Evolving Neural Networks Reveal Emergent Collective Behavior from Minimal Agent Interactions

Emergent collective behaviors, such as flocking and swarming, arise from simple interactions in multi-agent systems, yet their underlying mechanisms remain poorly understood. Here, we evolve shallow neural networks to govern agent movements in a simulated environment, revealing how network non-linearity drives the complexity of collective dynamics. Using multilinear regression and network visualization, we show that linear neural operations underpin simple patterns like lane formation. At the same time, non-linear processing enables intricate behaviors like flocking. We identify key environmental drivers---moderate noise, wider fields of view, and lower agent densities---that foster non-linear networks and richer dynamics. These findings, derived from a minimalistic evolutionary model based on proximity, offer a blueprint for tuning autonomous swarms and deepen our understanding of neural control in self-organizing systems, with applications in swarm robotics and beyond.