Translating Math Formula Images to LaTeX Sequences Using Deep Neural Networks with Sequence-level Training

-- In this paper we propose a deep neural network model with an encoder-decoder architecture that translates images of math formulas into their LaTeX markup sequences. The enc oder is a convolutional neural network (CNN) that transforms images into a group of feature maps. To better capture the spatia l relationships of math symbols, the feature maps are augmented with 2D positional encoding before being unfolded into a vector. The d ecoder is a stacked bidirectional long short-term memory (LSTM) model integrated with the soft attention mechanism, which works as a language model to translate the encoder output into a sequence of LaTeX tokens. The neural network is trained in two steps. The first step is token-level training using the Maximum-Like lihood Estimation (MLE) as the objective function. At comp letion of the token-level training, the sequence-level training objective function is employed to optimize the overall model based on the policy gradient algorithm from reinforcement learning. Our design a lso overcomes the exposure bias problem by closing the feedback l oop in the decoder during sequence-level training, i.e., feedi ng in the predicted token instead of the ground truth token at every time step. The model is trained and evaluated on the IM2LATEX-100K dataset and shows state-of-the-art performance on both sequence-based and image-based evaluation metrics. Math formulas often carry the most significant tech nical substances in many science, technology, engineering and math (STEM) fields. Being able to extract the math formulas from digital documents and translate them into markup la nguages is very useful for a wide range of information retriev al tasks. Portable Document Format (PDF) is the de facto standard publication format, which makes document distributi on very easy and reliable.