A Neurosymbolic Fast and Slow Architecture for Graph Coloring

Abstract: 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 LLMs alone struggle with CSPs because of their complexity. To bridge this gap, we build upon the existing SOFAI architecture (or 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 for solving CSPs like graph coloring. SOFAI-v2 combines a fast System 1 (S1) based on LLMs with a deliberative System 2 (S2) governed by a metacognition module. S1's initial solutions, often limited by non-adherence to constraints, are enhanced through metacognitive governance, which provides targeted feedback and examples to adapt S1 to CSP requirements. If S1 fails to solve the problem, metacognition strategically invokes S2, ensuring accurate and reliable solutions. With empirical results, we show that SOFAI-v2 for graph coloring problems achieves a 16.98% increased success rate and is 32.42% faster than symbolic solvers.