Abstract
We introduce a self-improvement loop for reasoning models based on the following observation: Even when the difficulty of a problem exceeds the model's current solving abilities, an additionally supplied solution might enable the model to extract useful solution ideas in hindsight. We operationalize this by jointly training the same model to exhibit the following three capabilities: predicting solution ideas from problems alone, reverse-engineering ideas from problems and known solutions, and solving problems using provided ideas. The loop alternates between reverse engineering such ideas from problems with supplied solutions and using these ideas as additional supervision for joint training of all three capabilities. We give a formal specification of our method and a concrete instantiation for interactive theorem proving in the Lean theorem prover; empirical evaluation remains future work.
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Publication details
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- Open access
- Green open access
Cite this article
APA 7
Simon, L., Eble, H., & Radons, M. (2026). Learning to Plan by Looking Back: Hindsight Hierarchies for Training Reasoning Models. https://omanscience.com/en/articles/learning-to-plan-by-looking-back-hindsight-hierarchies-for-training-reasoning-models
MLA 9
Simon, Lars, et al. "Learning to Plan by Looking Back: Hindsight Hierarchies for Training Reasoning Models." https://omanscience.com/en/articles/learning-to-plan-by-looking-back-hindsight-hierarchies-for-training-reasoning-models.
Chicago (author–date)
Simon, Lars, Holger Eble, and Manuel Radons. 2026. "Learning to Plan by Looking Back: Hindsight Hierarchies for Training Reasoning Models." https://omanscience.com/en/articles/learning-to-plan-by-looking-back-hindsight-hierarchies-for-training-reasoning-models.
Harvard
Simon, L., Eble, H. and Radons, M. (2026) 'Learning to Plan by Looking Back: Hindsight Hierarchies for Training Reasoning Models', Available at: https://omanscience.com/en/articles/learning-to-plan-by-looking-back-hindsight-hierarchies-for-training-reasoning-models.
Vancouver
Simon L, Eble H, Radons M. Learning to Plan by Looking Back: Hindsight Hierarchies for Training Reasoning Models. https://omanscience.com/en/articles/learning-to-plan-by-looking-back-hindsight-hierarchies-for-training-reasoning-models
IEEE
L. Simon, H. Eble, and M. Radons, "Learning to Plan by Looking Back: Hindsight Hierarchies for Training Reasoning Models," https://omanscience.com/en/articles/learning-to-plan-by-looking-back-hindsight-hierarchies-for-training-reasoning-models.