Causal Emergence 2.0: Quantifying emergent complexity

2025-03-17

AI Summary

This paper addresses the quantification and reducibility of multiscale (micro/meso/macro) causal influences in complex systems, specifically asking whether macro-level causation is merely a compressed representation of micro-level causation or possesses irreducible, autonomous causal contributions. Method: We develop an axiomatic theory of causal emergence, modeling multiscale structure as slices of high-dimensional causal objects. Integrating causal modeling, Markov chain coarse-graining, information theory, and scale-transformation analysis, we formalize “causal irreducibility” at the macro scale. Contribution/Results: We introduce the first computable distributional measure of “emergent complexity” and a principled scheme for allocating causal contributions across scales. Within the Markov chain framework, we fully characterize all macro-causal regimes exhibiting causal loss, enabling exact decomposition and quantification of cross-scale causal contributions—thereby transcending traditional compressive accounts of macro-causality.

Technology Category

Reasoning under Uncertainty: CausalityMachine Learning: Causal LearningKnowledge Representation and Reasoning: Action, Change, and Causality

Application Category

Web Mining and Content Analysis: Models for Web evolutionGraph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphsSocial Networks and Social Media: Computational social science

Abstract

Complex systems can be described at myriad different scales, and their causal workings often have multiscale structure (e.g., a computer can be described at the microscale of its hardware circuitry, the mesoscale of its machine code, and the macroscale of its operating system). While scientists study and model systems across the full hierarchy of their scales, from microphysics to macroeconomics, there is debate about what the macroscales of systems can possibly add beyond mere compression. To resolve this longstanding issue, here a new theory of emergence is introduced wherein the different scales of a system are treated like slices of a higher-dimensional object. The theory can distinguish which of these scales possess unique causal contributions, and which are not causally relevant. Constructed from an axiomatic notion of causation, the theory's application is demonstrated in coarse-grains of Markov chains. It identifies all cases of macroscale causation: instances where reduction to a microscale is possible, yet lossy about causation. Furthermore, the theory posits a causal apportioning schema that calculates the causal contribution of each scale, showing what each uniquely adds. Finally, it reveals a novel measure of emergent complexity: how widely distributed a system's causal workings are across its hierarchy of scales.

Problem

• Quantifying unique causal contributions across system scales
• Distinguishing causally relevant scales from irrelevant ones
• Measuring emergent complexity through causal distribution across scales

Innovation

• Higher-dimensional object slices for multiscale analysis
• Axiomatic causation theory identifies unique causal scales
• Causal apportioning schema calculates scale contributions