OmniOPD: Logit-Free On-Policy Distillation via Speculative Verification

2026-05-31

AI Summary

This work addresses the limitations of traditional on-policy distillation, which relies on token-level logits from the teacher model and thus fails with black-box teachers while being susceptible to noise and repetitive patterns. The authors propose a novel logits-free, chunk-level policy distillation method that approximates teacher preferences through multi-token semantic similarity and Monte Carlo rollouts, applying supervision selectively in regions where the student exhibits high uncertainty. Key innovations include a pioneering chunk-level semantic validation mechanism, a peak-entropy scheduling strategy, a Dirichlet-Multinomial Bayesian prior, and KL-anchor regularization, collectively preventing policy collapse. Experiments demonstrate a 28.64% improvement over standard on-policy distillation on mathematical reasoning benchmarks, with an additional 9.54% gain when using black-box teachers such as Claude-4.5-Haiku, outperforming self-exploratory reinforcement learning approaches.

Abstract

On-Policy Distillation (OPD) trains a student model on its own generative trajectories under dense token-level feedback from a stronger teacher, mitigating both the off-policy distribution shift of Supervised Fine-Tuning (SFT) and the sparse credit assignment of Reinforcement Learning (RL). However, standard OPD faces two coupled limitations. First, it requires direct access to the teacher's token-level logits, excluding a broad class of capable proprietary models from serving as teachers. Second, the token-level logit signal itself is brittle, depending on a narrow overlap of plausible next tokens between teacher and student, and prone to amplifying degenerate patterns such as repetition loops. In this paper, we introduce OmniOPD, a novel framework that addresses both limitations through a logit-free, chunk-level supervision signal. OmniOPD replaces deterministic logit matching with Monte Carlo rollouts that approximate the teacher's local preferences through a continuous semantic similarity metric over multi-token chunks, and concentrates this supervision via a peak-entropy scheduler that audits the student only at its high-uncertainty reasoning forks. A Dirichlet-Multinomial Bayesian prior and a base-model KL anchor further bound the variance of discrete sampling and prevent policy collapse across unaudited tokens. Across competitive benchmarks, OmniOPD surpasses the standard OPD approach by up to +28.64% on math, confirming that chunk-level semantic verification extracts a more reliable learning signal than token-level logit matching, whose high information density is offset by significant noise and brittleness. Furthermore, when paired with stronger black-box teachers such as Claude-4.5-Haiku and Gemini-2.5-Flash, OmniOPD achieves an additional +9.54% relative on math over its open-weight teacher counterpart, advancing the student past the performance of self-exploratory RL.

Problem

• On-Policy Distillation
• logit-free
• token-level logits
• distribution shift
• credit assignment

Innovation

• logit-free distillation
• chunk-level verification
• on-policy distillation
• semantic similarity
• peak-entropy scheduling