# PA1-OPD: One-Step Prefix-Augmented On-Policy Distillation for Language Model Pretraining

arXiv: https://arxiv.org/abs/2610.19601 · HTML: https://mlsanity.com/paper/2610.19601/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Knowledge distillation for LLMs, one of 12 directions in Knowledge distillation.
- Builds on 24 of its 38 references that are in the map.
- First posted on arXiv 14 Oct 2026.

## Placed in

- Knowledge distillation / [Knowledge distillation for LLMs](https://mlsanity.com/distill/knowledge-distillation-for-llms/)

## Builds on (most cited first, 24 of 24)

- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [DistilBERT, a distilled version of BERT: smaller, faster, cheaper and lighter](https://mlsanity.com/paper/1910.01108/) (2019)
- [The Pile: An 800GB Dataset of Diverse Text for Language Modeling](https://mlsanity.com/paper/2101.00027/) (2020)
- [Gemma 2: Improving Open Language Models at a Practical Size](https://mlsanity.com/paper/2408.00118/) (2024)
- [TinyBERT: Distilling BERT for Natural Language Understanding](https://mlsanity.com/paper/1909.10351/) (2019)
- [On-Policy Distillation of Language Models: Learning from Self-Generated Mistakes](https://mlsanity.com/paper/2306.13649/) (2023)
- [Medusa: Simple LLM Inference Acceleration Framework with Multiple Decoding Heads](https://mlsanity.com/paper/2401.10774/) (2024)
- [Scheduled Sampling for Sequence Prediction with Recurrent Neural Networks](https://mlsanity.com/paper/1506.03099/) (2015)
- [Sequence-Level Knowledge Distillation](https://mlsanity.com/paper/1606.07947/) (2016)
- [Compressive Transformers for Long-Range Sequence Modelling](https://mlsanity.com/paper/1911.05507/) (2019)
- [SpecInfer: Accelerating Generative Large Language Model Serving with Tree-based Speculative Inference and Verification](https://mlsanity.com/paper/2305.09781/) (2023)
- [Better & Faster Large Language Models via Multi-token Prediction](https://mlsanity.com/paper/2404.19737/) (2024)
- [Think before you speak: Training Language Models With Pause Tokens](https://mlsanity.com/paper/2310.02226/) (2023)
- [Entropy-Aware On-Policy Distillation of Language Models](https://mlsanity.com/paper/2603.07079/) (2026)
- [Speculative Knowledge Distillation: Bridging the Teacher-Student Gap Through Interleaved Sampling](https://mlsanity.com/paper/2410.11325/) (2024)
- [DistiLLM-2: A Contrastive Approach Boosts the Distillation of LLMs](https://mlsanity.com/paper/2503.07067/) (2025)
- [Autoregressive Knowledge Distillation through Imitation Learning](https://mlsanity.com/paper/2009.07253/) (2020)
- [Fast and Effective On-policy Distillation from Reasoning Prefixes](https://mlsanity.com/paper/2602.15260/) (2026)
- [Cut Your Losses in Large-Vocabulary Language Models](https://mlsanity.com/paper/2411.09009/) (2024)
- [Table-R1: Region-based Reinforcement Learning for Table Understanding](https://mlsanity.com/paper/2505.12415/) (2025)
- [MiniPLM: Knowledge Distillation for Pre-Training Language Models](https://mlsanity.com/paper/2410.17215/) (2024)
- [Prefix-Guided On-Policy Distillation: Mining Golden Trajectories from Rollouts](https://mlsanity.com/paper/2606.21994/) (2026)
- [Cache-Aware Joint Router Adaptation for Memory-Efficient MoE Inference](https://mlsanity.com/paper/2609.04895/) (2026)

## Abstract (arXiv)

Knowledge distillation (KD) improves language-model pretraining by matching teacher distributions at corpus prefixes, but provides no direct supervision at contexts induced by student predictions. We introduce PA1-OPD, which augments corpus-path distillation with teacher feedback after one student-sampled transition per selected prefix. This expands the supervised states while retaining next-token prediction and corpus-path KD. Data-anchored roots support parallel sampling, and differentiable tree attention shares prefix computation without changing inference. In two continued-pretraining settings, full coverage improves held-out cross-entropy over KD across C4, PG-19, and Pile at every evaluated checkpoint. In Stage2, selecting the 10% of roots with highest student surprisal adds 48.85% to KD's Macro cross-entropy gain over next-token training. Gains remain when branch supervision excludes successor states already on the corpus path, supporting the value of feedback beyond observed contexts. Additional depth or breadth improves aggregate results at unchanged per-term supervision weight, with benefits varying by corpus. These findings support local student-induced supervision as a complement to pretraining distillation.