Duality between predictability and reconstructability in complex systems

TL;DR

This paper explores the fundamental relationship between predictability and reconstructability in complex systems using information theory, revealing a duality that varies with process steps and system criticality.

Contribution

It introduces an information-theoretical framework linking predictability and reconstructability, demonstrating their dual behavior and universality across different complex systems.

Findings

Predictability and reconstructability are interconnected but can behave differently.

Duality between predictability and reconstructability emerges with process step changes.

Numerical evidence shows dualities near critical points in various systems.

Abstract

Predicting the evolution of a large system of units using its structure of interaction is a fundamental problem in complex system theory. And so is the problem of reconstructing the structure of interaction from temporal observations. Here, we find an intricate relationship between predictability and reconstructability using an information-theoretical point of view. We use the mutual information between a random graph and a stochastic process evolving on this random graph to quantify their codependence. Then, we show how the uncertainty coefficients, which are intimately related to that mutual information, quantify our ability to reconstruct a graph from an observed time series, and our ability to predict the evolution of a process from the structure of its interactions. Interestingly, we find that predictability and reconstructability, even though closely connected by the mutual information, can behave differently, even in a dual manner. We prove how such duality universally emerges when changing the number of steps in the process, and provide numerical evidence of other dualities occurring near the criticality of multiple different processes evolving on different types of structures.