# Learning from Teacher Continuations at Student States

arXiv: https://arxiv.org/abs/2609.36246 · HTML: https://mlsanity.com/paper/2609.36246/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 40 of its 49 references that are in the map.
- First posted on arXiv 28 Sep 2026.

## Builds on (most cited first, 30 of 40)

- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [ReAct: Synergizing Reasoning and Acting in Language Models](https://mlsanity.com/paper/2210.03629/) (2022)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [Asynchronous Methods for Deep Reinforcement Learning](https://mlsanity.com/paper/1602.01783/) (2016)
- [LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Code](https://mlsanity.com/paper/2403.07974/) (2024)
- [Instruction-Following Evaluation for Large Language Models](https://mlsanity.com/paper/2311.07911/) (2023)
- [ALFWorld: Aligning Text and Embodied Environments for Interactive Learning](https://mlsanity.com/paper/2010.03768/) (2020)
- [DeepSeek-V4: Towards Highly Efficient Million-Token Context Intelligence](https://mlsanity.com/paper/2606.19348/) (2026)
- [On-Policy Distillation of Language Models: Learning from Self-Generated Mistakes](https://mlsanity.com/paper/2306.13649/) (2023)
- [IMPALA: Scalable Distributed Deep-RL with Importance Weighted Actor-Learner Architectures](https://mlsanity.com/paper/1802.01561/) (2018)
- [Sequence-Level Knowledge Distillation](https://mlsanity.com/paper/1606.07947/) (2016)
- [Scheduled Sampling for Sequence Prediction with Recurrent Neural Networks](https://mlsanity.com/paper/1506.03099/) (2015)
- [GLM-5: from Vibe Coding to Agentic Engineering](https://mlsanity.com/paper/2602.15763/) (2026)
- [LIMO: Less is More for Reasoning](https://mlsanity.com/paper/2502.03387/) (2025)
- [ScienceWorld: Is your Agent Smarter than a 5th Grader?](https://mlsanity.com/paper/2203.07540/) (2022)
- [OpenThoughts: Data Recipes for Reasoning Models](https://mlsanity.com/paper/2506.04178/) (2025)
- [Rethinking On-Policy Distillation of Large Language Models: Phenomenology, Mechanism, and Recipe](https://mlsanity.com/paper/2604.13016/) (2026)
- [MathArena: Evaluating LLMs on Uncontaminated Math Competitions](https://mlsanity.com/paper/2505.23281/) (2025)
- [Symbolic Knowledge Distillation: from General Language Models to Commonsense Models](https://mlsanity.com/paper/2110.07178/) (2021)
- [BabyAI: A Platform to Study the Sample Efficiency of Grounded Language Learning](https://mlsanity.com/paper/1810.08272/) (2018)
- [SearchQA: A New Q&A Dataset Augmented with Context from a Search Engine](https://mlsanity.com/paper/1704.05179/) (2017)
- [Spurious Rewards: Rethinking Training Signals in RLVR](https://mlsanity.com/paper/2506.10947/) (2025)
- [MiMo-V2-Flash Technical Report](https://mlsanity.com/paper/2601.02780/) (2026)
- [RL's Razor: Why Online Reinforcement Learning Forgets Less](https://mlsanity.com/paper/2509.04259/) (2025)
- [ADaPT: As-Needed Decomposition and Planning with Language Models](https://mlsanity.com/paper/2311.05772/) (2023)
- [Kimi K3: Open Frontier Intelligence](https://mlsanity.com/paper/2607.24653/) (2026)
- [Reinforcement and Imitation Learning via Interactive No-Regret Learning](https://mlsanity.com/paper/1406.5979/) (2014)
- [Retaining by Doing: The Role of On-Policy Data in Mitigating Forgetting](https://mlsanity.com/paper/2510.18874/) (2025)
- [AgentGym-RL: Training LLM Agents for Long-Horizon Decision Making through Multi-Turn Reinforcement Learning](https://mlsanity.com/paper/2509.08755/) (2025)

## Abstract (arXiv)

We present OLIVE (OnLine InterVEntion). At each iteration, the evolving student policy generates a new prefix, the teacher continues it autoregressively, and the student is updated using cross-entropy computed on the teacher-generated tokens. Each design choice targets a corresponding limitation of existing distillation methods: (1) sequential covariate shift in offline supervised fine-tuning (SFT) on fixed teacher trajectories, (2) fragmented supervision under prefix failure in token-level on-policy distillation (OPD), and (3) the need for access to teacher token probabilities in distribution-matching distillation. OLIVE achieves higher reasoning performance than OPD (with a top-16 KL approximation) at comparable GPU-hour cost. Our asynchronous implementation further reduces OLIVE's total training time by 23.8%. We evaluate OLIVE on both hard reasoning tasks and agentic tasks which reflects modern post-training scenarios, and it consistently outperforms existing distillation methods under the same training budget. By regenerating prefixes from the evolving student, OLIVE continues improving after offline distillation plateaus while better preserving the general capabilities and plasticity of the student. Using only text from GPT-5.4-mini, continuously training with OLIVE outperforms offline SFT from the same teacher by 13% on ScienceWorld. These results support OLIVE as an effective and efficient approach to online language-model distillation.