Pairwise is Not Enough: Hypergraph Neural Networks for Multi-Agent Pathfinding

Abstract: Multi-Agent Path Finding (MAPF) is a representative multi-agent coordination problem, where multiple agents are required to navigate to their respective goals without collisions. Solving MAPF optimally is known to be NP-hard, leading to the adoption of learning-based approaches to alleviate the online computational burden. Prevailing approaches, such as Graph Neural Networks (GNNs), are typically constrained to pairwise message passing between agents. However, this limitation leads to suboptimal behaviours and critical issues, such as attention dilution, particularly in dense environments where group (i.e. beyond just two agents) coordination is most critical. Despite the importance of such higher-order interactions, existing approaches have not been able to fully explore them. To address this representational bottleneck, we introduce HMAGAT (Hypergraph Multi-Agent Attention Network), a novel architecture that leverages attentional mechanisms over directed hypergraphs to explicitly capture group dynamics. Empirically, HMAGAT establishes a new state-of-the-art among learning-based MAPF solvers: e.g., despite having just 1M parameters and being trained on 100$\times$ less data, it outperforms the current SoTA 85M parameter model. Through detailed analysis of HMAGAT's attention values, we demonstrate how hypergraph representations mitigate the attention dilution inherent in GNNs and capture complex interactions where pairwise methods fail. Our results illustrate that appropriate inductive biases are often more critical than the training data size or sheer parameter count for multi-agent problems.

• The paper introduces HMAGAT, a hypergraph-based neural network that models higher-order group interactions to overcome the limitations of pairwise approaches in MAPF.
• It integrates a CNN encoder, hypergraph attention layers, and an MLP decoder to achieve robust performance and high success rates in dense multi-agent environments.
• Empirical evaluations show HMAGAT's superior scalability and efficiency, using only 1M parameters and specialized hypergraph construction to mitigate attention dilution.

Hypergraph Neural Networks for Multi-Agent Pathfinding: Moving Beyond Pairwise Interactions

Motivation and Problem Formulation

Multi-Agent Path Finding (MAPF) is a prototypical challenge in multi-agent systems where multiple agents must coordinate to reach distinct goals without collisions. MAPF's complexity is primarily due to its NP-hardness and the high degree of coupling among agents, which impedes optimal solutions even in sparse environments. Prevailing learning-based approaches, notably Graph Neural Networks (GNNs) and transformer-based policies, largely restrict interaction modeling to pairwise relations. While adequate for low-density scenarios, these methods break down in dense environments or large team settings due to attention dilution and inability to explicitly capture group dynamics, undermining both solution quality and task success rates.

This paper argues that group-level coordination is fundamental in MAPF and posits that higher-order interaction modeling via hypergraphs can bridge this gap. Hypergraphs, as a generalization of graphs, permit modeling interactions among arbitrary-sized subsets of agents, enabling richer representations aligned with the combinatorial nature of optimal MAPF solutions.

HMAGAT: Architecture and Methodology

The proposed HMAGAT (Hypergraph Multi-Agent Attention Network) is an imitation learning-based policy for MAPF built on hypergraph neural network (HGNN) layers. The model architecture is a pipeline consisting of a CNN encoder for agent observations, stacked HGNN layers facilitating group-based message passing, and an MLP decoder for action selection. Directed hypergraphs are used where each hyperedge has a singleton head (the agent under decision) and a multi-agent tail, dynamically constructed based on spatial clustering via K-means or Lloyd’s algorithm, or shortest distance heuristics.

Attention is computed over hyperedges rather than over pairwise links, mitigating the adverse effects of attention score normalization that cause dilution in GNN-based models, especially when the neighborhood contains many irrelevant agents. Empirical attention analysis indicates that HMAGAT preserves high scores for relevant agent groups, thereby maintaining robust and meaningful dynamic coupling.

