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Information integration from distributed threshold-based interactions

We consider a collection of distributed units that interact with one another through the sending of messages. Each message carries a positive ($+1$) or negative ($-1$) tag and causes the receiving unit to send out messages as a function of the tags it has received and a threshold. This simple model abstracts some of the essential characteristics of several systems used in the field of artificial intelligence, and also of biological systems epitomized by the brain. We study the integration of information inside a temporal window as the model's dynamics unfolds. We quantify information integration by the total correlation, relative to the window's duration ($w$), of a set of random variables valued as a function of message arrival. Total correlation refers to the rise of information gain above and beyond that which the units already achieve individually, being therefore related to consciousness studies in some models. We report on extensive computational experiments that explore the interrelations of the model's parameters (two probabilities and the threshold), highlighting relevant scenarios of message traffic and how they impact the behavior of total correlation as a function of $w$. We find that total correlation can occur at significant fractions of the maximum possible value and provide semi-analytical results on the message-traffic characteristics associated with values of $w$ for which it peaks. We then reinterpret the model's parameters in terms of the current best estimates of some quantities pertaining to cortical structure and dynamics. We find the resulting possibilities for best values of $w$ to be well aligned with the time frames within which percepts are thought to be processed and eventually rendered conscious.

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