mlsanityData to 7 Oct 2026

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

arXiv 2606.16478 ↗First posted 15 Jun 2026cs.AIcited by 0

On the map: LLM agents and tool use → General LLM agent frameworks and benchmarks

Abstract (arXiv)

Large language models (LLMs) remain limited in multi-agent planning because independently generated plans can create coordination failures such as spatial collisions, resource contention, and temporal deadlocks. We introduce Tensor-Coord, a multilinear algebra framework that represents the joint plan of N agents as a third-order tensor (T ∈ RN × H × A) over agents, timesteps, and actions. Canonical Polyadic (CP) and Tucker decompositions are used to identify latent coordination structure. The minimal epsilon-approximate CP rank R* defines a computable coordination complexity measure, with (CC(Pi)=(R*-N)/N). We prove that R*=N is necessary and sufficient for plan independence. The residual (E=T-TR*) defines a conflict score over agent pairs, timesteps, and actions, localizing failures without domain-specific rules. Tucker factors provide interpretable agent roles, temporal phases, and action clusters that are converted into natural language constraints for iterative LLM replanning. Experiments on multi-robot delivery tasks across Easy (2 agents, 5x5 grid), Medium (3 agents, 5x5 grid), and Hard (4 agents, 5x5 grid) settings show convergence to conflict-free plans in 100% of 2-agent cases within 1.4 iterations on average, 80% of 3-agent cases within 3.2 iterations, and 60% of 4-agent cases within 4.0 iterations. CP rank scaled approximately linearly as (R*(N) = 3.9N + 0.5), supporting its use as a predictor of coordination complexity.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Placed in General LLM agent frameworks and benchmarks, one of 16 directions in LLM agents and tool use. Builds on 4 of its 13 references that are in the map. First posted on arXiv 15 Jun 2026.

Builds on

4 of 13 references.

Closest ancestors · 1

Same direction, newest first

  1. 2023Building Cooperative Embodied Agents Modularly with Large Language Models5 Jul

Other references · 3

  1. 2022Chain-of-Thought Prompting Elicits Reasoning in Large Language Modelscited by 12,302
  2. 2023Reflexion: Language Agents with Verbal Reinforcement Learningcited by 4,064
  3. 2014Speeding-up Convolutional Neural Networks Using Fine-tuned CP-Decompositioncited by 199

Built on by

Not cited yet.

Similar, not cited

Close in wording, no citation either way

  1. 2026Every Response Counts: Quantifying Uncertainty of LLM-based Multi-Agent Systems through Tensor Decomposition
  2. 2025Decentralized Multi-Agent Goal Assignment for Path Planning using Large Language Models
  3. 2024TwoStep: Multi-agent Task Planning using Classical Planners and Large Language Models
  4. 2023LLM-Coordination: Evaluating and Analyzing Multi-agent Coordination Abilities in Large Language Models
  5. 2026Scale-Plan: Scalable Language-Enabled Task Planning for Heterogeneous Multi-Robot Teams
  6. 2026Benchmarking Open-Ended Multi-Agent Coordination in Language Agents
  7. 2025Multi-Mission Tool Bench: Assessing the Robustness of LLM based Agents through Related and Dynamic Missions
  8. 2025Can LLM Agents Solve Collaborative Tasks? A Study on Urgency-Aware Planning and Coordination