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In this work, we investigate high-loss tokens, a token type that--as the most direct signal of student-teacher mismatch under OPD's per-token KL objective--should progressively diminish as training converges according to existing studies; however, our empirical analysis shows otherwise. Even after OPD training reaches apparent saturation, a substantial subset of tokens continues to exhibit persistently high loss; these tokens, which we term Rock Tokens, can account for up to 18\\% of the tokens in generated outputs. Our investigation reveals two startling paradoxes. First, despite their high occurrence frequency providing a disproportionately large share of total grad","title":"Cornerstones or Stumbling Blocks? Deciphering the Rock Tokens in On-Policy Distillation","url":"https://arxiv.org/abs/2605.09253","vendor":"arxiv_cs_ai"},"summary":"arXiv:2605.09253v3 Announce Type: replace-cross \nAbstract: While recent work in Reinforcement Learning with Verifiable Rewards (RLVR) has shown that a small subset of critical tokens disproportionately drives reasoning gains, an analogous token-level understanding of On-Policy Distillation (OPD) remains largely unexplored. In this work, we investigate high-loss tokens, a token type that--as the most direct signal of student-teacher mismatch under OPD's per-token KL objective--should progressively diminish as training converges according to existing studies; however, our empirical analysis shows otherwise. Even after OPD training reaches apparent saturation, a substantial subset of tokens continues to exhibit persistently high loss; these tokens, which we term Rock Tokens, can account for up to 18\\% of the tokens in generated outputs. Our investigation reveals two startling paradoxes. First, despite their high occurrence frequency providing a disproportionately large share of total grad","title":"Cornerstones or Stumbling Blocks? 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