On-policy training has emerged as a powerful post-training paradigm for improving the reasoning capabilities of large language models, and is often enhanced by golden trajectories from stronger expert models. However, when the expert fails on harder problems, existing trajectory-guided methods lose their main source of supervision, and these failed trajectories are typically discarded as negative samples. We argue that such failures, which we call Golden Negative Trajectories, can still provide valuable reasoning signals when treated not as demonstrations to imitate, but as flawed trajectories to reflect upon. We identify a Reflection Advantage: for hard problems, reflecting on a flawed trajectory can be easier and more effective than solving the problem directly from scratch. Motivated by this, we propose ReflectRL, a lightweight plug-and-play framework that learns from Golden Negative Trajectories during on-policy training. ReflectRL first uses these trajectories to elicit Reflective Reasoning, then applies Reflective-to-Direct Policy Transition to transfer the acquired reasoning behavior back to Direct Reasoning. Experiments across 9 benchmarks, 4 LLM backbones, and 4 on-policy training methods show that ReflectRL consistently improves reasoning performance with minimal overhead.
On-policy self-distillation (OPSD) trains a reasoning model on rollouts sampled from its own policy by matching a privileged teacher that also sees verified reference solutions. Existing OPSD objectives supervise only the output distribution, so privileged context affects training through a token-level divergence without directly supervising the internal computation that produced that distribution. We propose Privileged Hidden Flow (PHF), which additionally distills how a privileged teacher's hidden states move along the same rollout. Rather than forcing each student hidden vector to match the teacher vector at the same token position, PHF aligns token-to-token transition directions and trajectory geometry over selected generated positions. The all-layer recipe also includes an adjacent-layer relation computed from these same transitions, without pointwise hidden-state imitation. Under the same 100-step training schedule, PHF improves the Average@12 aggregate over our reproduced OPSD baseline on Qwen3-1.7B, 4B, and 8B, with observed gains of about +2.2, +1.5, and +1.7 points. The transport objective is exactly invariant to shared trajectory offsets; its local geometry term is also invariant to orthogonal transformations of transition directions. Ablations distinguish the fixed PHF recipe from pointwise hidden-state matching, single-channel transition losses, and layer-subset choices, supporting PHF as a compact hidden-flow extension to OPSD.