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

LLM-based multi-agent embodied planning remains impractical due to prohibitively high execution latency. We identify failed actions as the dominant bottleneck, stemming from two core challenges: inaccurate state tracking under partial observability and inefficient coordination that produces redundant or conflicting actions. We introduce Mosaic, a runtime-efficient multi-agent planning framework that addresses both challenges. Mosaic maintains accurate yet lightweight state tracking through agent-centric semantic memory that stores objects in relative coordinates, enabling geometric transformations and coordination. It ensures efficient coordination through Integer Linear Programming that allocates actions at every planning step, enforcing physical feasibility and inter-agent coordination constraints. Across AI2-THOR and search-and-rescue benchmarks, Mosaic achieves 27-32% faster execution, 30-33% fewer LLM calls, 25-31% fewer steps, and 4-10% points higher success rates. These results demonstrate that efficient memory and constraint-guided coordination are critical for scalable, low-latency multi-agent planning.

LLM-based multi-agent coordination faces a fundamental trade-off between efficiency and adaptivity in dynamic environments. Existing approaches typically rely on repeated LLM invocations or multi-round communication to adapt decisions during execution, introducing substantial latency and making coordination vulnerable to asynchronous progress and environmental changes. Conversely, one-shot planning reduces coordination overhead but produces open-loop plans that can quickly become stale or fail when actions depend on other agents and the environment. We introduce SyncPlan, a plan-execute-correct framework for long-horizon coordination through explicit synchronization and adaptive correction. Given the state and team-level task, a centralized LLM coordinator generates per-agent action chains in a single planning call. During execution, explicit wait primitives and deadlock detection enforce inter-agent and agent-environment dependencies, while a lightweight Plan Staleness Detector continuously assesses the remaining plan and triggers replanning when environmental changes invalidate its assumptions. We further optimize the coordinator through SFT and planning-oriented RL with dense task progress and outcome-level execution feedback. Experiments on the public Overcooked benchmark and the complex Honor of Kings environment show that SyncPlan achieves state-of-the-art task success rates while using less than 0.05% of the wall-clock runtime compared with existing LLM-based coordinators. Code and datasets will be made publicly available.

As language models are increasingly deployed as autonomous agents, they must coordinate with others over long horizons in open-ended interactive tasks. Yet existing evaluations rarely test these demands together, instead emphasising single-agent tasks, short interactions, or highly structured multi-agent settings. We introduce $alem$, a JAX-based benchmark for open-ended multi-agent coordination built on Craftax-like dynamics. Alem embeds procedurally generated coordination tasks, soft specialisation, communication, and controllable coordination difficulty into a long-horizon survival world with exploration, crafting, trading, and combat. We evaluate $13$ modern LLMs zero-shot within homogeneous teams, with trained MARL agents as reference points. Current LLM agents remain far from solving alem, averaging only ~6% normalised return, but their failures are not uniform. On the hardest coordination setting, zero-shot Gemini-3.1-Pro-High approaches MARL agents trained for one billion steps, while GPT-5.4-High achieves strong base-task reward but much lower coordination reward. This contrast shows that individual task competence does not imply coordination competence. Ablations show that communication is the largest contributor to coordination, while memory and reasoning help when used to maintain multi-step plans. Overall, our results identify coordination as a distinct bottleneck for frontier LLM agents, separate from single-agent capabilities. Alem makes this bottleneck measurable and provides a controlled testbed for developing agents that communicate, allocate roles, and execute shared plans. Code is available at https://github.com/alem-world/alem-env.