Evolving Neural Networks Reveal Emergent Collective Behavior from Minimal Agent Interactions

TL;DR

This study investigates how neural networks evolve to control agents' behavior in a dynamic environment, focusing on the relationship between the network's complexity and collective behavior patterns, and demonstrates that the degree of network non-linearity correlates with the complexity of emergent behaviors.

Abstract

Understanding the mechanisms behind emergent behaviors in multi-agent systems is critical for advancing fields such as swarm robotics and artificial intelligence. In this study, we investigate how neural networks evolve to control agents' behavior in a dynamic environment, focusing on the relationship between the network's complexity and collective behavior patterns. By performing quantitative and qualitative analyses, we demonstrate that the degree of network non-linearity correlates with the complexity of emergent behaviors. Simpler behaviors, such as lane formation and laminar flow, are characterized by more linear network operations, while complex behaviors like swarming and flocking show highly non-linear neural processing. Moreover, specific environmental parameters, such as moderate noise, broader field of view, and lower agent density, promote the evolution of non-linear networks that drive richer, more intricate collective behaviors. These results highlight the importance of tuning evolutionary conditions to induce desired behaviors in multi-agent systems, offering new pathways for optimizing coordination in autonomous swarms. Our findings contribute to a deeper understanding of how neural mechanisms influence collective dynamics, with implications for the design of intelligent, self-organizing systems.

Figures (9)

• Figure 1: Simplified diagrammatic representation of interacting agents with 3 nearest neighbors. In the diagram, the number of nearest neighbors has been defined as $k=3$ for simplicity. The variables $\mathbf{x}_{i}$ and $\theta_{i}$ are respectively agent $i$'s position and orientation, the pink sector of a circle represents its field of view. The variables $\mathbf{y}_{j}$ are the positions of neighboring agents inside agent $i$'s field of view, and the blue region denotes its neural network, with inputs $\mathbf{v} = [\mathbf{x}-\mathbf{y}_{i}]^{3}_{i=1}$, a weight matrix $\mathbf{W}$ with bias vector $\mathbf{b}$ whose result passes through an activation function $tanh$ and is fed into an output layer with a weight vector $\mathbf{u}$ and activation value $c$.
• Figure 2: Average fitness ($\langle\varphi(t)\rangle$) and average shared fitness ($\langle\varphi_{sh}(r)\rangle$) as a function of training steps.
• Figure 3: Migration regimes for different configurations of maximum turning angle, rotational noise, and field of vision.
• Figure 4: Different patterns obtained by exploring the parameter space: a) single flowing lane, b) multiple flowing lanes, c) stationary lanes, d) segments, e) crowded flocks, f) sparse flocks, g) bands, h) fronts, i) laminar flow, j) flowing swarm, k) stationary swarm, l) disordered. Arrows represent the overall flow direction.
• Figure 5: Probability density of the spectral gap time distribution of the connectivity graphs. Different colors represent distinct emergent patterns, and the red lines indicate the mean of each distribution.