Tensor-Coord: Algebraic Decomposition of Joint Plan Tensors for Conflict-Free Multi-Agent LLM Planning

Tensor-Coord introduces a multilinear algebra framework for multi-agent planning using a third-order tensor representation to mitigate coordination failures in large language models (LLMs). By employing Canonical Polyadic and Tucker decompositions, it quantifies coordination complexity and localizes conflicts, enabling LLMs to generate conflict-free plans iteratively. Experimental results demonstrate effective convergence to conflict-free plans across various multi-agent scenarios, with a notable correlation between CP rank and coordination complexity, making it a valuable tool for practitioners working on multi-agent systems.