How Reasoning Evolves from Post-Training Data: An Empirical Study Using Chess

Lucas Dionisopoulos, Nicklas Majamaki, Prithviraj Ammanabrolu
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:25451-25482, 2026.

Abstract

We study how reasoning evolves in a language model – from supervised fine-tuning (SFT) to reinforcement learning (RL) – by analyzing how a set of theoretically-inspired datasets impacts language model performance in chess. We find that fine-tuning a model to directly predict the best move leads to effective RL and the strongest downstream performance – however, the RL stage elicits unfaithful reasoning (reasoning inconsistent with the chosen move). Alternatively, training on multi-move trajectories yields comparable downstream performance with faithful reasoning and more stable RL. We show that RL induces a substantial positive shift in the distribution of move quality and reduces hallucination rates as a side effect. Finally, we find several SFT-checkpoint metrics – metrics spanning evaluation performance, hallucination rates, and reasoning quality – to be predictive of post-RL model performance. We release checkpoints and final models as well as training data, evaluations, and code that allowed us to surpass leading open-source reasoning models in chess with a 7B-parameter model.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-dionisopoulos26a, title = {How Reasoning Evolves from Post-Training Data: An Empirical Study Using Chess}, author = {Dionisopoulos, Lucas and Majamaki, Nicklas and Ammanabrolu, Prithviraj}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {25451--25482}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/dionisopoulos26a/dionisopoulos26a.pdf}, url = {https://proceedings.mlr.press/v306/dionisopoulos26a.html}, abstract = {We study how reasoning evolves in a language model – from supervised fine-tuning (SFT) to reinforcement learning (RL) – by analyzing how a set of theoretically-inspired datasets impacts language model performance in chess. We find that fine-tuning a model to directly predict the best move leads to effective RL and the strongest downstream performance – however, the RL stage elicits unfaithful reasoning (reasoning inconsistent with the chosen move). Alternatively, training on multi-move trajectories yields comparable downstream performance with faithful reasoning and more stable RL. We show that RL induces a substantial positive shift in the distribution of move quality and reduces hallucination rates as a side effect. Finally, we find several SFT-checkpoint metrics – metrics spanning evaluation performance, hallucination rates, and reasoning quality – to be predictive of post-RL model performance. We release checkpoints and final models as well as training data, evaluations, and code that allowed us to surpass leading open-source reasoning models in chess with a 7B-parameter model.} }
Endnote
%0 Conference Paper %T How Reasoning Evolves from Post-Training Data: An Empirical Study Using Chess %A Lucas Dionisopoulos %A Nicklas Majamaki %A Prithviraj Ammanabrolu %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-dionisopoulos26a %I PMLR %P 25451--25482 %U https://proceedings.mlr.press/v306/dionisopoulos26a.html %V 306 %X We study how reasoning evolves in a language model – from supervised fine-tuning (SFT) to reinforcement learning (RL) – by analyzing how a set of theoretically-inspired datasets impacts language model performance in chess. We find that fine-tuning a model to directly predict the best move leads to effective RL and the strongest downstream performance – however, the RL stage elicits unfaithful reasoning (reasoning inconsistent with the chosen move). Alternatively, training on multi-move trajectories yields comparable downstream performance with faithful reasoning and more stable RL. We show that RL induces a substantial positive shift in the distribution of move quality and reduces hallucination rates as a side effect. Finally, we find several SFT-checkpoint metrics – metrics spanning evaluation performance, hallucination rates, and reasoning quality – to be predictive of post-RL model performance. We release checkpoints and final models as well as training data, evaluations, and code that allowed us to surpass leading open-source reasoning models in chess with a 7B-parameter model.
APA
Dionisopoulos, L., Majamaki, N. & Ammanabrolu, P.. (2026). How Reasoning Evolves from Post-Training Data: An Empirical Study Using Chess. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:25451-25482 Available from https://proceedings.mlr.press/v306/dionisopoulos26a.html.

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