The Value of Information in Multi-Scale Feedback Systems
Louisa Jane Di Felice, Ada Diaconescu, Payam Zahadat, Patricia Mellodge
TL;DR
This work develops an informational framework for multi-scale feedback in Complex Adaptive Systems, distinguishing syntactic, semantic, and pragmatic information to quantify how information flows across micro-, meso-, and macro-scales drive adaptation. It formalizes measures including $C_{syn}$, $C_{sm}$, $ riangle_{sm}$, $V_{sm,th}$, $V_{sm,gl}$, $ riangle_{pr}$, and $V_{pr,gl}$, and applies them to four case studies (Robotic Collective, Collective Decision-Making, Task Distribution, Hierarchical Oscillators) to illustrate how information value depends on context, delays, and abstraction. Across the cases, coarse-graining can reduce processing demands but alter the utility of information, with memory and estimation accuracy shaping semantic and pragmatic outcomes; delays can both help and hinder performance depending on system dynamics. The results illuminate an informational theory of CAS, offering guidelines for measuring and tuning information flows to improve reactivity, stability, and scalability in multi-scale adaptive systems.
Abstract
Complex adaptive systems (CAS) can be described as systems of information flows dynamically interacting across scales in order to adapt and survive. CAS often consist of many components that work towards a shared goal, and interact across different informational scales through feedback loops, leading to their adaptation. In this context, understanding how information is transmitted among system components and across scales becomes crucial for understanding the behavior of CAS. Shannon entropy, a measure of syntactic information, is often used to quantify the size and rarity of messages transmitted between objects and observers, but it does not measure the value that information has for each specific observer. For this, semantic and pragmatic information have been conceptualized as describing the influence on an observer's knowledge and actions. Building on this distinction, we describe the architecture of multi-scale information flows in CAS through the concept of Multi-Scale Feedback Systems, and propose a series of syntactic, semantic and pragmatic information measures to quantify the value of information flows. While the measurement of values is necessarily context-dependent, we provide general guidelines on how to calculate semantic and pragmatic measures, and concrete examples of their calculation through four case studies: a robotic collective model, a collective decision-making model, a task distribution model, and a hierarchical oscillator model. Our results contribute to an informational theory of complexity, aiming to better understand the role played by information in the behavior of Multi-Scale Feedback Systems.