Shaohua Hu

Haoran Liao, Qinyi Du, Shaohua Hu et al.

Large language models (LLMs) face challenges in solving complex mathematical problems that require comprehensive capacities to parse the statements, associate domain knowledge, perform compound logical reasoning, and integrate the intermediate rationales. Tackling all these problems once could be arduous for LLMs, thus leading to confusion in generation. In this work, we explore the potential of enhancing LLMs with agents by meticulous decomposition and modeling of mathematical reasoning process. Specifically, we propose a formal description of the mathematical solving and extend LLMs with an agent-based zero-shot framework named $\bf{P}$lanner-$\bf{R}$easoner-$\bf{E}$xecutor-$\bf{R}$eflector (PRER). We further provide and implement two MathAgents that define the logical forms and inherent relations via a pool of actions in different grains and orientations: MathAgent-M adapts its actions to LLMs, while MathAgent-H aligns with humankind. Experiments on miniF2F and MATH have demonstrated the effectiveness of PRER and proposed MathAgents, achieving an increase of $12.3\%$($53.9\%\xrightarrow{}66.2\%$) on the MiniF2F, $9.2\%$ ($49.8\%\xrightarrow{}59.0\%$) on MATH, and $13.2\%$($23.2\%\xrightarrow{}35.4\%$) for level-5 problems of MATH against GPT-4. Further analytical results provide more insightful perspectives on exploiting the behaviors of LLMs as agents.

Haoran Liao, Jidong Tian, Shaohua Hu et al.

Large language models (LLMs) still grapple with complex tasks like mathematical reasoning. Despite significant efforts invested in improving prefix prompts or reasoning process, the crucial role of problem context might have been neglected. Accurate recognition of inputs is fundamental for solving mathematical tasks, as ill-formed problems could potentially mislead LLM's reasoning. In this study, we propose a new approach named Problem Elaboration Prompting (PEP) to enhance the mathematical capacities of LLMs. Specifically, PEP decomposes and elucidates the problem context before reasoning, therefore enhancing the context modeling and parsing efficiency. Experiments across datasets and models demonstrate promising performances: (1) PEP demonstrates an overall enhancement in various mathematical tasks. For instance, with the GPT-3.5 model, PEP exhibits improvements of 9.93% and 8.80% on GSM8k through greedy decoding and self-consistency, respectively. (2) PEP can be easily implemented and integrated with other prompting methods. (3) PEP shows particular strength in handling distraction problems.