I don't think you've ever done either of these training steps. You are just handwaving.
replyyou know what they say about making assumptions, yea?
replyand then you are going to ignore all the research and results that clearly show otherwise? why?
what might we infer about the importance of data from a learning algorithm like decision trees?
Read the paper. They train RLCR on existing big math problems. They subtract a brier score penalty from the correctness reward. No new confidence labels are needed.
replyExisting datasets, different reward function.