DenseSteer: Steering Small Language Models towards Dense Math Reasoning

Yang Ouyang, Shuhang Lin, Jung-Eun Kim
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:95274-95289, 2026.

Abstract

Large language models (LLMs) demonstrate strong chain-of-thought (CoT) reasoning abilities, while smaller models ($\leq$ 3B parameters) significantly underperform on multi-step reasoning tasks. Based on empirical analyses of the Qwen-2.5 model family on math reasoning benchmarks, we find that more proficient reasoning is associated with fewer reasoning steps but higher information density per step, a property we term Dense Reasoning. Motivated by this observation, we propose DenseSteer, a training-free inference-time steering framework that enhances small-model reasoning by modulating internal representations toward dense reasoning patterns. Experiments show that our method yields consistent accuracy improvements without increasing token-level Negative Log-Likelihood, highlighting dense reasoning as an effective structural approach to mathematical problem solving.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-ouyang26d, title = {{D}ense{S}teer: Steering Small Language Models towards Dense Math Reasoning}, author = {Ouyang, Yang and Lin, Shuhang and Kim, Jung-Eun}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {95274--95289}, 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/ouyang26d/ouyang26d.pdf}, url = {https://proceedings.mlr.press/v306/ouyang26d.html}, abstract = {Large language models (LLMs) demonstrate strong chain-of-thought (CoT) reasoning abilities, while smaller models ($\leq$ 3B parameters) significantly underperform on multi-step reasoning tasks. Based on empirical analyses of the Qwen-2.5 model family on math reasoning benchmarks, we find that more proficient reasoning is associated with fewer reasoning steps but higher information density per step, a property we term Dense Reasoning. Motivated by this observation, we propose DenseSteer, a training-free inference-time steering framework that enhances small-model reasoning by modulating internal representations toward dense reasoning patterns. Experiments show that our method yields consistent accuracy improvements without increasing token-level Negative Log-Likelihood, highlighting dense reasoning as an effective structural approach to mathematical problem solving.} }
Endnote
%0 Conference Paper %T DenseSteer: Steering Small Language Models towards Dense Math Reasoning %A Yang Ouyang %A Shuhang Lin %A Jung-Eun Kim %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-ouyang26d %I PMLR %P 95274--95289 %U https://proceedings.mlr.press/v306/ouyang26d.html %V 306 %X Large language models (LLMs) demonstrate strong chain-of-thought (CoT) reasoning abilities, while smaller models ($\leq$ 3B parameters) significantly underperform on multi-step reasoning tasks. Based on empirical analyses of the Qwen-2.5 model family on math reasoning benchmarks, we find that more proficient reasoning is associated with fewer reasoning steps but higher information density per step, a property we term Dense Reasoning. Motivated by this observation, we propose DenseSteer, a training-free inference-time steering framework that enhances small-model reasoning by modulating internal representations toward dense reasoning patterns. Experiments show that our method yields consistent accuracy improvements without increasing token-level Negative Log-Likelihood, highlighting dense reasoning as an effective structural approach to mathematical problem solving.
APA
Ouyang, Y., Lin, S. & Kim, J.. (2026). DenseSteer: Steering Small Language Models towards Dense Math Reasoning. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:95274-95289 Available from https://proceedings.mlr.press/v306/ouyang26d.html.

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