A Mathematical Framework for Understanding Biological Recognition Systems

Recognition plays a crucial role in the formation of social bonds, mate selection, kin selection and survival across species. However, a unifying framework for understanding recognition systems in biology is lacking. We, therefore, propose a theoretical framework for biological recognition utilizing basic principles from category theory, information theory, dynamical systems modeling and optimization theory. We define the two types of recognition, individual recognition (IR) and class-level recognition (CR), as functors between categories of stimuli and responses. IR produces unique responses for each individual, while CR produces shared responses for multiple individuals of the same class. We identify five conditions - universality, low entropy, unfalsifiability, uniform convergence and cognitive limit - that must hold for robust IR systems, which we term "signature systems." Further, we model signature systems as attractor states with perspectives from both statistical information processing and dynamical systems. Our framework provides a basis for advancing understanding of the mechanisms underlying biological recognition and its implications for communication and behavior. Overall, the mathematical conceptualization of IR provides a basis for advancing our understanding of communication and the evolution of language.