Large Language Models (LLMs) trained on extensive scientific research are increasingly integrated as assistants for scientific discovery. However, most research papers omit the fine-grained cognitive process of examining constraints, failed alternatives, and iterative decisions required to achieve the desired goal. Such cognitive processes are vital for real-world scientists working toward specific goals under constraints. In this paper, we show that LLMs, when trained to produce such cognitive traces, perform better as scientific discovery assistants than when trained solely on scientific literature. We propose COGTRL, a trajectory-level reinforcement learning framework that trains LLMs to emulate cognitively grounded reasoning by jointly optimizing cognitive traces and the scientific steps produced in an interleaved manner. Across two 3B-parameter models and two scientific domains (AI and Materials Science), COGTRL improves method quality by an average of 7.85 points over comparable 3B model baselines and achieves competitive performance relative to 70B parameter models. Moreover, analysis by domain experts shows a preference for methods generated by COGTRL over the baselines.

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