# SIGMA: Sheaf-Informed Geometric Multi-Agent Pathfinding

arXiv: https://arxiv.org/abs/2502.06440 · HTML: https://mlsanity.com/paper/2502.06440/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 35 references that are in the map.
- First posted on arXiv 10 Feb 2025.

## Builds on (most cited first, 19 of 19)

- [Neural Sheaf Diffusion: A Topological Perspective on Heterophily and Oversmoothing in GNNs](https://mlsanity.com/paper/2202.04579/) (2022)
- [PRIMAL: Pathfinding via Reinforcement and Imitation Multi-Agent Learning](https://mlsanity.com/paper/1809.03531/) (2018)
- [Sheaf Neural Networks](https://mlsanity.com/paper/2012.06333/) (2020)
- [Lifelong Multi-Agent Path Finding in Large-Scale Warehouses](https://mlsanity.com/paper/2005.07371/) (2020)
- [PRIMAL2: Pathfinding via Reinforcement and Imitation Multi-Agent Learning -- Lifelong](https://mlsanity.com/paper/2010.08184/) (2020)
- [Message-Aware Graph Attention Networks for Large-Scale Multi-Robot Path Planning](https://mlsanity.com/paper/2011.13219/) (2020)
- [Mobile Robot Path Planning in Dynamic Environments through Globally Guided Reinforcement Learning](https://mlsanity.com/paper/2005.05420/) (2020)
- [SCRIMP: Scalable Communication for Reinforcement- and Imitation-Learning-Based Multi-Agent Pathfinding](https://mlsanity.com/paper/2303.00605/) (2023)
- [Distributed Heuristic Multi-Agent Path Finding with Communication](https://mlsanity.com/paper/2106.11365/) (2021)
- [Learning Selective Communication for Multi-Agent Path Finding](https://mlsanity.com/paper/2109.05413/) (2021)
- [MAPPER: Multi-Agent Path Planning with Evolutionary Reinforcement Learning in Mixed Dynamic Environments](https://mlsanity.com/paper/2007.15724/) (2020)
- [Multi-Agent Path Finding with Prioritized Communication Learning](https://mlsanity.com/paper/2202.03634/) (2022)
- [Hierarchical Consensus-Based Multi-Agent Reinforcement Learning for Multi-Robot Cooperation Tasks](https://mlsanity.com/paper/2407.08164/) (2024)
- [Leveraging Partial Symmetry for Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2401.00167/) (2023)
- [Topological Signal Processing over Generalized Cell Complexes](https://mlsanity.com/paper/2201.08993/) (2022)
- [ESP: Exploiting Symmetry Prior for Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2307.16186/) (2023)
- [GraphRARE: Reinforcement Learning Enhanced Graph Neural Network with Relative Entropy](https://mlsanity.com/paper/2312.09708/) (2023)
- [ALPHA: Attention-based Long-horizon Pathfinding in Highly-structured Areas](https://mlsanity.com/paper/2310.08350/) (2023)
- [CLGT: A Graph Transformer for Student Performance Prediction in Collaborative Learning](https://mlsanity.com/paper/2308.02038/) (2023)

## Built on by (most cited first, 4 of 4)

- [Latent Theory of Mind: A Decentralized Diffusion Architecture for Cooperative Manipulation](https://mlsanity.com/paper/2505.09144/) (2025)
- [Can a Robot Walk the Robotic Dog: Triple-Zero Collaborative Navigation for Heterogeneous Multi-Agent Systems](https://mlsanity.com/paper/2603.21723/) (2026)
- [Symmetry-Guided Multi-Agent Inverse Reinforcement Learning](https://mlsanity.com/paper/2509.08257/) (2025)
- [Towards Information-Optimized Multi-Agent Path Finding: A Hybrid Framework with Reduced Inter-Agent Information Sharing](https://mlsanity.com/paper/2510.09469/) (2025)

## Abstract (arXiv)

The Multi-Agent Path Finding (MAPF) problem aims to determine the shortest and collision-free paths for multiple agents in a known, potentially obstacle-ridden environment. It is the core challenge for robotic deployments in large-scale logistics and transportation. Decentralized learning-based approaches have shown great potential for addressing the MAPF problems, offering more reactive and scalable solutions. However, existing learning-based MAPF methods usually rely on agents making decisions based on a limited field of view (FOV), resulting in short-sighted policies and inefficient cooperation in complex scenarios. There, a critical challenge is to achieve consensus on potential movements between agents based on limited observations and communications. To tackle this challenge, we introduce a new framework that applies sheaf theory to decentralized deep reinforcement learning, enabling agents to learn geometric cross-dependencies between each other through local consensus and utilize them for tightly cooperative decision-making. In particular, sheaf theory provides a mathematical proof of conditions for achieving global consensus through local observation. Inspired by this, we incorporate a neural network to approximately model the consensus in latent space based on sheaf theory and train it through self-supervised learning. During the task, in addition to normal features for MAPF as in previous works, each agent distributedly reasons about a learned consensus feature, leading to efficient cooperation on pathfinding and collision avoidance. As a result, our proposed method demonstrates significant improvements over state-of-the-art learning-based MAPF planners, especially in relatively large and complex scenarios, demonstrating its superiority over baselines in various simulations and real-world robot experiments. The code is available at https://github.com/marmotlab/SIGMA