[Paper Review] Information decomposition reveals hidden high-order contributions to temporal irreversibility

Andrea I. Luppi, Fernando E. Rosas+3 more|arXiv (Cornell University)|Aug 10, 2023

Neural dynamics and brain function4 citations

TL;DR

This paper introduces a novel information-theoretic framework that decomposes temporal irreversibility in multivariate time series into distinct, high-order dynamical modes, revealing previously hidden contributions to the arrow of time. The method uncovers dominant high-order irreversibility in a biophysical brain model beyond criticality, challenging scalar metrics and linking irreversibility to complex information processing dynamics.

ABSTRACT

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.

Motivation & Objective

• To address the limitation of scalar metrics in capturing the multidimensional nature of temporal irreversibility in multivariate time series.
• To formally connect heuristic markers of irreversibility with information processing metrics using a principled information-theoretic framework.
• To identify and quantify previously unreported high-order modes of irreversibility in complex dynamical systems.
• To demonstrate the framework's empirical utility in a biophysically realistic model of brain dynamics.

Proposed method

• Applies Integrated Information Decomposition (ΦID) to decompose mutual information between timepoints into distinct information atoms: Red (redundant), UnX (unique to X), UnY (unique to Y), and Syn (synergistic).
• Uses the minimum mutual information (MMI) redundancy function to define information atoms and compute irreversible contributions across time series.
• Employs a Dynamic Mean Field (DMF) model to simulate multivariate brain activity with realistic structural connectivity derived from human dMRI data.
• Applies the INSIDEOUT marker to quantify irreversibility and compares it with the decomposition across varying global coupling strengths (G).
• Aggregates results across all region pairs by averaging to assess overall irreversibility dynamics across the network.
• Uses a Balloon-Windkessel hemodynamic model to convert neuronal activity into simulated BOLD signals for realistic time-series analysis.

Figure 1: Irreversible modes of information dynamics . a) Examples of different irreversible modes of information dynamics and their time-reversed counterparts: irreversibility due to asymmetry between copy and erasure of information (top); irreversibility due to asymmetry of information transfer be

Experimental results

Research questions

• RQ1 What types of information dynamics contribute to temporal irreversibility beyond simple pairwise transfer or copy-erasure asymmetries?
• RQ2 Can high-order information dynamics—such as asymmetric whole-part information transfer—contribute significantly to observed irreversibility?
• RQ3 How does the contribution of high-order irreversibility modes change across different dynamical regimes of a biophysical brain model?
• RQ4 To what extent do heuristic markers of irreversibility (e.g., INSIDEOUT) reflect underlying information-theoretic mechanisms?

Key findings

• The proposed framework reveals qualitatively distinct irreversible information dynamics, including high-order modes not previously reported in the literature.
• High-order irreversibility, particularly from asymmetric transfer between the whole system and its parts, dominates irreversibility in the hyperactive regime of the DMF model.
• The INSIDEOUT marker is formally linked to information dynamics through the ΦID framework, providing a theoretical foundation for its use.
• The copy-erasure mode of irreversibility vanishes under the MMI redundancy function, indicating that this mode is not universally present and depends on the choice of redundancy function.
• Beyond the critical point of the DMF model, high-order contributions to irreversibility exceed those from lower-order modes, suggesting their functional significance in complex systems.
• The framework successfully disentangles the contributions of different information dynamics, offering a multidimensional characterization of irreversibility.

Figure 2: Distinct modes of temporal irreversibility in simulated brain dynamics. a) A biophysical model of excitatory (E) and inhibitory (I) neural masses coupled according to the structural connectivity of the human brain is used to simulate the neural dynamics of different brain regions. The mode