# Learning Multi-Agent Coordination via Sheaf-ADMM

arXiv: https://arxiv.org/abs/2605.31005 · HTML: https://mlsanity.com/paper/2605.31005/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 43 references that are in the map.
- First posted on arXiv 29 May 2026.

## Builds on (most cited first, 24 of 24)

- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Gated Graph Sequence Neural Networks](https://mlsanity.com/paper/1511.05493/) (2015)
- [Deep Equilibrium Models](https://mlsanity.com/paper/1909.01377/) (2019)
- [OptNet: Differentiable Optimization as a Layer in Neural Networks](https://mlsanity.com/paper/1703.00443/) (2017)
- [Adaptive Computation Time for Recurrent Neural Networks](https://mlsanity.com/paper/1603.08983/) (2016)
- [Differentiable Convex Optimization Layers](https://mlsanity.com/paper/1910.12430/) (2019)
- [Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processing](https://mlsanity.com/paper/1912.10557/) (2019)
- [Learned Primal-dual Reconstruction](https://mlsanity.com/paper/1707.06474/) (2017)
- [Neural Sheaf Diffusion: A Topological Perspective on Heterophily and Oversmoothing in GNNs](https://mlsanity.com/paper/2202.04579/) (2022)
- [Global Convergence of ADMM in Nonconvex Nonsmooth Optimization](https://mlsanity.com/paper/1511.06324/) (2015)
- [Sheaf Neural Networks](https://mlsanity.com/paper/2012.06333/) (2020)
- [Convergence Analysis of Alternating Direction Method of Multipliers for a Family of Nonconvex Problems](https://mlsanity.com/paper/1410.1390/) (2014)
- [On Vanishing Gradients, Over-Smoothing, and Over-Squashing in GNNs: Bridging Recurrent and Graph Learning](https://mlsanity.com/paper/2502.10818/) (2025)
- [Collective Intelligence for Deep Learning: A Survey of Recent Developments](https://mlsanity.com/paper/2111.14377/) (2021)
- [Optimal parameter selection for the alternating direction method of multipliers (ADMM): quadratic problems](https://mlsanity.com/paper/1306.2454/) (2013)
- [Cooperative Sheaf Neural Networks](https://mlsanity.com/paper/2507.00647/) (2025)
- [Deep Distributed Optimization for Large-Scale Quadratic Programming](https://mlsanity.com/paper/2412.12156/) (2024)
- [Adaptive ADMM with Spectral Penalty Parameter Selection](https://mlsanity.com/paper/1605.07246/) (2016)
- [ADMM Penalty Parameter Selection by Residual Balancing](https://mlsanity.com/paper/1704.06209/) (2017)
- [Distributed Multi-agent Coordination over Cellular Sheaves](https://mlsanity.com/paper/2504.02049/) (2025)
- [A Survey of ADMM Variants for Distributed Optimization: Problems, Algorithms and Features](https://mlsanity.com/paper/2208.03700/) (2022)
- [Learning to accelerate distributed ADMM using graph neural networks](https://mlsanity.com/paper/2509.05288/) (2025)
- [Heterogeneous Multi-Agent Multi-Target Tracking using Cellular Sheaves](https://mlsanity.com/paper/2512.24886/) (2025)
- [DiffCoord: Differentiable Coordination for Distributed Multi-Agent Trajectory Optimization](https://mlsanity.com/paper/2509.01630/) (2025)

## Built on by (most cited first, 2 of 2)

- [Stable Unsupervised Continual Chunking with Sheaf SyncMap](https://mlsanity.com/paper/2609.25143/) (2026)
- [Reasoning with Neural Cellular Automata](https://mlsanity.com/paper/2609.36126/) (2026)

## Abstract (arXiv)

We present a differentiable optimization framework for multi-agent coordination. An input is decomposed into overlapping local views, each processed by an agent that solves a convex subproblem parameterized by a neural encoder. Agents coordinate through the Alternating Direction Method of Multipliers (ADMM) with inter-agent constraints specified by a cellular sheaf. The sheaf specifies which aspects of neighboring solutions must agree, allowing for heterogeneous notions of global consensus. Backpropagating through the unrolled optimization jointly trains all components of the multi-agent system. We evaluate on maze pathfinding, image classification, and Sudoku, where agents with individually insufficient local views learn to coordinate to produce correct global outputs. On MNIST, the local-view decomposition yields improved robustness to distribution shifts relative to a standard CNN. On Sudoku, the optimization-derived structure yields markedly higher solve rates than parameter-matched MPNN baselines. Finally, the ADMM structure exposes distinct primal, consensus, and dual state variables, opening the coordination dynamics to direct analysis and intervention -- a property unavailable in standard message-passing architectures.