# Reason in the Words You Speak: Idiolectal Paraphrasing Off-Policy Traces for Reasoning Distillation in VideoLLMs

arXiv: https://arxiv.org/abs/2608.26684 · HTML: https://mlsanity.com/paper/2608.26684/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 19 of its 43 references that are in the map.
- First posted on arXiv 27 Aug 2026.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)
- Knowledge distillation / [On-policy and self-distillation for LLMs](https://mlsanity.com/distill/on-policy-and-self-distillation-for-llms/)

## Builds on (most cited first, 19 of 19)

- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Qwen3-VL Technical Report](https://mlsanity.com/paper/2511.21631/) (2025)
- [InternVL3.5: Advancing Open-Source Multimodal Models in Versatility, Reasoning, and Efficiency](https://mlsanity.com/paper/2508.18265/) (2025)
- [OpenAI o1 System Card](https://mlsanity.com/paper/2412.16720/) (2024)
- [Group Sequence Policy Optimization](https://mlsanity.com/paper/2507.18071/) (2025)
- [Self-Distilled Reasoner: On-Policy Self-Distillation for Large Language Models](https://mlsanity.com/paper/2601.18734/) (2026)
- [Seed1.5-VL Technical Report](https://mlsanity.com/paper/2505.07062/) (2025)
- [OpenThoughts: Data Recipes for Reasoning Models](https://mlsanity.com/paper/2506.04178/) (2025)
- [VideoChat-R1: Enhancing Spatio-Temporal Perception via Reinforcement Fine-Tuning](https://mlsanity.com/paper/2504.06958/) (2025)
- [Video-MMMU: Evaluating Knowledge Acquisition from Multi-Discipline Professional Videos](https://mlsanity.com/paper/2501.13826/) (2025)
- [Aligning Modalities in Vision Large Language Models via Preference Fine-tuning](https://mlsanity.com/paper/2402.11411/) (2024)
- [Time-R1: Post-Training Large Vision Language Model for Temporal Video Grounding](https://mlsanity.com/paper/2503.13377/) (2025)
- [Beyond Benchmarks: MathArena as an Evaluation Platform for Mathematics with LLMs](https://mlsanity.com/paper/2605.00674/) (2026)
- [Video-Holmes: Can MLLM Think Like Holmes for Complex Video Reasoning?](https://mlsanity.com/paper/2505.21374/) (2025)
- [TinyLLaVA-Video-R1: Towards Smaller LMMs for Video Reasoning](https://mlsanity.com/paper/2504.09641/) (2025)
- [Revisiting Group Relative Policy Optimization: Insights into On-Policy and Off-Policy Training](https://mlsanity.com/paper/2505.22257/) (2025)
- [Exploring the Effect of Reinforcement Learning on Video Understanding: Insights from SEED-Bench-R1](https://mlsanity.com/paper/2503.24376/) (2025)

## Abstract (arXiv)

Recent large language models achieve strong performance on complex reasoning tasks, where reinforcement learning with Group Relative Policy Optimization (GRPO) has emerged as a leading paradigm for optimizing models on self-generated trajectories. However, the on-policy nature of GRPO bounds the model to the reasoning skills it can already produce, restricting to learn more advanced capabilities. Prior works inject privileged reasoning traces from a stronger teacher policy to guide training, yet these traces are inherently out of distribution with respect to the student policy. We observe that this mismatch between on-policy and off-policy causes gradient clipping on semantically critical reasoning tokens, ultimately rewarding correct answers while leaving the reasoning that justifies them unlearned. Hence, we propose Echo-GRPO, a framework that lets the model reason in the words it speaks. Rather than imitating low-probability privileged traces from the teacher model, Echo-GRPO rewrites them into the student policy's own textitidiolect, that is, its own characteristic vocabulary and expression patterns, while preserving their semantics via Dual-Reference Decoding. We instantiate this framework as VideoEcho-R1 for video reasoning distillation, achieving consistent improvements across three multimodal LLM backbones and five benchmarks. Finally, we show that our idiolectal paraphrasing is a plug-in module that consistently improves both RL and supervised fine-tuning frameworks for reasoning distillation, demonstrating that policy-aligned supervision extends beyond GRPO.