Incorporating Graph Attention Mechanism into Geometric Problem Solving Based on Deep Reinforcement Learning

📄 arXiv: 2403.14690v1 📥 PDF

作者: Xiuqin Zhong, Shengyuan Yan, Gongqi Lin, Hongguang Fu, Liang Xu, Siwen Jiang, Lei Huang, Wei Fang

分类: cs.CY, cs.AI, cs.CL, cs.LG

发布日期: 2024-03-14

💡 一句话要点

提出基于图注意力机制的深度强化学习框架以解决几何问题

🎯 匹配领域: 支柱二：RL算法与架构 (RL & Architecture)

关键词: 深度强化学习 图注意力机制 几何问题求解 自动化教育 自然语言处理

📋 核心要点

  1. 现有方法在自动添加辅助组件时面临复杂的选择问题，导致效率低下。
  2. 本文提出了一种基于图注意力机制的深度强化学习框架，旨在高效自动添加辅助组件。
  3. 实验结果显示，A3C-RL算法的平均精度提升了32.7%，并在几何问题上超越了人类表现。

📝 摘要（中文）

在在线教育背景下，设计自动几何问题求解器被视为通用数学人工智能的重要一步。现有方法在添加辅助组件时面临选择合适组件的复杂性，通常需要耗费大量策略搜索以提高准确性。为此，本文提出了一种基于语言模型（如BERT）的深度强化学习框架，通过引入图注意力机制来减少策略搜索空间，并提出了名为A3C-RL的新算法。实验结果表明，A3C-RL算法在精度上比传统的MCTS提升了32.7%，并在中国年度大学入学数学考试中超越了人类表现。

🔬 方法详解

问题定义：本文旨在解决在线教育中几何问题的自动求解难题。现有方法在添加辅助组件时，需进行大量策略搜索，导致效率低下。

核心思路：通过引入图注意力机制来减少策略搜索空间，聚焦于与结论相关的组件，同时设计A3C-RL算法以强制代理选择最佳策略，从而提高求解效率和准确性。

技术框架：整体框架包括数据输入、图注意力机制模块、策略选择模块（A3C-RL）和输出模块。首先，通过图注意力机制筛选出相关组件，然后利用强化学习选择最佳策略。

关键创新：引入图注意力机制（AttnStrategy）以减少策略搜索空间，并结合BERT作为记忆组件，显著提高了求解效率和准确性。与传统方法相比，A3C-RL算法在策略选择上更具针对性。

关键设计：在A3C-RL算法中，设置了特定的奖励机制以鼓励选择高效策略，同时优化了网络结构以适应图注意力机制的输入特征。

📊 实验亮点

实验结果显示，A3C-RL算法在平均精度上比传统的蒙特卡洛树搜索（MCTS）提升了32.7%。此外，该算法在中国年度大学入学数学考试的几何问题上超越了人类表现，展现出其强大的求解能力。

🎯 应用场景

该研究的潜在应用领域包括在线教育、自动化数学求解和智能辅导系统。通过提高几何问题的求解效率和准确性，能够为学生提供更好的学习支持，推动教育技术的发展。

📄 摘要（原文）

In the context of online education, designing an automatic solver for geometric problems has been considered a crucial step towards general math Artificial Intelligence (AI), empowered by natural language understanding and traditional logical inference. In most instances, problems are addressed by adding auxiliary components such as lines or points. However, adding auxiliary components automatically is challenging due to the complexity in selecting suitable auxiliary components especially when pivotal decisions have to be made. The state-of-the-art performance has been achieved by exhausting all possible strategies from the category library to identify the one with the maximum likelihood. However, an extensive strategy search have to be applied to trade accuracy for ef-ficiency. To add auxiliary components automatically and efficiently, we present deep reinforcement learning framework based on the language model, such as BERT. We firstly apply the graph attention mechanism to reduce the strategy searching space, called AttnStrategy, which only focus on the conclusion-related components. Meanwhile, a novel algorithm, named Automatically Adding Auxiliary Components using Reinforcement Learning framework (A3C-RL), is proposed by forcing an agent to select top strategies, which incorporates the AttnStrategy and BERT as the memory components. Results from extensive experiments show that the proposed A3C-RL algorithm can substantially enhance the average precision by 32.7% compared to the traditional MCTS. In addition, the A3C-RL algorithm outperforms humans on the geometric questions from the annual University Entrance Mathematical Examination of China.