Federated Reasoning Distillation Framework with Model Learnability-Aware Data Allocation

Large language models (LLMs) exhibit strong reasoning capabilities when guided by high-quality demonstrations, yet such data is often distributed across organizations that cannot centralize it due to regulatory, proprietary, or institutional constraints. We study federated reasoning, where a server improves multi-step reasoning by coordinating with heterogeneous clients holding private demonstrations, without centralized training or raw data sharing. The key challenge is that client reliability is query-dependent, while the server cannot inspect client data to determine which contributions are trustworthy. To address this, we propose Uncertainty-Aware Federated Reasoning (FERA), a training-free framework based on iterative server-client co-refinement. Across communication rounds, clients generate reasoning traces with lightweight uncertainty estimates, and the server synthesizes them into improved reasoning that is redistributed as context for the next round, progressively improving both server outputs and client-side reasoning. Within each round, Uncertainty-Aware Self-Critique Aggregation (UA-SCA) resolves conflicts among heterogeneous client traces through query-dependent trust weighting and structured cross-client verification. Rather than simply discarding low-quality traces, UA-SCA revises flawed reasoning steps to recover useful information. We provide theoretical guarantees showing that the proposed iterative protocol converges and that uncertainty-aware weighting accelerates convergence. Experiments on multiple reasoning benchmarks show that FERA consistently outperforms both federated training and training-free baselines, achieving progressively higher accuracy across rounds while maintaining communication and computational efficiency.

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 \ours{}, 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. Our code is made publicly available at https://github.com/DIaacKr/FedCoT

Reasoning capabilities are critical for advancing Large Language Models, yet current approaches either require massive computational budgets or struggle to effectively distill reasoning to smaller models. Standard distillation methods rely on outcome-based rewards, failing to distinguish between sound reasoning and lucky guesses. We propose Collaborative Reasoning Distillation (CRD), a framework that enhances reasoning in compact models through three innovations: (1) interactive cross-feedback where teachers iteratively critique each other's reasoning, (2) fine-grained step-wise quality assessment capturing logical validity independent of final answers, and (3) coherence-aware step stitching that synthesizes complementary strengths. Students are trained via Reasoning Quality Optimization (RQO) with budget constraints. Our model, CRD-4B, achieves 97.3% on MATH-500 and 70.3% on AIME'25, surpassing baselines while using only 50K training examples, up to 12 times smaller than the datasets of comparable models.