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

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 off-policy mismatch causes gradient clipping on semantically critical reasoning tokens, ultimately rewarding correct answers while leaving the reasoning that justifies them unlearned. Hence, we propose $\textbf{Echo-GRPO}$, 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 $\textit{idiolect}$, that is, its own characteristic vocabulary and expression patterns, while preserving their semantics via Dual-Reference Decoding. We instantiate this framework as $\textbf{VideoEcho-R1}$ 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 reinforcement learning and supervised fine-tuning frameworks for reasoning distillation, demonstrating that policy-aligned supervision extends beyond GRPO.