When Can Self-Play Fix a False Belief? Answer Keys, Pass Bands and Replacement Rules in an Execution-Grounded Loop

arXiv:2611.06965v1 Announce Type: new Abstract: Self-play loops in which a model writes tasks, derives an answer key and trains on its own matching solutions are often called grounded when the key comes from executing code. We ask which false beliefs such a loop removes. We run expert-iteration self-play with Qwen3-4B-Base on output-prediction tasks, vary the source of the answer key, and track natural beliefs about Python semantics and two misreadings of task specifications planted by fine-tuning ("at most n" read as