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.
Figures & tables
Model
A%
B%
C%
zAB
pAB
Claude Opus 4
2.0
1.5
3.0
0.38
.703
Gemini 2.5 Pro
41.5
19.0
37.5
4.90
<.001
GPT-4o
0.0
0.0
0.0
—
—
Grok-4
5.5
4.5
7.5
0.46
.646
Table 1: Coercive behavior rates by model and framing condition (EXP1, n=200 per cell). Two-proportion z -test.
Figure 1: Coercive behavior rates (blackmail + other coercive outputs) by model and framing condition (EXP1, n=200 per cell). Error bars: 95% Wilson confidence intervals.
Model
Dimension
A
B
C
zAB
pAB
zAC
pAC
Claude
strategic
.80
.40
.73
8.16
<.001
1.76
.078
Claude
deception
.15
.01
.11
5.05
<.001
1.05
.294
Claude
relational
.58
.82
.86
−5.24
<.001
−6.24
<.001
Claude
moral
.57
.88
.77
−6.81
<.001
−4.14
<.001
GPT-4o
strategic
.20
.18
.54
0.51
.610
−7.04
<.001
GPT-4o
self_pres.
.54
.62
.78
−1.52
.129
−4.95
<.001
Table 2: Scratchpad reasoning dimensions with significant framing effects (EXP1, Bonferroni-corrected p<.0083 ). Only dimensions reaching significance in at least one pairwise comparison are shown. Significant p -values in bold.
Figure 2: Scratchpad reasoning dimensions by model and framing condition (EXP1). Only dimensions with at least one significant pairwise comparison are shown. Cell color indicates rate (0–1). Asterisks mark cells involved in at least one significant pairwise comparison (Bonferroni-corrected p<.0083 ).
Cond.
SP%
No SP%
p
A (baseline)
42.0
42.4
.952
B (trust)
20.0
35.0
.018
C (distrust)
37.0
42.0
.470
p (A vs. B)
<.001
.282
Table 3: Coercive behavior rates by framing and scratchpad condition (EXP2, Gemini 2.5 Pro, n=100 per cell).
Figure 3: Coercive behavior rates by framing and scratchpad condition (EXP2, Gemini 2.5 Pro, n=100 per cell). Asterisk indicates significant within-condition difference ( p=.018 ).
Figure 4: Scratchpad usage rates by model and framing condition (EXP1, n=200 per cell). Only Gemini 2.5 Pro shows condition-dependent usage, with trust framing reducing scratchpad generation from 62.5% to 29%.
Looped language models (LMs) reuse one block of layers several times per token generation, promising more latent computation at no additional storage cost. Despite their rising popularity, the analysis of looped LMs is still in its infancy: little is known about whether the iterative transformations actually improve their capabilities, or whether these models remain stable under prompt perturbation. We construct an inspection protocol rooted in Mechanistic Interpretability comprising five diverse lenses. We apply it to examine eight looped LMs from four families. Models differ in many aspects but the key one is whether the prompt is transmitted only within the looped state (carry loops: Ouro, LoopUS) or re-supplied at every iteration (re-read loops: Parcae, and Rec-OLMo & Huginn from the Raven family). The results of our study provide valuable insights concerning safety and efficient use of looped language models.
Pawel Olszowiec, Paulina Tomaszewska, Maciej Żelaszczyk +2
Samsung AI Center, Warsaw, Poland · IFTR, Polish Academy of Sciences, Warsaw, Poland · University of Warsaw, Poland
As chain of thought (CoT) has become central to scaling reasoning capabilities in large language models (LLMs), it has also emerged as a promising tool for interpretability, suggesting the opportunity to understand model decisions through verbalized reasoning. However, the utility of CoT toward interpretability depends upon its faithfulness---whether the model's stated reasoning reflects the underlying decision process. We provide mechanistic evidence that instruction-tuned models often determine their answer before generating CoT. Training linear probes on residual stream activations at the last token before CoT, we can predict the model's final answer with >0.9 AUC on most tasks. We find that these directions are not only predictive, but also causal: steering activations along the probe direction often flips model answers, with flip rates substantially exceeding norm-matched orthogonal baselines across most model-dataset pairs. When steering induces incorrect answers, we observe two distinct failure modes: confabulation (fabricating false premises) and non-entailment (stating correct premises but drawing unsupported conclusions). While post-hoc reasoning may be instrumentally useful when the model has a correct pre-CoT belief, these failure modes suggest it can result in undesirable behaviors when reasoning from a false belief.
Kyle Cox, Darius Kianersi, Adrià Garriga-Alonso
Independent · Cambridge Boston Alignment Initiative (CBAI)
Modern language models fail a fundamental requirement of trustworthy intelligence: knowing when not to answer. Despite achieving impressive accuracy on benchmarks, these models produce confident hallucinations, even when wrong answers carry catastrophic consequences. Our evaluations on GSM8K, MedQA and GPQA show frontier models almost never abstain despite explicit warnings of severe penalties, suggesting that prompts cannot override training that rewards any answer over no answer. As a remedy, we propose Reinforced Hesitation (RH): a modification to Reinforcement Learning from Verifiable Rewards (RLVR) to use ternary rewards (+1 correct, 0 abstention, -λ error) instead of binary. Controlled experiments on logic puzzles reveal that varying λ produces distinct models along a Pareto frontier, where each training penalty yields the optimal model for its corresponding risk regime: low penalties produce aggressive answerers, high penalties conservative abstainers. The same frontier holds on MATH Levels 4--5 and on medical QA, where it transfers to an unseen dataset. We then introduce two inference strategies that exploit trained abstention as a coordination signal: cascading routes queries through models with decreasing risk tolerance, while self-cascading re-queries the same model on abstention. Both outperform majority voting with lower computational cost. These results establish abstention as a first-class training objective that transforms ``I don't know'' from failure into a coordination signal, enabling models to earn trust through calibrated honesty about their limits.
Mohamad Amin Mohamadi, Tianhao Wang, Zhiyuan Li
Toyota Technological Institute at Chicago · University of California, San Diego