A general spectral decomposition of causal influences applied to integrated information

Abstract Quantifying causal influences between elements of a system remains a central topic in many fields of research. In neuroscience, causal influences among neurons, quantified as integrated information, have been suggested to play a critical role in supporting subjective conscious experience. Recent empirical work has shown that the spectral decomposition of causal influences can reveal frequency-specific influences that are not observed in the time-domain. To date however, a spectral decomposition of integrated information has not been put forward. In this paper, we propose a spectral decomposition of integrated information in linear autoregressive processes. Our proposal is based on a general and flexible framework for deriving the spectral decompositions of causal influences in autoregressive processes. We show that the framework can retrieve the spectral decompositions of other well-known measures such as Granger causality. In simulation, we demonstrate a complex interplay between the spectral decomposition of integrated information and other measures that is not observed in the time-domain. We propose that the spectral decomposition of integrated information will be particularly useful when the underlying frequency-specific causal influences are masked in the time-domain. The proposed method opens the door for empirically investigating the relevance of integrated information to subjective conscious experience in a frequency-specific manner. Author summaryUnderstanding how different parts of the brain influence each other is fundamental to neuroscience. Integrated information measures overall causal influences in the brain and has been theorized to directly relate to subjective consciousness experience. For example, integrated information is predicted to be high during wakefulness and low during sleep or general anesthesia. At the same time, neural activity is characterized by well-known spectral signatures. For example, there is a prominent increase in low frequency power of neural activity during sleep and general anesthesia. Taking account of the spectral characteristics of neural activity, it is important to separately quantify integrated information at each frequency. In this paper, we propose a method for decomposing integrated information in the frequency domain. The proposed framework is general and can be used to derive the spectral decomposition of other well-known measures such as Granger causality. The spectral decomposition of integrated information we propose will allow empirically investigating the relationship between neural spectral signatures, integrated information and subjective consciousness experience.