nick-rui/proofwriter-qwen25-7b-rar-delta

proofwriter-qwen25-7b-rar-delta

Per-question delta_RaR annotations on ProofWriter: how much a model's own rephrasing of a logic problem improves its ability to solve it. Computed with Qwen/Qwen2.5-7B-Instruct, 30,000 queries at k=32 samples per side.

The "teacher" is not a stronger model and does not think longer. It is the same frozen model answering the same question, with one extra thing in context — a rephrasing it generated itself.

How each row is produced

1. 1.Sample k=32 answers to the bare question -> student_reward
2. 2.If student_reward > 0.75, stop: there is no headroom left for the context to buy. The row is kept with skipped_reason set, so the threshold can be changed without re-annotating.
3. 3.Otherwise sample one rephrasing of the theory
4. 4.Sample k=32 answers to question + rephrasing -> teacher_reward
5. 5.delta_rar = teacher_reward - student_reward

Student and teacher prompts are identical apart from the inserted rephrasing, and both use the same decoding parameters, so the delta isolates the contribution of the context.

Task. ProofWriter depth-5, QDep >= 2: a theory of unstructured facts and rules plus a statement to judge True/False/Unknown.

What the delta looks like

30,000 rows, 20,801 labelled and 9,199 skipped at the ceiling. Mean delta_rar +0.0330.

The rephrasing helps on about half of questions and actively hurts on a substantial minority. This is a distribution to select from, not a uniformly helpful intervention.

Read this before selecting on delta_rar

delta_rar is quantised to 1/32 and carries sampling noise with SE ~0.125.

The smallest delta reaching an uncorrected one-sided Fisher p<0.05 is +0.156 (teacher clearly ahead with the student at 0/32). 3,176 of 20,801 labelled rows clear that bar. The minimum attainable p-value at k=32 is 5.5e-19, so a Bonferroni threshold over ~20,801 comparisons is reachable.

Selecting the top of the distribution buys a winner's curse: the selected rows' true delta is materially below their measured delta. Select on these labels, then re-measure before reporting.

Because the original samples are kept first in each list and k_original marks the boundary, the estimate that selection was made on can be recovered exactly and compared against the later samples. That measures the winner's curse directly rather than by split-half proxy.

No answer leakage

A sibling math annotation had to warn that rewrites often solve the problem rather than restate it. That failure was traced to a final-answer format instruction baked into the question text and then repaired. In this file:

• —0 of 20,801 rewrites contain `\boxed{}`
• —rewrite median 217 tokens, teacher answer median 440 tokens (a transcribing teacher answers in ~6)

The teacher here is reasoning, not reading back an answer it already wrote.

Caveats

• —skipped_reason = student_reward_above_threshold rows carry no delta: the teacher was never run.
• —Capped samples are graded, not dropped — these rollouts measure accuracy, so a sample that runs out of tokens is a wrong answer. (The opposite rule applies to training targets, where an unterminated sequence must be discarded.)