Paper List

Journal: ArXiv Preprint
Published: Unknown
Computational NeuroscienceInformation Theory

Translating Measures onto Mechanisms: The Cognitive Relevance of Higher-Order Information

University of Amsterdam | University of Cambridge | Queen Mary University of London | Imperial College London | University of Vermont | Indiana University | University of Glasgow | Universidad Catolica del Maule | University of Helsinki

Daniel Rebbin, Keenan J. A. Down, Thomas F. Varley, Robin Ince, Andres Canales-Johnson
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The 30-Second View

IN SHORT: This review addresses the core challenge of translating abstract higher-order information theory metrics (e.g., synergy, redundancy) into defensible, mechanistic explanations for cognitive function in neuroscience.

Innovation (TL;DR)

  • Methodology Systematizes Shannon-based multivariate metrics (e.g., Total Correlation, Dual Total Correlation, O-information) into a unified framework defined by two independent axes: interaction strength and redundancy-synergy balance.
  • Theory Proposes that a balanced layering of synergistic integration and redundant broadcasting optimizes multiscale complexity, formalizing a fundamental computation-communication tradeoff in neural systems.
  • Methodology Provides a pragmatic guide for applying Partial Information Decomposition (PID) to neural data, emphasizing the critical conceptual and practical consequences of choosing a specific redundancy function.

Key conclusions

  • Higher-order dependence in multivariate systems can be parsimoniously characterized by two largely independent axes: interaction strength (e.g., quantified by S-information) and redundancy-synergy balance (e.g., quantified by O-information).
  • Prototypical systems demonstrate this duality: a purely redundant COPY distribution yields O-information = +1 bit, while a purely synergistic XOR distribution yields O-information = -1 bit, despite both having an S-information of 3 bits.
  • The balanced integration of synergistic (head-to-head) and redundant (tail-to-tail) information motifs is proposed as a mechanism optimizing multiscale complexity, formalizing a tradeoff critical for cognitive function.
Background and Gap： A significant gap exists between the rapid application of higher-order information measures (like synergy/redundancy) in cognitive neuroscience and the lack of principled, mechanistic arguments linking these statistical quantities to underlying cognitive processes.

Abstract: Higher–order information theory has become a rapidly growing toolkit in computational neuroscience, motivated by the idea that multivariate dependencies can reveal aspects of neural computation and communication invisible to pairwise analyses. Yet functional interpretations of synergy and redundancy often outpace principled arguments for how statistical quantities map onto mechanistic cognitive processes. Here we review the main families of higher-order measures with the explicit goal of translating mathematical properties into defensible mechanistic inferences. Firstly, we systematize Shannon-based multivariate metrics and demonstrate that higher-order dependence is parsimoniously characterized by two largely independent axes: interaction strength and redundancy-synergy balance. We argue that balanced layering of synergistic integration and redundant broadcasting optimizes multiscale complexity, formalizing a computation-communication tradeoff. We then examine the partial information decomposition and outline pragmatic considerations for its deployment in neural data. Equipped with the relevant mathematical essentials, we connect redundancy-synergy balance to cognitive function by progressively embedding their mathematical properties in real-world constraints, starting with small synthetic systems before gradually building up to neuroimaging. We close by identifying key future directions for mechanistic insight: cross-scale bridging, intervention-based validation, and thermodynamically grounded unification of information dynamics.