Abstract
Edge devices host domain-specific small language models (SLMs) with limited resources, while private clouds offer larger LLMs. We propose G-Boost, an adaptive edge-cloud framework that improves a deployed SLM's task performance without parameter updates. It formulates reasoning as a tree search, choosing at each step between SLM-only inference and SLM-LLM logit fusion---which transfers domain knowledge from the SLM's adapted version to the cloud LLM without exposing private data. A process reward model guides Monte Carlo tree search to select beneficial collaboration steps dynamically. The edge runs the SLM and search controller; the cloud hosts the LLM and reward model, exchanging only current context. Evaluated on GSM8K and MATH-500 with Qwen2.5 and LLaMA2, G-Boost outperforms the SLM alone, static fusion, and fine-tuned baselines, gaining up to 8.6 and 10.7 percentage points over MCTS and Proxy-Tuning, respectively. Results confirm that step-level, reward-guided dynamic collaboration enhances reasoning and domain utilization for deployed edge SLMs.