Excited to share our paper, “Learning Multi-Agent Coordination via Sheaf-ADMM” to be presented at ICML 2026.
Most AI models process information as one giant, monolithic block. But in nature, intelligence often comes from a group of individuals working together, where each individual only has a limited view of the world.
We built a framework called Sheaf-ADMM to study how this kind of collective problem-solving works. We divide a complex task into smaller overlapping pieces, and assign one agent to each piece.
To solve the global puzzle, the agents negotiate in three simple steps:
Local Guesses: Every agent looks at its limited view and proposes a solution.
Finding Common Ground: Agents communicate with their direct neighbors to smooth out conflicts. They do not need to agree on everything, but they must agree on the boundaries where their tasks overlap.
Remembering Disagreements: If neighbors cannot agree, they keep a memory of that conflict. This memory forces them to try harder to compromise in the next round.
We tested this on problems where no single agent has enough information to succeed alone:
Multi-Agent Sudoku: Each agent sees only a single row, column, or 3x3 box. The framework achieved a 93% solve rate, while a parameter-matched message-passing baseline scored 11%.
Image Classification: When we tested canvas-size domain shifts, a standard CNN dropped to 11% accuracy on MNIST, while our method retained 86%.
Maze Pathfinding: Sheaf-ADMM matches a message-passing baseline’s accuracy while agents communicate over a 5-dimensional channel, 8x smaller than that required of the baseline (42).
Traditional message-passing networks hide their reasoning inside opaque hidden states. Our framework makes coordination completely transparent. You can watch exactly how local agents debate, compromise, and eventually reach a global consensus.
Sheaf-ADMM draws inspiration from two fields with long histories in distributed consensus: ADMM from distributed optimization, and sheaves from applied topology. We think these perspectives may offer insights for the distributed, multi-agent AI systems increasingly being built today.