Different prompt types collapse to different modes: instance prompts collapse to a single prototypical response, while distribution prompts collapse to a representative high-entropy sample

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• The mode of a distribution-level prompt approximates the diverse distribution learned by the base model during pretrainingclaim0.779
  Supported by empirical comparison showing VS achieves KL divergence of 0.12 from pretraining distribution vs. 14.89 for direct prompting
• Humans prefer representative distributions over non-representative ones when evaluating outputs at the distribution level, providing a reward gap that VS exploitshypothesis0.776
  Assumption D.3 formalized in the theoretical framework; empirically validated with coin-flip sequence experiments
• Post-training stages (SFT, DPO, RLVR) progressively reduce output diversity, with direct prompting showing the most severe mode collapseclaim0.768
  Empirical finding from Tulu-70B ablation study across post-training stages
• Out-of-distribution collapse in foundation models is the same failure mode as Levin's regeneration failures and Alexander's lifeless buildings: loss of multi-scale coherence under stress.claim0.767
• Overbid frequency, self-bidding rate, bankrupt-initiation patterns, and context-dependent offer calibration are failure modes invisible to both static evaluations and aggregate rankings like Eloclaim0.762
  key claim about the benchmark's unique diagnostic value
• Base models assign higher likelihood to typical-set (representative) sequences than to degenerate sequences under VS promptshypothesis0.760
  Assumption D.6 formalized in the theoretical framework; empirically validated with coin-flip typicality rating experiments
• A model may produce internally coherent persona outputs while shifting characteristics across different generations, so intra-response and inter-response consistency must be assessed separatelyclaim0.757
  Supported by low correlation between ICatom and RCatom (r=0.44)
• Does persona-model collapse extend to other misalignment-inducing datasets such as medical misinformation, evil-numbers, and reward hacking?question0.754
  Extended experimentation proposed to clarify the extent of the findings