A Neurosymbolic Fast and Slow Architecture for Graph Coloring

2024-12-02

arXiv.org

AI Summary

To address the dual bottlenecks of low efficiency in symbolic solvers and poor reliability of large language models (LLMs) for constraint satisfaction problems (CSPs) such as graph coloring, this paper proposes SOFAI-v2, a neuro-symbolic architecture. It integrates an LLM-driven intuitive system (System 1, S1) with a verifiable symbolic solver (System 2, S2), coordinated by a learnable metacognitive module that dynamically adapts constraint refinement in S1 and triggers precise solving in S2 on demand. Our key contributions are: (i) the first metacognition-guided dual-system collaboration mechanism for CSPs; and (ii) integration of chain-of-thought feedback reinforcement and example-driven fine-tuning. Experiments on graph coloring show that SOFAI-v2 achieves a 16.98% higher success rate and 32.42% faster solving time compared to conventional symbolic solvers, significantly balancing accuracy and efficiency.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability
• Cognitive Modeling & Cognitive Systems: Symbolic Representations
• Machine Learning: Neuro-Symbolic Learning

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

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 Large Language Models (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.

Problem

• Enhancing AI adaptability for complex graph coloring problems
• Integrating fast LLM processing with slow symbolic reasoning
• Improving constraint satisfaction through metacognitive governance mechanisms

Innovation

• Combines fast LLM system with slow symbolic reasoning
• Uses metacognitive governance to switch between systems
• Tailored for graph coloring constraint satisfaction problems