SIGMAS: Second-Order Interaction-based Grouping for Overlapping Multi-Agent Swarms

TL;DR

This work introduces the novel task of group prediction in overlapping multi-agent swarms, where latent group structures must be inferred directly from agent trajectories without ground-truth supervision, and proposes SIGMAS (Second-order Interaction-based Grouping for Multi-Agent Swarms), a self-supervised framework that goes beyond direct pairwise interactions and model second-order interaction across agents.

Abstract

Swarming systems, such as drone fleets and robotic teams, exhibit complex dynamics driven by both individual behaviors and emergent group-level interactions. Unlike traditional multi-agent domains such as pedestrian crowds or traffic systems, swarms typically consist of a few large groups with inherent and persistent memberships, making group identification essential for understanding fine-grained behavior. We introduce the novel task of group prediction in overlapping multi-agent swarms, where latent group structures must be inferred directly from agent trajectories without ground-truth supervision. To address this challenge, we propose SIGMAS (Second-order Interaction-based Grouping for Multi-Agent Swarms), a self-supervised framework that goes beyond direct pairwise interactions and model second-order interaction across agents. By capturing how similarly agents interact with others, SIGMAS enables robust group inference and adaptively balances individual and collective dynamics through a learnable gating mechanism for joint reasoning. Experiments across diverse synthetic swarm scenarios demonstrate that SIGMAS accurately recovers latent group structures and remains robust under simultaneously overlapping swarm dynamics, establishing both a new benchmark task and a principled modeling framework for swarm understanding.

Figures (9)

• Figure 1: (a) Overlapping swarms with distinct coordination patterns, making group identification difficult based on proximity alone. (b) First-order interactions capture direct motion correlations between agents. (c) Second-order interactions compare agents’ first-order attention patterns to measure how similarly they interact with others. This captures social behavior similarity and enables robust group identification, even in the absence of direct interactions.
• Figure 2: Illustration of emergent swarm behaviors. Top: Intra-swarm convergence, where agents within the same swarm gradually align and form cohesive clusters. Bottom: Inter-swarm overlap, where distinct swarms simultaneously share spatial regions while maintaining separate coordination dynamics.
• Figure 3: SIGMAS architecture. Agent-level and swarm-level features are extracted via separate encoders, and fused using balancing and gating to form swarm-aware embeddings for trajectory prediction and group inference.
• Figure 4: Overview of second-order interaction modeling in the Swarm-Level Encoder. (a) First-order interactions encode directional influence between agents. (b) Second-order interactions compare first-order attention patterns across agents, revealing social behavior similarity. The resulting matrix highlights agents with similar interaction profiles, enabling group identification via clustering. In the attention matrix, rows correspond to attending agents and columns to agents being attended to. Darker cells indicate stronger outgoing attention.
• Figure 5: SIGMAS-based CVAE prediction framework. Dotted paths are used during training only.