Temperature sampling is incorporated to calibrate action confidence, using a lightweight RL-trained module that dynamically modulates softmax temperature based on local observability. HMAGAT's pipeline also features expert trajectory aggregation and post-training refinement to improve solution quality and address distributional shift inherent in IL settings.

Empirical Evaluation and Results

HMAGAT is evaluated against multiple state-of-the-art MAPF solvers including MAGAT (GNN-based), MAPF-GPT/transformer variants, and other recent IL and RL policies. The assessment spans sparse and dense maps, small and large grid sizes, and varying agent densities. Metrics include success rate (all agents reach goals), solution quality (sum-of-costs relative to a strong search-based oracle, lacam3), and computational efficiency.

HMAGAT with k-means hypergraph construction consistently outperforms MAGAT and all smaller transformer variants, maintaining competitive or superior performance to the largest MAPF-GPT (85M parameters) model, despite using only 1M parameters and 100× less training data. Specifically, HMAGAT achieves higher solution quality in maze-like maps, and dramatically higher success rates under high agent density in dense warehouse settings (e.g., 75.8% vs. 2.3% for GNNs). HMAGAT also demonstrates superior scalability, maintaining high solution robustness on large-scale maps where transformer models fail to scale.

Ablation studies isolate the contributions of hypergraph modeling, expert online aggregation, post-training, and temperature calibration, confirming additive improvements in performance and demonstrating that group interaction modeling is indispensable in highly coupled environments.

Attention Dilution and Group Interaction Analysis

Quantitative and qualitative analyses substantiate the theoretical claims regarding attention dilution. Entropy and coefficient of variation measures show that attention scores in GNNs become increasingly uniform (diluted) as more agents populate irrelevant regions, severely weakening informative message propagation. In contrast, HGNN-based architectures (HMAGAT) remain robust, keeping attention concentrated on relevant agent subsets, unaffected by the presence of additional noisy agents. Shapley value analysis further demonstrates HMAGAT's ability to appropriately rank agent contributions based on group dynamics, a feat unachievable by GNNs with pairwise-only modeling.

Hand-crafted scenarios illustrate critical failure modes of GNNs, including intractable deadlocks and livelocks under high density, and reinforce the necessity of explicit group-level interaction modeling for optimal MAPF policies.

Practical Implications and Theoretical Advancements

The study's primary implication is that inductive bias alignment with the underlying joint action space of MAPF is more influential than increased parameter count or training data size for learning-based solvers. HMAGAT’s compactness and data efficiency directly translate to practical advantages in settings with limited computational resources, data availability, or strict real-time requirements. The hypergraph approach enables straightforward scaling, generalizing well to large maps and diverse agent densities.

Theoretically, explicit group interaction modeling via HGNNs advances the modeling toolkit for multi-agent systems, suggesting that pairwise abstraction is fundamentally insufficient for tasks with strong collective coupling. These insights extend to domains beyond MAPF, including multi-robot coordination, warehouse automation, traffic management, and formation control.

Future Directions

The results motivate further exploration of hypergraph-based architectures for other highly coupled multi-agent tasks, including cooperative decision-making, collective navigation in dynamic or adversarial environments, and decentralized planning under partial observability. Improvements in hypergraph construction—possibly leveraging adaptive clustering or hierarchical group representations—could further enhance robustness and scalability. Additionally, integrating deadlock/livelock detection mechanisms and adaptive action sampling could address residual failure modes and refine solution rates.

Conclusion

This paper establishes that pairwise interaction modeling is insufficient for MAPF and multi-agent coordination under high coupling. The HMAGAT model, leveraging hypergraph neural networks, achieves state-of-the-art results at a fraction of the computational and data cost of transformer-based policies. Explicit group-based attention modeling over hypergraphs enables improved inductive bias alignment, counteracts attention dilution, and scales efficiently to large and dense environments. These findings advocate hypergraph-centric paradigms as a fundamental advancement in learning-based multi-agent systems and lay the groundwork for further investigation into higher-order relational modeling in AI.