Inject a Turn, Not a Token: Learning Where to Redirect LLM Reasoning for Self-Correction

Current large language models have difficulty in reliably identifying and correcting errors in their own reasoning. While existing training-based remedies fine-tune a full LLM using substantial correction data, we approach the correction problem from a different perspective with two questions: where a failed rollout diverges and how to redirect it, based on the observation that failures often result from a wrong direction caused by a rare mistake at some point in reasoning not from many mistakes throughout the reasoning course. To choose where to intervene, we train a 130K-parameter MLP head on a frozen encoder using only final-answer correctness, without step-level supervision. Regarding redirection of reasoning, we show that inline injection fails regardless of content because the inserted text is absorbed as the model's own reasoning, but presenting the same text in a new user turn changes the model's course. The resulting framework, UPTURN (User-Prompt TURN injection at a learned position), enables correction without fine-tuning a language model, training only lightweight position and gate heads with both the reasoner and encoder frozen. Across six math benchmarks, UPTURN raises average accuracy from 48.1% to 59.8%, outperforming heuristic position baselines and every inline variant.