LoopBench: Discovering Emergent Symmetry Breaking Strategies with LLM Swarms

LoopBench: Discovering Emergent Symmetry Breaking Strategies with LLM Swarms Ali Parsaee1, Yashar Talebirad1, Csongor Szepesvári1, Vishwajeet Ohal1, and Eden Redman2 1 University of Alberta, Edmonton, Canada {parsaee,talebira,csongor,ohal}@ualberta.ca 2 Network for Applied Technology, Edmonton, Canada eden@nat.ltd Abstract. Large Language Models (LLMs) are increasingly being uti- lized as autonomous agents, yet their ability to coordinate in distributed systems remains poorly understood. We introduce LoopBench, a bench- mark to evaluate LLM reasoning in distributed symmetry breaking and meta-cognitive thinking. The benchmark focuses on coloring odd cy- cle graphs (C3, C5, C11) with limited colors, where deterministic, non- communicating agents fail in infinite loops. A strategy passing mech- anism is implemented as a form of consistent memory. We show that while standard LLMs and classical heuristics struggle, advanced reason- ing models (e.g., O3) devise strategies to escape deadlocks. LoopBench allows the study of emergent distributed algorithms based on language- based reasoning, offering a testbed for collective intelligence. Keywords: multi-agent systems · collective intelligence · large language models · distributed systems · swarm intelligence · reasoning benchmarks 1 Introduction Large Language Models (LLMs) are evolving beyond isolated chatbots into the building blocks of autonomous multi-agent systems. The true potential of these "AI swarms" lies not just in individual problem-solving, but in their ability to solve complex problems without a central coordinator. However, coordinat- ing a distributed system of reasoning agents presents a fundamental challenge: can independent LLMs, driven by local prompts and limited observations, au- tonomously invent the strategies necessary to collaborate? This ability hinges on meta-cognitive reasoning, which we define as the capacity to adopt strategies that go beyond immediate local optimization. We wanted to test for meta-cognitive reasoning by creating a setting where thinking narrowly results in deadlock, but ’zooming out’ reveals the solution. This led us to the fundamental problem of loop breaking in graphs. Specifically, we focus on over-constrained odd cycles, a scenario where perfect solutions are impossible and simple greedy heuristics lead to endless oscillation loops and fail. arXiv:2512.13713v1 [cs.AI] 7 Dec 2025 2 A. Parsaee et al. This setting forces agents to go beyond immediate conflict resolution and adopt novel strategies that benefit the collective instead. We introduce LoopBench, a benchmark focused on symmetry breaking in over-constrained odd-cycle graphs (C3, C5, C11). By analyzing quantitative per- formance (conflict minimization) and qualitative strategy evolution (via feed- forward strategies), we measure the "Reasoning Gap" between models. We demonstrate that advanced reasoning models like O3 successfully break symmetries by developing strategies such as "waiting" or history-based pseudo- randomness. We interpret this capacity to detect and escape deadlock as a form of meta-cognitive thinking, enabling agents to override immediate greedy in- centives for long-term coordination. In contrast, classical heuristics and weaker LLMs often remain stuck. This work explores the following: 1. A framework for evaluating distributed agents on symmetry-breaking tasks. 2. An LLM-agent architecture using consistent memory to enable emergent and evolving strategies. 3. Experiments showing a performance gap between different LLMs as well as algorithmic baselines. 4. Qualitative analysis of emergent strategies showing how meta-cognitive rea- soning arises from local observations. 2 Related Work General multi-agent frameworks like AgentVerse [2] and AgentBench [6] investi- gate how LLM agents collaborate within structured environments. GPTSwarm [9] takes a graph-optimization approach, refining both agent prompts and their connectivity. For graph-based tasks specifically, GraphAgent [5] employs a dis- tributed approach where node-specific agents communicate synchronously, achiev- ing high accuracy on large-scale polynomial-time problems. The AgentsNet bench- mark [4] evaluates decentralized protocols like leader election and coloring under strict communication constraints. Self-improvement mechanisms have also proven effective. Reflexion [8] uses verbal reinforcement and episodic memory to help agents correct mistakes in subsequent trials. Research on self-reflection indicates that structured templates, such as prompts for retrying or summarizing solutions, enhance performance across various domains [7]. Additionally, FINEREASON [1] Demonstrates that practicing self-correction in puzzles improves mathematical reasoning. LoopBench aligns with multi-agent reasoning and reflective frameworks, but instead of introducing a new solver, we provide a minimal benchmark de- signed to test symmetry breaking under severe information constraints. Our feed-forward

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