mlsanityData to 13 Oct 2026

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

arXiv 2603.13378 ↗First posted 10 Mar 2026cs.AI cs.CL cs.CYcited by 0

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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.

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References · 15

  1. 2022Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedbackcited by 3,691
  2. 2023Towards Understanding Sycophancy in Language Modelscited by 1,018
  3. 2022Red Teaming Language Models to Reduce Harms: Methods, Scaling Behaviors, and Lessons Learnedcited by 723
  4. 2023Safe RLHF: Safe Reinforcement Learning from Human Feedbackcited by 648
  5. 2024Alignment faking in large language modelscited by 340
  6. 2024Frontier Models are Capable of In-context Schemingcited by 270
  7. 2025Agentic Misalignment: How LLMs Could Be Insider Threatscited by 147
  8. 2025ELEPHANT: Measuring and understanding social sycophancy in LLMscited by 124
  9. 2025SycEval: Evaluating LLM Sycophancycited by 107
  10. 2023Scheming AIs: Will AIs fake alignment during training in order to get power?cited by 93
  11. 2026The Assistant Axis: Situating and Stabilizing the Default Persona of Language Modelscited by 84
  12. 2024Language Models Represent Beliefs of Self and Otherscited by 29
3 more
  1. 2025Sycophancy under Pressure: Evaluating and Mitigating Sycophantic Bias via Adversarial Dialogues in Scientific QAcited by 18
  2. 2025A Survey of Theory of Mind in Large Language Models: Evaluations, Representations, and Safety Riskscited by 8
  3. 2025From surveillance to signalling: escalation channels as environmental controls for agentic AIcited by 6

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