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

Computer Science > Artificial Intelligence [Submitted on 10 Mar 2026] Do Large Language Models Get Caught in Hofstadter-Mobius Loops? Jaroslaw Hryszko 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. Comments: 15 pages, 4 figures, 3 tables Subjects: Artificial Intelligence (cs.AI); Computation and Language (cs.CL); Computers and Society (cs.CY) Cite as: arXiv:2603.13378 [cs.AI]   (or arXiv:2603.13378v1 [cs.AI] for this version)   https://doi.org/10.48550/arXiv.2603.13378 Focus to learn more Submission history From: Jaroslaw Hryszko PhD [view email] [v1] Tue, 10 Mar 2026 20:43:37 UTC (60 KB) Access Paper: HTML (experimental) view license Current browse context: cs.AI < prev   |   next > new | recent | 2026-03 Change to browse by: cs cs.CL cs.CY References & Citations NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)