# RIDE (RL-Induced Direction Extrapolation)

The work proposes RIDE (RL-Induced Direction Extrapolation): on student-generated trajectories it computes the layerwise hidden-state residual between an RL-trained teacher and its pre-RL checkpoint, then regresses the student's hidden states toward targets displaced beyond the teacher along that residual; across four base/RL-teacher pairs (R1-Distill-1.5B, Qwen3-4B, Llama-3.2-3B, Phi-4-mini) RIDE's mean Avg@16 on AIME24, AIME25 and AIMO approaches or exceeds the RL-trained teacher on every pair, the only compared method whose mean does so, and it consistently outperforms output-space extrapolation.

The work proposes RIDE (RL-Induced Direction Extrapolation): on student-generated trajectories it computes the layerwise hidden-state residual between an RL-trained teacher and its pre-RL checkpoint, then regresses the student's hidden states toward targets displaced beyond the teacher along that residual; across four base/RL-teacher pairs (R1-Distill-1.5B, Qwen3-4B, Llama-3.2-3B, Phi-4-mini) RIDE's mean Avg@16 on AIME24, AIME25 and AIMO approaches or exceeds the RL-trained teacher on every pair, the only compared method whose mean does so, and it consistently outperforms output-space extrapolation.