Teach-to-Reason: Competition-Guided Reasoning with a Self-Improving Teacher

Long Chain-of-Thought (CoT) traces can improve reasoning accuracy, but repeatedly generating them is costly for smaller or latency-constrained language models. This paper studies a practical alternative: produce a rich rationale once with a capable \emph{thinking} model, compress it, and reuse the compressed trace as context for a cheaper \emph{answering} model. We introduce CoT-X, an adaptive framework for cross-model CoT transfer. CoT-X segments reasoning traces into semantic units, scores their diagnostic and logical importance, selects budget-feasible evidence paths, and reconstructs a coherent compressed rationale for the answering model. On $7,501$ Japanese medical licensing questions spanning $10$ specialties, CoT-X improves accuracy over direct truncation by up to $40.5\%$ under the same token budget, with the largest gains at $64$--$256$ tokens. Across $64$ thinking--answering pairs from eight DeepSeek-R1 and Qwen3 models (1.5B--32B parameters), reasoning transfer is most reliable within a model family, yet remains effective across families once compression normalizes the trace. A Gaussian Process Bayesian optimization layer finds near-optimal model--budget configurations with $15$ evaluations rather than an exhaustive search over all $64$ pairs, reducing evaluation cost by $84\%$. These results show that reasoning quality, token budget, and model compatibility can be optimized jointly, making CoT-style reasoning more practical under realistic deployment constraints.

High-stakes clinical use of large vision-language models (LVLMs) requires reasoning that is grounded in visual evidence and clinical knowledge, not just correct final answers. We introduce OpenMedReason, a large-scale, open multimodal medical reasoning corpus comprising approximately 450K image-question-answer instances whose reasoning traces are primarily derived from curated biomedical, human-authored scientific articles. OpenMedReason provides high-fidelity supervision beyond synthetic chains of thought, covering diverse medical domain vision modalities such as radiological scans, microscopic images, visible light photographs, charts, and others. We complement it with OpenMedReason-Bench, a held-out benchmark that allows fine-grained evaluation of LVLMs along three complementary axes of capability, including perception, medical knowledge, and rationale, enabling diagnostic evaluation beyond final-answer accuracy. OpenMedReason is a rich training resource that exhibits its effectiveness in both supervised fine-tuning (SFT) and reinforcement-based alignment. Training with OpenMedReason yields a 20% average improvement in VQA accuracy over the base model and achieves performance within 4.2% of the strongest comparable-scale medical LVLMs. Fine-grained performance analysis confirms that the gains are not concentrated in any single axis: OpenMedReason improves perception, medical knowledge, and rationale jointly, and its reasoning traces are preferred over those of the base model in 86.1% of pairwise comparisons. We release the code and dataset at huggingface.co/datasets/neginb/OpenMedReason.

Reinforcement Fine-Tuning (RFT) has enabled medical Multimodal Large Language Models (MLLMs) to produce Chain-of-Thought (CoT) reasoning for visual question answering, yet these models suffer from $\textit{confidence miscalibration}$---a systematic gap between expressed certainty and actual diagnostic accuracy that undermines clinical trust. We propose $\textbf{CARE}$, a $\textbf{C}$onfidence-$\textbf{A}$ware medical $\textbf{RE}$asoning framework that jointly optimizes accuracy and calibration through a dual-stage pipeline. First, a scalable Medical-CoT synthesis provides structured cold-start data for Supervised Fine-Tuning. Second, Group Relative Policy Optimization (GRPO) with a novel $\textbf{Confidence-Aware Reward (CAR)}$ mechanism ties the model's confidence to diagnostic correctness within the reward signal. Across three Medical VQA benchmarks, $\textbf{CARE}$ achieves the highest diagnostic accuracy while obtaining the lowest Expected Calibration Error and Hallucination Rate, establishing a foundation for trustworthy clinical decision support. Our code is available at https://github.com/anotherbricki/CARE.