Research digest · COLM 2026 · Efficient Reasoning

Before You Scale

The Cost of Supervision Mismatch in PRM Distillation

One result · visually

Evidence before interpretation.

A teacher-level advantage can disappear at the distillation boundary.

01Privileged teacher+0.051 F1 on MATH

02Distillation boundarysignal becomes diffuse

031.5B studentverified transfer null

The same object · seven altitudes

From question
to falsifier.

A paper becomes easier to inspect when its claim, boundary, intervention, measurement, failure mode, and next disconfirming result are kept separate.

01Question
Does privileged teacher feedback remain useful after it is compressed into a much smaller verifier?
02Claim
Teacher advantage and student learnability are separate variables; expensive supervision can collapse at the transfer boundary.
03System boundary
A teacher with worked-solution context supervising a 1.5B student that lacks that context at inference time.
04Intervention
Compare privileged and non-privileged supervision while holding the student evaluation target fixed.
05Measurement
Threshold-free discrimination and downstream selection performance, not a single tuned classification cutoff.
06Failure mode
A fixed threshold can manufacture an apparent gain that disappears under calibration or downstream evaluation.
07Next falsifier
A capacity or data regime where the privileged signal transfers reproducibly and improves selection over majority vote.

The setup

A large teacher sees a worked solution and labels each reasoning step with both a score and a natural-language critique. A much smaller student then tries to reproduce that behavior without access to the answer at inference time.

The attraction is obvious: turn expensive, privileged supervision into a cheap process verifier. The risk is that a small student learns the surface of the feedback while losing the information that made it correct.

The supervision sweet spot

Privileged context helps the teacher only where the problem is difficult enough to require a reference but still tractable enough for the teacher to use it. On easy problems the reference is redundant; on the hardest tail it cannot rescue an incapable judge.

A bare final answer carries almost none of this benefit. The worked solution—the structure of how the answer is reached—is the useful signal.

The result that matters

The teacher’s advantage did not transfer into the tested 1.5B student. Privileged and non-privileged students were statistically indistinguishable, and neither produced a verifier that beat the simple majority-vote baseline.

That null result is the point. Scaling a labeling pipeline before checking whether its information survives the teacher-student boundary can turn a real expert advantage into expensive supervision noise.

Teacher quality and student learnability are separate variables.
Threshold-free and downstream evaluations matter; a fixed threshold can manufacture a success story.
The next experiment should first make the student competent, then ask whether privilege transfers.

Still open

Does the privileged signal transfer at a larger data scale or student capacity? And can the feedback be reorganized into a cleaner directional target instead of a diffuse churn of step labels?