High‑uncertainty positions are the blind spot that lets dense teacher supervision waste effort. SPOT flips the script by probing exactly those spots and calibrating targets to downstream outcomes, turning uncertainty into a guide rather than noise.
Standard on‑policy distillation treats every token equally, assuming teacher entropy alone signals difficulty. In practice, entropy conflates a few plausible continuations with a long tail of low‑probability tokens, and it ignores whether the student already captures those candidates well.
Targeting high‑uncertainty token positions lifts student reasoning accuracy by up to 1.48 macro Avg@8 points and boosts coverage by over five Pass@8 points compared with vanilla on‑policy distillation. “Relative to standard OPD, SPOT improves macro Avg@8 by 0.47–1.48 points and macro Pass@8 by 4.55–5.28 points.” [1]
Across three student sizes, SPOT consistently tops macro Pass@8 and ranks in the top two for macro Avg@8, proving the method scales without extra data or compute. “SPOT achieves the best macro Pass@8 at all three evaluated student scales and the best or second‑best macro Avg@8.” [1]
The full acquisition score that blends entropy, top‑k mass, and mismatch yields a peak macro Avg@8/Pass@8 of 21.51/41.60, underscoring that holistic uncertainty probing drives solution coverage. “Table 2 shows that Full achieves the best macro Avg@8/Pass@8 (21.51/41.60), with its larger advantage in Pass@8 suggesting improved solution coverage.” [1]
