arXiv AI October 9, 2026 By Lars Simon, Holger Eble, Manuel Radons

Learning to Plan by Looking Back: Hindsight Hierarchies for Training Reasoning Models

The paper proposes a self‑improvement loop for reasoning models that leverages hindsight: when a problem is too hard, a supplied solution can help the model learn useful solution ideas. The method trains a single model to (1) predict solution ideas from problems alone, (2) reverse‑engineer ideas from problems and known solutions, and (3) solve problems using provided ideas. The loop alternates between reverse‑engineering ideas from problems with supplied solutions and using these ideas as additional supervision for joint training of all three capabilities, with a formal specification and an instantiation for interactive theorem proving in Lean.

Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv AI.

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