🤖 AI Summary
This study investigates how percolation phase transitions in network structure regulate information processing capabilities. Using the Erdős–Rényi random graph model, we integrate cascade dynamics with information-theoretic measures—including transfer entropy, output entropy, and functional complexity metrics—to systematically characterize the evolution of input–output functional space near the critical point. We introduce the novel concept of “functional percolation,” revealing that the emergence of the giant connected component coincides with synchronous, discontinuous increases in functional complexity, functional diversity, and directed information flow—establishing percolation criticality as a universal organizational principle for information processing in locally interacting systems. At the critical average degree, a Pareto-optimal trade-off between functional complexity and diversity is achieved; output entropy rises markedly, and transfer entropy extends beyond local neighborhoods, uncovering a fundamental mechanism whereby structural criticality induces qualitative enhancements in global information processing capacity.
📝 Abstract
Understanding the physical constraints and minimal conditions that enable information processing in extended systems remains a central challenge across disciplines, from neuroscience and artificial intelligence to social and physical networks. Here we study how network connectivity both limits and enables information processing by analyzing random networks across the structural percolation transition. Using cascade-mediated dynamics as a minimal and universal mechanism for propagating state-dependent responses, we examine structural, functional, and information-theoretic observables as functions of mean degree in Erdos-Renyi networks. We find that the emergence of a giant connected component coincides with a sharp transition in realizable information processing: complex input-output response functions become accessible, functional diversity increases rapidly, output entropy rises, and directed information flow quantified by transfer entropy extends beyond local neighborhoods. These coincident transitions define a regime of functional percolation, referring to a sharp expansion of the space of realizable input-output functions at the structural percolation transition. Near criticality, networks exhibit a Pareto-optimal tradeoff between functional complexity and diversity, suggesting that percolation criticality provides a universal organizing principle for information processing in systems with local interactions and propagating influences.