Source
Hossain, Kousar and Tourni (2026), LIT-1883, §§3.2–5.3, Tables 1, 2, 4–6, Figs. 2 and 5; read in NOTE-1479.
What was actually shown
From prefixes of failed student rollouts, the frozen initial model given the gold reference recovered the correct answer in 77% of continuations against 37% for the student at 1.7B, and 67% against 50% at 4B. From prefixes of verified rollouts the difference was at most 4 points (Table 1). Unrelated or empty references gave no gain, so the advantage comes from the reference’s content. OPSD supervises mostly failed trajectories (about 70%, Table 5). Its gain over the base model fell from 3.05 to 1.98 to 0.14 points at 1.7B, 4B and 8B. OASIS, which supervises only verified trajectories and conditions the teacher on another rollout, gained 3.64, 3.84 and 3.19 (Table 2). On verified scaffolds the teacher’s distribution moved by TV of at most 0.065 when the gold reference was replaced by the student’s own failed attempt (Fig. 2b).
What could have come out otherwise: OASIS’s gain could have faded with scale as OPSD’s did, or the teacher could have needed the gold reference on verified scaffolds too.
What this does not say
- That the privileged-information gap causes OPSD’s decline. The two are reported together. Per-entry clipping, which reverses gradients on the teacher’s preferred tokens and affects about a third of tokens, is present in every run, and the authors offer it as a second explanation of late drift.
- That the advantage keeps shrinking. It was measured at 1.7B and 4B only.
- That the teacher adds nothing on verified trajectories. OASIS beats GRPO with the same verifier (Table 2), so the dense teacher signal helps there; what it carries is mostly not the reference.
- Anything beyond Qwen3 and competition mathematics, or beyond 100 steps of LoRA training.