Phase Behavior of Leader–Follower Active Particle Systems Inspired by Contrastive Learning

A fundamental question in soft matter physics is how collective behavior emerges from interactions among many particles. Understanding such self-organization is not only central to active matter but also to modern machine learning, where data representations evolve through analogous interaction rules. Motivated by this connection, we introduce a minimal leader–follower active particle model to investigate how motion coupling reshapes the phase behavior of multicomponent, repulsively interacting systems. In our model, a small fraction of particles is randomly selected as "leaders" at each time step and evolve under short-range repulsive interactions. The remaining "followers" couple their motion to the leaders of the same type. By varying the leader selection scheme and coupling strength, we uncover a rich variety of dynamical regimes. The emergent phase-separated structures parallel those observed in contrastive learning, where data representations self-organize geometrically under repulsive constraints. This correspondence offers a unified perspective on machine learning and collective dynamics, illustrating how simple interaction rules can generate complex collective order.