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

Minah Lee; Saibal Mukhopadhyay

cs.MAFeb 23, 2026

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

Authors: Minah Lee, Saibal Mukhopadhyay

Organizations: The University of Texas at Dallas, Richardson, TX, USA · Georgia Institute of Technology, Atlanta, GA, USA

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 & tables

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.

Models	Method	Traj.	Inter.	Group	Group
		Pred.	Type	Modeling	Inference
SocialGAN [ 15 ]	LSTM	✓	1st	✗	✗
Trajectron++ [ 16 ]	LSTM	✓	1st	✗	✗
AgentFormer [ 17 ]	Transformer	✓	1st	✗	✗
Leapfrog [ 18 ]	Diffusion	✓	1st	✗	✗
GroupNet [ 19 ]	GNN	✓	1st	$\triangle$	✗

Table 1: Comparison of key capabilities for group prediction in overlapping multi-agent swarms. ’Traj. Pred.’ denotes trajectory prediction and ’Inter. Type’ refers to the modeled interaction type.

\triangle

indicates that group modeling is used internally in the latent space to support trajectory prediction, but is not evaluated as a standalone group prediction objective.

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.

Figure 6: Comparison of first-order and second-order attention for group inference. (a) Agent trajectories show two overlapping swarms. (b) Agent-level attention $\mathbf{A}^{(1)}$ reflects direct interaction relevance for trajectory prediction. (c) Swarm-level attention $\mathbf{A}^{(2)}$ captures second-order interaction similarity across agents, enabling accurate latent group discovery via spectral clustering.

Swarm Config	Cohesion	Separation	Alignment	Speed
Swarm A	[0.005, 0.007]	[0.1, 0.2]	[0.3, 0.1]	[1.0, 1.2]
Swarm B	[0.005, 0.010]	[0.1, 0.3]	[0.1, 0.3]	[1.0, 1.3]
Swarm C	[0.005, 0.010]	[0.1, 0.4]	[0.1, 0.3]	[1.0, 1.5]

Table 2: Swarm configurations for different scenarios.

Figure 7: Adaptive balancing factor $\alpha$ over time in response to swarm dynamics. The model increases $\alpha$ during inter-swarm overlap and decreases it when individual motion cues are more predictive. $\alpha=0$ corresponds to relying solely on agent-level trajectory embeddings, while $\alpha=1$ reflects full reliance on swarm-level embeddings.

	AgentFormer [ 17 ]	SIGMAS_IG	SIGMAS
ARI $\uparrow$	0.3155	0.3306	0.4045
NMI $\uparrow$	0.3739	0.3860	0.4086
F-score $\uparrow$	0.6863	0.6887	0.6968

Table 3: Comparison of group prediction performance across baselines.

Figure 8: Qualitative results of group prediction. Red dotted ellipses indicate incorrect group assignments. Group labels are permutation-invariant, so different colors indicate distinct predicted clusters. Results videos are in Supplementary.

Figure 9: Group prediction performance across three heterogeneous swarm configurations ( Swarm A, B, C ) with increasing intra-swarm disparity. Shaded regions indicate standard deviation across multiple runs. Results videos are in Supplementary.

Multi-Agent Systems

Multi-Agent Systems studies how autonomous agents coordinate, compete, communicate, and learn in shared or interdependent tasks.

See all 675 papers

Socialality Anchors: Towards Group-bounded Trajectory Prediction
Sep 29, 2026Ziqian Zou, Conghao Wong, Qinmu Peng +1Pedestrian Trajectory Prediction Multi-Agent Trajectory Prediction
Huazhong University of Science and Technology, Wuhan, 430074, Hubei, China.
Learning Self-Orchestration in Decentralized Agent Swarms
Oct 15, 2026Guowei Xu, Zhenting Qi, Amani Kiruga +2Multi-Agent Orchestration Multi-Agent Coordination
Harvard University
Waggle: Learning One Anonymous Local Law for Self-Organizing LLM Swarms
Sep 28, 2026Mingxi Zou, Wei Zhu, Zhuo Wang +4Multi-Agent LLM Systems Multi-Agent Coordination
Shanghai Academy of AI for Science (SAIS) · AI3 Institute, Fudan University · Yunnan University

Sep 29, 2026J/K move · Enter open · S save

Socialality Anchors: Towards Group-bounded Trajectory Prediction

Ziqian Zou, Conghao Wong, Qinmu Peng, Xinge You

Huazhong University of Science and Technology, Wuhan, 430074, Hubei, China.

Pedestrian Trajectory Prediction Multi-Agent Trajectory Prediction

Open paper AskPDF arXiv

Trajectory prediction is a key component for understanding human behavior patterns in dynamic scenes. Researchers have devoted substantial efforts to modeling social interactions, especially group-wise interactions, since group membership often reflects shared intention, coordinated motion, and stable mutual adaptation, thus providing a persistent and semantically meaningful social prior for forecasting. However, existing group modeling methods may rely on a fixed threshold and infer groups mainly from agents' relative positions within the observation window, overlooking the fact that grouping rules should be agent-specific, temporally coherent, and context-adaptive across diverse personalities, culturalities, and evolving interaction contexts. Inspired by human social perception that alternates between interpersonal distance in boundary-sensitive situations and relative speed consistency in dynamic interactions, we propose Socialality, a human-inspired trajectory prediction framework with interpretable Socialality anchors and an extended grouping window for stable, context-aware grouping inference. Concretely, Socialality introduces a duo-scalar-controlled grouping kernel Socialality that jointly leverages historical observations and short-term future trajectory previews to learn agent-specific grouping rules, and employs a group-wise perception mechanism to model in-group and out-of-group interactions in an intuitive and explainable manner. Furthermore, we conduct extensive experiments on standard benchmarks to demonstrate the performance gains of Socialality, and provide qualitative analyses and statistical studies of anchor distributions to verify the interpretability and stability of the proposed Socialality anchors.

Abstract

Multi-Agent Systems

Explore similar work

Socialality Anchors: Towards Group-bounded Trajectory Prediction

Learning Self-Orchestration in Decentralized Agent Swarms

Waggle: Learning One Anonymous Local Law for Self-Organizing LLM Swarms