Lyria: A Genetic Algorithm-Driven Neuro-Symbolic Reasoning Framework for LLMs

While LLMs have demonstrated impressive abilities across various domains, they struggle with two major issues. The first is that LLMs trap themselves into local optima and the second is that they lack exhaustive coverage of the solution space. To investigate and improve these two issues, we propose Lyria, a neuro-symbolic reasoning framework building on the integration of LLMs, genetic algorithms, and symbolic systems, comprising 7 essential components. Through conducting extensive experiments with 4 LLMs across 3 types of problems, we demonstrated the efficacy of Lyria. Furthermore, with 7 additional ablation experiments, we further systematically analyzed and elucidated the factors that affect its performance. In addition, based on Lyria, we extend the ideas to the fine-tuning process of LLMs and introduce LAFT which enables a weaker model to imitate the reasoning process of a stronger model that reason under the Lyria reasoning framework. We demonstrate that the significant effectiveness of LAFT by conducting extensive experiments against 9 constructed baselines. We finally reveal the limitations and provide insights into future directions.