Enhancing LLM reasoning in federated settings is nontrivial due to stringent computational, communication, and privacy constraints, especially in healthcare, where clinically consequential decisions require not only accuracy but also interpretable, auditable rationales to meet safety, accountability, and regulatory requirements. Conventional federated fine-tuning largely imitates final answers rather than cultivating step-by-step reasoning, often relying on privacy-sensitive centralized distillation and still incurring substantial communication overhead. We address this gap with FedCoT, a federated reasoning framework that combines lightweight chain-of-thought resampling with a compact discriminator for selection, and client-aware LoRA stacking with weighted classifier aggregation to accommodate heterogeneity while reducing aggregation noise and communication; clients generate candidate chains and supervision locally, and only lightweight modules are aggregated on the server. Experiments on medical reasoning benchmarks show consistent gains under tight resource budgets while keeping data local and respecting privacy, offering an interpretable and resource-efficient solution.

Despite the advanced capabilities of Large Language Models (LLMs), training specialized reasoning models for the medical domain remains a significant challenge due to the scarcity of high-quality, large-scale Chain-of-Thought (CoT) data. Moreover, the intermediate reasoning steps in teacher-generated CoT data can be redundant and noisy, leading models to acquire spurious patterns and resulting in suboptimal performance. To address these issues, we propose MedCoach, a novel framework that introduces a dedicated coach role to guide the student model through question decomposition, thereby smoothing its learning curve in medical reasoning. The framework employs a curriculum-oriented warm-up on simplified sub-questions, facilitating domain adaptation before advancing to complex long-chain reasoning. To ensure the fidelity of the intermediate chain-of-thought signals, we augment this phase with medical knowledge graphs to suppress factual drift and mitigate reasoning noise at a granular level.Subsequently, we introduce a targeted factual perturbation mechanism to foster fine-grained discrimination between valid fact utilization and subtle factual misapplications. Extensive experiments across diverse benchmarks demonstrate notable improvements over existing methods, validating the effectiveness of MedCoach.

Developing reliable models for clinical tasks, such as Medical Question Answering (QA), is severely constrained by the limited availability of high-quality, expert-annotated training data. This challenge is exacerbated by stringent privacy requirements and the impracticality of utilizing large open-source corpora or proprietary cloud APIs within resource-limited clinical settings. To address these obstacles, we introduce SAGE (Semantic Anchor-Guided Evolution), a novel data synthesis framework that enables small, locally deployed models to generate high-quality medical training data. SAGE leverages lightweight, publicly available taxonomies such as MeSH as semantic anchors, imposing a structured prior to effectively guide and ground the data generation process. At its core, SAGE iteratively interleaves atomic (individual concept-based) and associative (relation-based) synthesis, bootstrapping training data from minimal seeds. This approach eliminates the need for large collections of medical documents or reliance on external APIs, providing a practical solution for on-premises data creation. Extensive experiments across multiple medical question-answering benchmarks demonstrate that models fine-tuned with SAGE-synthesized data consistently outperform those trained using self-derived or conventional document-based paradigms, highlighting tangible improvements in data efficiency and resource utilization for medical LLM development.

Multi-task learning in the medical domain remains a significant challenge for large language models (LLMs), plagued by conflicting task objectives and substantial computational overhead associated with full fine-tuning. Although parameter-efficient tuning methods help reduce these resource demands, their effectiveness is limited by two critical issues: (i) rigid allocation of expert capacity across layers, and (ii) lack of regularization mechanisms to partition shared components from task-specific signals. To address these limitations, we propose LAK-LoRA, a novel architecture that enables adaptive, depth-aware scaling of expert capacity, allowing more efficient resource allocation throughout the model. Furthermore, to resolve conflicting task objectives, LAK-LoRA divides experts into two distinct groups dedicated to modeling general and task-specific features, respectively. This separation is implemented via a feature separator module, which disentangles representations into shared and task-specific subspaces before assigning them to the appropriate experts. To foster diversity and minimize representational redundancy, orthogonality constraints are imposed among specialized experts. Extensive experiments on benchmark medical datasets demonstrate that LAK-LoRA achieves the best average performance.