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OPSD, SDFT, and SDPO share one mechanism. A frozen teacher scores the student's prefix while receiving additional evidence. The evidence source defines the method.

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The student distribution is p theta given the issue and its prefix. Teacher target q scores the same next token at the same prefix, but also conditions on evidence e.

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Training matches q into p; deployment removes e.

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On-Policy Self-Distillation, or OPSD, gives the teacher a trusted solution. Here that is the verified repair: preserve cleanup and raise Cancelled Error.

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The teacher uses it to guide the student's own prefix without placing the privileged patch in the deployed student's prompt.

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The OPSD paper evaluated this mechanism on reasoning tasks; the animation maps the information flow onto our code case.

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Self-Distillation Fine-Tuning, or SDFT, gives the teacher an expert demonstration. A related repair shows the sequence inspect the flag, run cleanup, then raise the exception.

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Unlike offline imitation, SDFT scores the current student's return-None prefix, so the demonstration guides the state the student actually reached.

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Self-Distillation Policy Optimization, or SDPO, gives the teacher feedback about the current failure. The scalar reward is zero, but the test trace says test-cancel failed, expected Cancelled Error, and return skipped cancellation.

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The teacher converts that explanation into dense token probabilities along the failed prefix.

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The choice follows the evidence. A trusted solution supports OPSD. A demonstration supports SDFT. An explanatory failure trace supports SDPO.

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If all you have is a binary outcome, GRPO may be the honest baseline; inventing a generic “feedback” field would hide these different trust boundaries.

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None of the dense methods is automatically safe. A privileged patch can leak. A demonstration can be irrelevant. A teacher can misread feedback and densify an error.

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New capability can overwrite old behavior, entropy can collapse, and teacher forward passes can erase claimed efficiency savings.

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So the durable comparison is not acronym against acronym. Hold the student prefix fixed, vary the evidence, record the cost, and measure both the cancellation repair and unrelated retained capability.