Neural Information Squeezer for Causal Emergence

An Exact Theory of Causal Emergence for Linear Stochastic Iteration Systems

After coarse-graining a complex system, the dynamics of its macro-state may exhibit more pronounced causal effects than those of its micro-state. This phenomenon, known as causal emergence, is quantified by the indicator of effective information. However, two challenges confront this theory: the absence of well-developed frameworks in continuous stochastic dynamical systems and the reliance on coarse-graining methodologies. In this study, we introduce an exact theoretic framework for causal emergence within linear stochastic iteration systems featuring continuous state spaces and Gaussian noise. Building upon this foundation, we derive an analytical expression for effective information across general dynamics and identify optimal linear coarse-graining strategies that maximize the degree of causal emergence when the dimension averaged uncertainty eliminated by coarse-graining has an upper bound. Our investigation reveals that the maximal causal emergence and the optimal coarse-graining methods are primarily determined by the principal eigenvalues and eigenvectors of the dynamic system's parameter matrix, with the latter not being unique. To validate our propositions, we apply our analytical models to three simplified physical systems, comparing the outcomes with numerical simulations, and consistently achieve congruent results.

Emergence and Causality in Complex Systems: A Survey of 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 (CE) 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 CE. It focuses on two primary challenges: quantifying CE and identifying it from data. The latter task requires the integration of machine learning and neural network techniques, establishing a significant link between causal emergence and machine learning. We highlight two problem categories: CE with machine learning and CE for machine learning, both of which emphasize the crucial role of effective information (EI) as a measure of causal emergence. The final section of this review explores potential applications and provides insights into future perspectives.

Correction: Zhang, J.; Liu, K. Neural Information Squeezer for Causal Emergence. Entropy 2023, 25, 26

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Is information the other face of causation in biological systems?

Is information the other face of causation? This issue cannot be clarified without discussing how these both are related to physical laws, logic, computation, networks, bio-signaling, and the mind-body problem. The relation between information and causation is also intrinsically linked to many other concepts in complex systems theory such as emergence, self-organization, synergy, criticality, and hierarchy, which in turn involve various notions such as observer-dependence, dimensionality reduction, and especially downward causation. A canonical example proposed for downward causation is the collective behavior of the whole system at a macroscale that may affect the behavior of each its member at a microscale. In neuroscience, downward causation is suggested as a strong candidate to account for mental causation (free will). However, this would be possible only on the condition that information might have causal power. After introducing the Causal Equivalence Principle expanding the relativity principle for coarse-grained and fine-grained linear causal chains, and a set-theoretical definition of multiscale nested hierarchy composed of modular ⊂-chains, it is shown that downward causation can be spurious. It emerges only in the eyes of an observer, though, due to information that could not be obtained by "looking" exclusively at the behavior of a system at a microscale. On the other hand, since biological systems are hierarchically organized, this information gain is indicative of how information can be a function of scale in these systems and a prerequisite for scale-dependent emergence of cognition and consciousness in neural networks.