A Neurosymbolic Fast and Slow Architecture for Graph Coloring

Constraint Satisfaction Problems (CSPs) present significant challenges to artificial intelligence due to their intricate constraints and the necessity for precise solutions. Existing symbolic solvers are often slow, and prior research has shown that Large Language Models (LLMs) alone struggle with CSPs because of their complexity. To bridge this gap, we build upon the existing SOFAI architecture (SOFAI_v1), which adapts Daniel Kahneman's ''Thinking, Fast and Slow'' cognitive model to AI. Our enhanced architecture, SOFAI_v2, integrates refined metacognitive governance mechanisms to improve adaptability across complex domains, specifically tailored here for solving the graph coloring problem, a specific type of CSP. SOFAI_v2 combines a fast System 1 (S1), leveraging LLMs, with a deliberative System 2 (S2), governed by a metacognition module. S1's initial solutions, often limited by constraint adherence issues, are improved through targeted feedback and examples from metacognition, aligning S1 more closely with CSP requirements. If S1 fails to resolve the problem, metacognition strategically invokes S2, ensuring accurate and reliable solutions. Our empirical results demonstrate that SOFAI_v2 achieves a 10.5% higher success rate and is up to 30% faster than a traditional symbolic solver in solving graph coloring problems.