Complex systems reveal distinct modes of collective computation
An information-geometric formulation of distributed computation
Information Theory
Summary
Understanding how many parts of a complex system work together to process information is a big challenge. The authors introduce a new way to break down and describe how groups of parts collectively compute, without simply looking at each part alone. They tested their approach on simulated data and applied it to diverse areas like brain structures and financial markets, finding unique patterns relevant to each system. This method provides a new lens to quantitatively study the information processing of complex systems.
What this means in practice
- •For neuroscience research teams: Map brain information processing to identify distributed computational features across species using multidimensional computational profiles.
- •For financial analysis teams: Dissect market data to uncover modular sector organization through collective computation patterns in financial systems.
Authors
Alberto Liardi, George Blackburne, Pedro A. M. Mediano
Abstract
Understanding how complex systems perform computations, i.e. how they store, transmit, and transform information across their components, is a major goal across the natural sciences. However, characterising genuinely collective computations across multiple inputs and outputs that cannot be reduced to contributions from individual components remains an open problem. In this work, we introduce $Φ\text{ID}^{IG}$, a geometric theory of information dynamics that captures irreducible collective phenomena and enables a complete decomposition of multi-input multi-output operations into interpretable computational modes, providing a complete informational profile of a system. We first validate our framework to identify and quantify distinct computational modes in discrete and Gaussian systems with known ground truth. We then apply it to uncover the computational architecture of complex systems across synthetic and real-world scenarios, including chaotic maps, where distinct universality classes are associated with characteristic modes of computation; brain anatomy of over 100 mammalian species, revealing an evolutionary shift towards more distributed computation in the human neocortex; and financial markets, where collective computations recover the modular organisation of market sectors. Overall, our results show how complex systems can be quantitatively investigated through multidimensional computational portraits derived from the geometry of their underlying probability distributions.