Higher-Order Interactions: Understanding the knowledge capacity of social groups using simplicial sets

A predominant benefit of social living is the ability to share knowledge that cannot be gained through the information an individual accumulates based on its personal experience alone. Traditional computational models have portrayed sharing knowledge through interactions among members of social groups via dyadic networks. Such models aim at understanding the percolation of information among individuals and groups to identify potential limitations to successful knowledge transfer. However, because many real-world interactions are not solely pairwise, i.e., several group members may obtain information from one another simultaneously, it is necessary to understand more than dyadic communication and learning processes to capture their full complexity. We detail a modeling framework based on the simplicial set, a concept from algebraic topology, which allows elegant encapsulation of multi-agent interactions. Such a model system allows us to analyze how individual information within groups accumulates as the group's collective set of knowledge, which may be different than the simple union of individually contained information. Furthermore, the simplicial modeling approach we propose allows us to investigate how information accumulates via sub-group interactions, offering insight into complex aspects of multi-way communication systems. The fundamental change in modeling strategy we offer here allows us to move from portraying knowledge as a “token”, passed from signaler to receiver, to portraying knowledge as a set of accumulating building blocks from which novel ideas can emerge. We provide an explanation of relevant mathematical concepts in a way that promotes accessibility to a general audience [Current Zoology 61 (1): 114–127, 2015].