一个模型同时支持快慢思维，推理更准更省时。

In cognition theory, human thinking is governed by two systems: the fast and intuitive System 1 and the slower but more deliberative System 2. Analogously, Large Language Models (LLMs) can operate in two reasoning modes: outputting only the solutions (\emph{fast mode}) or both the reasoning chain and the final solution (\emph{slow mode}). We present \dualformer, a single Transformer model that seamlessly integrates both the fast and slow reasoning modes by training on randomized reasoning traces, where different parts of the traces are strategically dropped during training. At inference time, \dualformer can be easily configured to execute in either fast or slow mode, or automatically decide which mode to engage (\emph{auto mode}). It outperforms baselines in both performance and computational efficiency across all three modes: (1) in slow mode, \dualformer achieves $97.6\%$ optimal rate on unseen $30 \times 30$ maze tasks, surpassing the \searchformer baseline ($93.3\%$) trained on data with complete reasoning traces, with $45.5\%$ fewer reasoning steps; (2) in fast mode, \dualformer achieves $80\%$ optimal rate, significantly outperforming the Solution-Only model trained on solution-only data, which has an optimal rate of only $30\%$; (3) in auto mode, \dualformer achieves $96.6\%$ optimal rate with $59.9\%$ fewer steps than \searchformer. Moreover, \dualformer produces more diverse reasoning traces than \searchformer{}. For math reasoning problems, our techniques have also achieved improved performance with LLM fine-tuning, demonstrating its generalization beyond task-specific models. We open source our code at https://github.com/facebookresearch/dualformer.