Emergence and Causality in Complex Systems: A Survey on Causal Emergence and Related Quantitative Studies

Emergence and causality are two fundamental concepts for understanding complex systems. They are interconnected. On one hand, emergence refers to the phenomenon where macroscopic properties cannot be solely attributed to the cause of individual properties. On the other hand, causality can exhibit emergence, meaning that new causal laws may arise as we increase the level of abstraction. Causal emergence theory aims to bridge these two concepts and even employs measures of causality to quantify emergence. This paper provides a comprehensive review of recent advancements in quantitative theories and applications of causal emergence. Two key problems are addressed: quantifying causal emergence and identifying it in data. Addressing the latter requires the use of machine learning techniques, thus establishing a connection between causal emergence and artificial intelligence. We highlighted that the architectures used for identifying causal emergence are shared by causal representation learning, causal model abstraction, and world model-based reinforcement learning. Consequently, progress in any of these areas can benefit the others. Potential applications and future perspectives are also discussed in the final section of the review.Comment: 57 pages, 17 figures, 1 tabl

A method for system of systems definition and modeling using patterns of collective behavior

The Department of Defense ship and aircraft acquisition process, with its capability-based assessments and fleet synthesis studies, relies heavily on the assumption that a functional decomposition of higher-level system of systems (SoS) capabilities into lower-level system and subsystem behaviors is both possible and practical. However, SoS typically exhibit “non-decomposable” behaviors (also known as emergent behaviors) for which no widely-accepted representation exists. The presence of unforeseen emergent behaviors, particularly undesirable ones, can make systems vulnerable to attacks, hacks, or other exploitation, or can cause delays in acquisition program schedules and cost overruns in order to mitigate them. The International Council on Systems Engineering has identified the development of methods for predicting and managing emergent behaviors as one of the top research priorities for the Systems Engineering profession. Therefore, this thesis develops a method for rendering quantifiable SoS emergent properties and behaviors traceable to patterns of interaction of their constitutive systems, so that exploitable patterns identified during the early stages of design can be accounted for. This method is designed to fill two gaps in the literature. First, the lack of an approach for mining data to derive a model (i.e. an equation) of the non-decomposable behavior. Second, the lack of an approach for qualitatively and quantitatively associating emergent behaviors with the components that cause the behavior. A definition for emergent behavior is synthesized from the literature, as well as necessary conditions for its identification. An ontology of emergence that enables studying the emergent behaviors exhibited by self-organized systems via numerical simulations is adapted for this thesis in order to develop the mathematical approach needed to satisfy the research objective. Within the confines of two carefully qualified assumptions (that the model is valid, and that the model is efficient), it is argued that simulated emergence is bona-fide emergence, and that simulations can be used for experimentation without sacrificing rigor. This thesis then puts forward three hypotheses: The first hypothesis is that self-organized structures imply the presence of a form of data compression, and this compression can be used to explicitly calculate an upper bound on the number of emergent behaviors that a system can possess. The second hypothesis is that the set of numerical criteria for detecting emergent behavior derived in this research constitutes sufficient conditions for identifying weak and functional emergent behaviors. The third hypothesis states that affecting the emergent properties of these systems will have a bigger impact on the system’s performance than affecting any single component of that system. Using the method developed in this thesis, exploitable properties are identified and component behaviors are modified to attempt the exploit. Changes in performance are evaluated using problem-specific measures of merit. The experiments find that Hypothesis 2 is false (the numerical criteria are not sufficient conditions) by identifying instances where the numerical criteria produce a false-positive. As a result, a set of sufficient conditions for emergent behavior identification remains to be found. Hypothesis 1 was also falsified based on a worst-case scenario where the largest possible number of obtainable emergent behaviors was compared against the upper bound computed from the smallest possible data compression of a self-organized system. Hypothesis 3, on the other hand, was supported, as it was found that new behavior rules based on component-level properties provided less improvement to performance against an adversary than rules based on system-level properties. Overall, the method is shown to be an effective, systematic approach to non-decomposable behavior exploitation, and an improvement over the modern, largely ad hoc approach.Ph.D

Formalization of weak emergence in multiagent systems

Emergence becomes a distinguishing system feature as system complexity grows with the number of components, interactions, and connectivities. Examples of emergent behaviors include the flocking of birds, traffic jams, and hubs in social networks, among others. Despite significant research interest in recent years, there is a lack of formal methods to understand, identify, and predict emergent behavior in multiagent systems. Existing approaches either require detailed prior knowledge about emergent behavior or are computationally infeasible. This article introduces a grammar-based approach to formalize and identify the existence and extent of emergence without the need for prior knowledge of emergent properties. Our approach is based on weak (basic) emergence that is both generated and autonomous from the underlying agents. We employ formal grammars to capture agent interactions in the forms of words written on a common tape. Our formalism captures agents of diverse types and open systems. We propose an automated approach for the identification of emergent behavior and show its benefits through theoretical and experimental analysis. We also propose a significant reduction of state-space explosion through the use of our proposed degree of interaction metrics. Our experiments using the boids model show the feasibility of our approach but also highlight future avenues of improvement.Claudia Szabo, Yong Meng Te