Modeling Complex Mathematical Reasoning via Large Language Model based
  MathAgent
Authors: name: Haoran Liao, name: Qinyi Du, name: Shaohua Hu, name: Hao He, name: Yanyan Xu, name: Jidong Tian, name: Yaohui Jin

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
Planner-Reasoner-Executor-Reflector (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%66.2%) on the MiniF2F, 9.2%
(49.8%59.0%) on MATH, and
13.2%(23.2%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.