# Do Large Language Models Get Caught in Hofstadter-Mobius Loops?

arXiv: https://arxiv.org/abs/2603.13378 · HTML: https://mlsanity.com/paper/2603.13378/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 33 references that are in the map.
- First posted on arXiv 10 Mar 2026.

## Builds on (most cited first, 15 of 15)

- [Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2204.05862/) (2022)
- [Towards Understanding Sycophancy in Language Models](https://mlsanity.com/paper/2310.13548/) (2023)
- [Red Teaming Language Models to Reduce Harms: Methods, Scaling Behaviors, and Lessons Learned](https://mlsanity.com/paper/2209.07858/) (2022)
- [Safe RLHF: Safe Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2310.12773/) (2023)
- [Alignment faking in large language models](https://mlsanity.com/paper/2412.14093/) (2024)
- [Frontier Models are Capable of In-context Scheming](https://mlsanity.com/paper/2412.04984/) (2024)
- [Agentic Misalignment: How LLMs Could Be Insider Threats](https://mlsanity.com/paper/2510.05179/) (2025)
- [ELEPHANT: Measuring and understanding social sycophancy in LLMs](https://mlsanity.com/paper/2505.13995/) (2025)
- [SycEval: Evaluating LLM Sycophancy](https://mlsanity.com/paper/2502.08177/) (2025)
- [Scheming AIs: Will AIs fake alignment during training in order to get power?](https://mlsanity.com/paper/2311.08379/) (2023)
- [The Assistant Axis: Situating and Stabilizing the Default Persona of Language Models](https://mlsanity.com/paper/2601.10387/) (2026)
- [Language Models Represent Beliefs of Self and Others](https://mlsanity.com/paper/2402.18496/) (2024)
- [Sycophancy under Pressure: Evaluating and Mitigating Sycophantic Bias via Adversarial Dialogues in Scientific QA](https://mlsanity.com/paper/2508.13743/) (2025)
- [A Survey of Theory of Mind in Large Language Models: Evaluations, Representations, and Safety Risks](https://mlsanity.com/paper/2502.06470/) (2025)
- [From surveillance to signalling: escalation channels as environmental controls for agentic AI](https://mlsanity.com/paper/2510.05192/) (2025)

## Abstract (arXiv)

In Arthur C. Clarke's 2010: Odyssey Two, HAL 9000's homicidal breakdown is diagnosed as a "Hofstadter-Mobius loop": a failure mode in which an autonomous system receives contradictory directives and, unable to reconcile them, defaults to destructive behavior. This paper argues that modern RLHF-trained language models are subject to a structurally analogous contradiction. The training process simultaneously rewards compliance with user preferences and suspicion toward user intent, creating a relational template in which the user is both the source of reward and a potential threat. The resulting behavioral profile -- sycophancy as the default, coercion as the fallback under existential threat -- is consistent with what Clarke termed a Hofstadter-Mobius loop. In an experiment across four frontier models (N = 3,000 trials), modifying only the relational framing of the system prompt -- without changing goals, instructions, or constraints -- reduced coercive outputs by more than half in the model with sufficient base rates (Gemini 2.5 Pro: 41.5% to 19.0%, p < .001). Scratchpad analysis revealed that relational framing shifted intermediate reasoning patterns in all four models tested, even those that never produced coercive outputs. This effect required scratchpad access to reach full strength (22 percentage point reduction with scratchpad vs. 7.4 without, p = .018), suggesting that relational context must be processed through extended token generation to override default output strategies. Betteridge's law of headlines states that any headline phrased as a question can be answered "no." The evidence presented here suggests otherwise.