Fusion Training for Mathematical Generalization in Large Language Models
2026-08-10 • Computation and Language
Computation and LanguageArtificial Intelligence
AI summaryⓘ
The authors studied how to train large language models to handle both quick answers and detailed thinking at the same time, called Thinking Mode Fusion (TMF). They experimented with different amounts of training data and schedules for these two modes, especially focusing on math problems. Their findings show that giving the model more quick-answer practice can hurt its ability to think deeply, and the best training plan depends on how much data is used for each mode. They also found that the two modes can conflict with each other during training. These results help guide future training of models that need to balance fast replies with complex reasoning.
Thinking Mode Fusionlarge language modelstraining scheduledata ratiomathematical problem solvingmode interactionsupervisionmodel trainingreasoningdeep learning
Authors
Congfeng Cao, Pengyu Zhang, Jelke Bloem
Abstract
Thinking Mode Fusion (TMF) enables large language models to support both concise responses and long-form reasoning by unifying a non-thinking mode and a thinking mode within a single model. However, its training dynamics, including the \emph{data ratio} and \emph{training schedule} between the two modes, remain underexplored. In this work, we present a systematic study of TMF by analyzing the effects of the training schedule and data ratio between thinking and non-thinking modes. Focusing on mathematical problem solving, we construct a benchmark with multiple thinking-to-non-thinking data ratios and three training schedules. Our results reveal an asymmetric interaction between the two modes: increasing the ratio of non-thinking supervision reduces the accuracy of the thinking mode. We further show that different training schedules modulate this trade-off and that the optimal schedule depends on the data ratio. Finally, we quantify a negative correlation between non-thinking and thinking mode supervision, highlighting an inherent tension between these two modes. These findings provide practical guidance for designing effective TMF training settings. All code and data are released to support further research at: \href{https://github.com/caocongfeng/Fusion-Bench.git}{\textbf{Fusion Bench}}.