CoG: Controllable Graph Reasoning via Relational Blueprints and Failure-Aware Refinement over Knowledge Graphs

Large Language Models (LLMs) have demonstrated remarkable reasoning capabilities but often grapple with reliability challenges like hallucinations. While Knowledge Graphs (KGs) offer explicit grounding, existing paradigms of KG-augmented LLMs typically exhibit cognitive rigidity--applying homogeneous search strategies that render them vulnerable to instability under neighborhood noise and structural misalignment leading to reasoning stagnation. To address these challenges, we propose CoG, a training-free framework inspired by Dual-Process Theory that mimics the interplay between intuition and deliberation. First, functioning as the fast, intuitive process, the Relational Blueprint Guidance module leverages relational blueprints as interpretable soft structural constraints to rapidly stabilize the search direction against noise. Second, functioning as the prudent, analytical process, the Failure-Aware Refinement module intervenes upon encountering reasoning impasses. It triggers evidence-conditioned reflection and executes controlled backtracking to overcome reasoning stagnation. Experimental results on three benchmarks demonstrate that CoG significantly outperforms state-of-the-art approaches in both accuracy and efficiency.