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

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.

Utilizing Complex-valued Network for Learning to Compare Image Patches

At present, the great achievements of convolutional neural network(CNN) in feature and metric learning have attracted many researchers. However, the vast majority of deep network architectures have been used to represent based on real values. The research of complex-valued networks is seldom concerned due to the absence of effective models and suitable distance of complex-valued vector. Motived by recent works, complex vectors have been shown to have a richer representational capacity and efficient complex blocks have been reported, we propose a new approach for learning image descriptors with complex numbers to compare image patches. We also propose a new architecture to learn image similarity function directly based on complex-valued network. We show that our models can significantly outperform the state-of-the art on benchmark datasets. We make the source code of our models publicly available.