Incorporating Graph Attention Mechanism into Geometric Problem Solving
  Based on Deep Reinforcement Learning
Xiuqin Zhong Shengyuan Yan Gongqi Lin Hongguang Fu Liang Xu Siwen Jiang Lei Huang Wei Fang
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.