Statistical Dark Matter: Synergy is everywhere but is hard to capture
Abstract
The information-theoretic construct of synergy refers to the statistical structure that is contained in three or more variables, but not in any subset of them. Here we leverage recent advances in multivariate information theory to show that synergy is far more prevalent in complex systems than previously thought. In particular, we show that many-body systems tend to become strongly dominated by synergy as the number of subcomponents grows. At the same time, our results also reveal that commonly used tools for statistical modelling severely underestimate synergistic structures. These findings imply that synergy constitutes a prevalent, yet often invisible, informational component of complex systems. With a certain poetic licence, we interpret these results as suggesting that synergy is the dark matter of statistics - interdependencies that we know exist, but standard instruments fail to detect.
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BibTeX
@misc{liardi2026statistical,
title = {{Statistical Dark Matter: Synergy is everywhere but is hard to capture}},
author = {Alberto Liardi and Fernando E. Rosas and Daniele Marinazzo and Thomas F. Varley and Michael Gastpar and Pedro A. M. Mediano},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.03764},
eprint = {2610.03764},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.03764},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Statistical Dark Matter: Synergy is everywhere but is hard to capture
AU - Alberto Liardi
AU - Fernando E. Rosas
AU - Daniele Marinazzo
AU - Thomas F. Varley
AU - Michael Gastpar
AU - Pedro A. M. Mediano
PY - 2026
DA - 2026/10/06
PB - arXiv
DO - 10.48550/arxiv.2610.03764
UR - https://arxiv.org/abs/2610.03764
AB - The information-theoretic construct of synergy refers to the statistical structure that is contained in three or more variables, but not in any subset of them. Here we leverage recent advances in multivariate information theory to show that synergy is far more prevalent in complex systems than previously thought. In particular, we show that many-body systems tend to become strongly dominated by synergy as the number of subcomponents grows. At the same time, our results also reveal that commonly used tools for statistical modelling severely underestimate synergistic structures. These findings imply that synergy constitutes a prevalent, yet often invisible, informational component of complex systems. With a certain poetic licence, we interpret these results as suggesting that synergy is the dark matter of statistics - interdependencies that we know exist, but standard instruments fail to detect.
ER -