Advanced Weakly-Supervised Formula Exploration for Neuro-Symbolic Mathematical Reasoning

Abstract: In recent years, neuro-symbolic methods have become a popular and powerful approach that augments artificial intelligence systems with the capability to perform abstract, logical, and quantitative deductions with enhanced precision and controllability. Recent studies successfully performed symbolic reasoning by leveraging various machine learning models to explicitly or implicitly predict intermediate labels that provide symbolic instructions. However, these intermediate labels are not always prepared for every task as a part of training data, and pre-trained models, represented by LLMs, also do not consistently generate valid symbolic instructions with their intrinsic knowledge. On the other hand, existing work developed alternative learning techniques that allow the learning system to autonomously uncover optimal symbolic instructions. Nevertheless, their performance also exhibits limitations when faced with relatively huge search spaces or more challenging reasoning problems. In view of this, in this work, we put forward an advanced practice for neuro-symbolic reasoning systems to explore the intermediate labels with weak supervision from problem inputs and final outputs. Our experiments on the Mathematics dataset illustrated the effectiveness of our proposals from multiple aspects.