RLVR improves accuracy without reliably producing causally important or sufficient reasoning, but supervised fine-tuning or auxiliary rewards can remedy this while preserving performance.
Therefore, the minimum number of swaps required is -1 because both scenarios require the same number of swaps
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Outcome Rewards Do Not Guarantee Verifiable or Causally Important Reasoning
RLVR improves accuracy without reliably producing causally important or sufficient reasoning, but supervised fine-tuning or auxiliary rewards can remedy this while preserving performance.