# LoopBench: Discovering Emergent Symmetry Breaking Strategies with LLM Swarms

arXiv: https://arxiv.org/abs/2512.13713 · HTML: https://mlsanity.com/paper/2512.13713/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 9 references that are in the map.
- First posted on arXiv 7 Dec 2025.

## Builds on (most cited first, 6 of 6)

- [Reflexion: Language Agents with Verbal Reinforcement Learning](https://mlsanity.com/paper/2303.11366/) (2023)
- [AgentBench: Evaluating LLMs as Agents](https://mlsanity.com/paper/2308.03688/) (2023)
- [AgentVerse: Facilitating Multi-Agent Collaboration and Exploring Emergent Behaviors](https://mlsanity.com/paper/2308.10848/) (2023)
- [Language Agents as Optimizable Graphs](https://mlsanity.com/paper/2402.16823/) (2024)
- [Scalable and Accurate Graph Reasoning with LLM-based Multi-Agents](https://mlsanity.com/paper/2410.05130/) (2024)
- [FINEREASON: Evaluating and Improving LLMs' Deliberate Reasoning through Reflective Puzzle Solving](https://mlsanity.com/paper/2502.20238/) (2025)

## Built on by (most cited first, 3 of 3)

- [Equal Access, Unequal Interaction: A Counterfactual Audit of LLM Fairness](https://mlsanity.com/paper/2602.02932/) (2026)
- [From Signals to Structure: How Memory Architecture Drives Language Emergence in LLM Agents](https://mlsanity.com/paper/2607.00233/) (2026)
- [Memory Is Communication: The Frontier Between Remembering and Signaling](https://mlsanity.com/paper/2608.17053/) (2026)

## Abstract (arXiv)

Large Language Models (LLMs) are increasingly being utilized as autonomous agents, yet their ability to coordinate in distributed systems remains poorly understood. We introduce LoopBench, a benchmark to evaluate LLM reasoning in distributed symmetry breaking and meta-cognitive thinking. The benchmark focuses on coloring odd cycle graphs (C3, C5, C11) with limited colors, where deterministic, non-communicating agents fail in infinite loops. A strategy passing mechanism is implemented as a form of consistent memory. We show that while standard LLMs and classical heuristics struggle, advanced reasoning 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.