We demonstrate the prevalence of high-order irreversibility in the hyperactive regime of a biophysical model of brain dynamics, showing that our framework is both theoretically principled and empirically useful. This work challenges the view of the arrow of time as a monolithic entity, enhancing both our theoretical understanding of irreversibility and our ability to detect it in practical applications.

q-bio.NC↗

arXiv2023

Quantifying synergy and redundancy in multiplex networks

Understanding how different networks relate to each other is key for obtaining a greater insight into complex systems. Here, we introduce an intuitive yet powerful framework to characterise the relationship between two networks comprising the same nodes. We showcase our framework by decomposing the shortest paths between nodes as being contributed uniquely by one or the other source network, or redundantly by either, or synergistically by the two together. Our approach takes into account the networks' full topology, and it also provides insights at multiple levels of resolution: from global statistics, to individual paths of different length. We show that this approach is widely applicable, from brains to the London public transport system. In humans and across 123 other mammalian species, we demonstrate that reliance on unique contributions by long-range white matter fibers is a conserved feature of mammalian structural brain networks. Across species, we also find that efficient communication relies on significantly greater synergy between long-range and short-range fibers than expected by chance, and significantly less redundancy. Our framework may find applications to help decide how to trade-off different desiderata when designing network systems, or to evaluate their relative presence in existing systems, whether biological or artificial.

cs.SI↗

arXiv2023

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 times-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 towards elucidating their origin and function in complex systems like the human brain.

nlin.AO↗

arXiv2023

Geometric Structures Induced by Deformations of the Legendre Transform

The recent link discovered between generalized Legendre transforms and non-dually flat statistical manifolds suggests a fundamental reason behind the ubiquity of Rényi's divergence and entropy in a wide range of physical phenomena. However, these early findings still provide little intuition on the nature of this relationship and its implications for physical systems. Here we shed new light on the Legendre transform by revealing the consequences of its deformation via symplectic geometry and complexification. These findings reveal a novel common framework that leads to a principled and unified understanding of physical systems that are not well-described by classic information-theoretic quantities.

cond-mat.stat-mech↗

arXiv2023

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 paradigm shift in how we 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.

q-bio.QM↗

arXiv2022

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

Striking progress has recently been made in understanding human cognition by analyzing how its neuronal underpinnings are engaged in different modes of information processing. Specifically, neural information can be decomposed into synergistic, redundant, and unique features, with synergistic components being particularly aligned with complex cognition. However, two fundamental questions remain unanswered: (a) precisely how and why a cognitive system can become highly synergistic; and (b) how these informational states map onto artificial neural networks in various learning modes. To address these questions, here we employ an information-decomposition framework to investigate the information processing strategies adopted by simple artificial neural networks performing a variety of cognitive tasks in both supervised and reinforcement learning settings. Our results show that synergy increases as neural networks learn multiple diverse tasks. Furthermore, performance in tasks requiring integration of multiple information sources critically relies on synergistic neurons. Finally, randomly turning off neurons during training through dropout increases network redundancy, corresponding to an increase in robustness. Overall, our results suggest that while redundant information is required for robustness to perturbations in the learning process, synergistic information is used to combine information from multiple modalities -- and more generally for flexible and efficient learning. These findings open the door to 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 in the system's information dynamics.

q-bio.NC↗

arXiv2022

Gradients of O-information: low-order descriptors of high-order dependencies

O-information is an information-theoretic metric that captures the overall balance between redundant and synergistic information shared by groups of three or more variables. To complement the global assessment provided by this metric, here we propose the gradients of the O-information as low-order descriptors that can characterise how high-order effects are localised across a system of interest. We illustrate the capabilities of the proposed framework by revealing the role of specific spins in Ising models with frustration, and on practical data analysis on US macroeconomic data. Our theoretical and empirical analyses demonstrate the potential of these gradients to highlight the contribution of variables in forming high-order informational circuits

cs.IT↗

arXiv2022

An information-theoretic approach to hypergraph psychometrics

Psychological network approaches propose to see symptoms or questionnaire items as interconnected nodes, with links between them reflecting pairwise statistical dependencies evaluated cross-sectional, time-series, or panel data. These networks constitute an established methodology to assess the interactions and relative importance of nodes/indicators, providing an important complement to other approaches such as factor analysis. However, focusing the modelling solely on pairwise relationships can neglect potentially critical information shared by groups of three or more variables in the form of higher-order interdependencies. To overcome this important limitation, here we propose an information-theoretic framework based on hypergraphs as psychometric models. As edges in hypergraphs are capable of encompassing several nodes together, this extension can thus provide a richer representation of the interactions that may exist among sets of psychological variables. Our results show how psychometric hypergraphs can highlight meaningful redundant and synergistic interactions on either simulated or state-of-art, re-analyzed psychometric datasets. Overall, our framework extends current network approaches while leading to new ways of assessing the data that differ at their core from other methods, extending the psychometric toolbox and opening promising avenues for future investigation.

stat.ME↗

arXiv2022

A generalization of the maximum entropy principle for curved statistical manifolds

The maximum entropy principle (MEP) is one of the most prominent methods to investigate and model complex systems. Despite its popularity, the standard form of the MEP can only generate Boltzmann-Gibbs distributions, which are ill-suited for many scenarios of interest. As a principled approach to extend the reach of the MEP, this paper revisits its foundations in information geometry and shows how the geometry of curved statistical manifolds naturally leads to a generalization of the MEP based on the Rényi entropy. By establishing a bridge between non-Euclidean geometry and the MEP, our proposal sets a solid foundation for the numerous applications of the Rényi entropy, and enables a range of novel methods for complex systems analysis.

cond-mat.stat-mech↗

arXiv2022

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↗

arXiv2021

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↗