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Pairwise interactions between individuals are taken as fundamental drivers ofcollective behavior responsible for group cohesion and decision-making. Whilean individual directly influences only a few neighbors, over time indirectinfluences penetrate a much larger group. The abiding question is how thisspread of influence comes to affect the collective. One or a few individualsare often identified as leaders, being more influential than others. Transferentropy and time-delayed mutual information are used to identify underlyingasymmetric interactions, such as leader-follower classification in aggregatedindividuals--cells, birds, fish, and animals. However, these conflate distinctfunctional modes of information flow between individuals. Computing informationmeasures conditioning on multiple agents requires the proper sampling of aprobability distribution whose dimension grows exponentially with the number ofagents being conditioned on. Employing simple models of interactingself-propelled particles, we examine the pitfalls of using time-delayed mutualinformation and transfer entropy to quantify the strength of influence from aleader to a follower. Surprisingly, one must be wary of these pitfalls even fortwo interacting particles. As an alternative we decompose transfer entropy andtime-delayed mutual information into intrinsic, shared, and synergistic modesof information flow. The result not only properly reveals the underlyingeffective interactions, but also facilitates a more detailed diagnosis of howindividual interactions lead to collective behavior. This exposes the role ofindividual and group memory in collective behaviors. In addition, wedemonstrate in a multi-agent system how knowledge of the decomposed informationmodes between a single pair of agents reveals the nature of many-bodyinteractions without conditioning on additional agents.

Modes of Information Flow in Collective Cohesion