Exploring Human-Like Mathematical Reasoning: Perspectives on Generalizability and Efficiency

Mathematical reasoning, a fundamental aspect of human cognition, poses significant challenges for artificial intelligence (AI) systems. Despite recent advancements in natural language processing (NLP) and large language models (LLMs), AI's ability to replicate human-like reasoning, generalization, and efficiency remains an ongoing research challenge. In this dissertation, we address key limitations in MWP solving, focusing on the accuracy, generalization ability and efficiency of AI-based mathematical reasoners by applying human-like reasoning methods and principles.

This dissertation introduces several innovative approaches in mathematical reasoning. First, a numeracy-driven framework is proposed to enhance math word problem (MWP) solvers by integrating numerical reasoning into model training, surpassing human-level performance on benchmark datasets. Second, a novel multi-solution framework captures the diversity of valid solutions to math problems, improving the generalization capabilities of AI models. Third, a customized knowledge distillation technique, termed Customized Exercise for Math Learning (CEMAL), is developed to create tailored exercises for smaller models, significantly improving their efficiency and accuracy in solving MWPs. Additionally, a multi-view fine-tuning paradigm (MinT) is introduced to enable smaller models to handle diverse annotation styles from different datasets, improving their adaptability and generalization. To further advance mathematical reasoning, a benchmark, MathChat, is introduced to evaluate large language models (LLMs) in multi-turn reasoning and instruction-following tasks, demonstrating significant performance improvements. Finally, new inference-time verifiers, Math-Rev and Code-Rev, are developed to enhance reasoning verification, combining language-based and code-based solutions for improved accuracy in both math and code reasoning tasks.

In summary, this dissertation provides a comprehensive exploration of these challenges and contributes novel solutions that push the boundaries of AI-driven mathematical reasoning. Potential future research directions are also discussed to further extend the impact of this dissertation.