Post-training reasoning models is computationally expensive, and the allocation between supervised fine-tuning (SFT) and reinforcement learning (RL) substantially affects reasoning quality. Existing methods operate at the training-procedure level and treat the reasoning corpus as homogeneous, ignoring the structural heterogeneity of individual traces. We propose GROVE (Graph-based Routing Over Variant Experts), an adaptive framework that routes each example to SFT or RL based on the structural topology of its reasoning trace. GROVE parses each trace into a Reasoning Tree, scores its complexity via graph entropy, and partitions the corpus through a data-driven Gaussian Mixture Model with no hand-tuned threshold. Low-complexity traces are trained with SFT and high-complexity traces with GRPO as parallel LoRA adapters from a shared frozen base, merged into a single deployable model with no inference-time overhead. Across two training corpora and five reasoning benchmarks, GROVE consistently outperforms single-stage and naive-hybrid baselines, and a reversed-routing ablation confirms that this mapping is intrinsic rather than arbitrary.

Federated fine-tuning enables privacy-preserving LLM adaptation but faces a critical bottleneck: the disparity between LLMs’ high memory demands and edge devices’ limited capacity. To break the memory barrier, we propose Chain Federated Fine-tuning (ChainFed), an innovative paradigm that forgoes end-to-end updates in favor of a sequential, layer-by-layer manner. It first trains the initial adapter to convergence, freezes its weights, and then proceeds to the next. This iterative train-and-freeze process forms an optimization chain, gradually enhancing the model’s task-specific proficiency. ChainFed further integrates three core techniques: 1) Dynamic Layer Co-Tuning to bridge semantic gaps between sequentially tuned layers and facilitate information flow; 2) Globally Perceptive Optimization to endow each adapter with foresight beyond its local objective; 3) Function-Oriented Adaptive Tuning to automatically identify the optimal fine-tuning starting point. Extensive experiments on multiple benchmarks demonstrate the superiority of ChainFed over existing methods, boosting average accuracy by up to 46.46%.