A novel practical measure called Φ* quantifies integrated information in the brain, a property predicted by Integrated Information Theory (IIT) to reflect levels of consciousness. Earlier measures failed to satisfy theoretical lower and upper bounds: zero when no information is generated or when parts are independent, and the total information generated by the whole system. By applying mismatched decoding from information theory, Φ* meets these bounds. Under a Gaussian assumption, Φ* has an analytical expression applicable to experimental neural data. Φ* can serve as a measure of integrated information in consciousness research and as a tool for network analysis in biology.
A unified theoretical framework based on information geometry is proposed for quantifying spatio-temporal interactions in stochastic dynamical systems. The degree of interaction is measured by the divergence between the actual probability distribution and a constrained distribution where the interactions of interest are removed. This approach provides novel geometric interpretations of mutual information, transfer entropy, and stochastic interaction, clarifying their relationships. Extending transfer entropy, the authors introduce a new measure of integrated information that quantifies causal interactions between parts of a system, capturing the extent to which the whole exceeds the sum of its parts. This measure is suggested as a potential biological indicator of consciousness levels.
Integrated Information Theory (IIT) proposes that a brain's capacity to integrate information is essential for consciousness and that a measure called integrated information, Φ, should reflect levels of consciousness. Practical application has been hindered because existing measures fail to satisfy theoretical lower and upper bounds: zero when the system generates no information or consists of independent parts, and equal to the whole system's information when its parts generate no information independently. The authors derive a new practical measure, Φ*, using mismatched decoding from information theory. This measure satisfies the required bounds. They also provide an analytical expression for Φ* under a Gaussian assumption, making it applicable to experimental neural data.