Beyond Surface Semantics: Logic-Guided Privacy-Preserving Cloud-Edge LLM Reasoning

Large language models (LLMs) excel at complex reasoning, but their large resource demands make them difficult to deploy on edge devices. Thus, many users rely on APIs to access cloud-side LLMs for complex reasoning tasks, raising privacy concerns when sending queries to the cloud. Existing methods protect user queries on the edge before cloud reasoning. Recent work further explores cloud-edge collaboration, where the cloud-side LLM provides guidance and the edge-side small language model (SLM) completes reasoning with private data. However, to balance utility and privacy, these methods mainly preserve surface semantics and often fail to retain the logical structure needed for solving the query, making cloud guidance unstable. In this paper, we propose LoGic, a logic-guided analogical reasoning framework that shifts the focus from preserving surface semantics to preserving reasoning-critical logical structure under privacy constraints. This enables the cloud-side LLM to provide more effective guidance for improving edge-side SLM reasoning. Specifically, LoGic decouples each private query on the edge side into a logic skeleton and an entity mapping, applying sensitivity-aware differentiated LDP protection and a privacy-aware GRPO strategy to preserve useful logical structure under privacy guarantees. The cloud-side LLM then generates a structure-consistent query from the protected structure and derives its step-by-step solution, serving as a query-specific analogical example for the edge side. Finally, the edge-side SLM transfers the cloud-side LLM's reasoning pattern from the structurally similar query to solve the original query. Experiments on complex reasoning tasks show that LoGic delivers stronger reasoning performance with lower leakage than existing baselines.