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 encoder is a convolutional neural network that transforms images into a group of feature maps. To better capture the spatial relationships of math symbols, the feature maps are augmented with 2D positional encoding before being unfolded into a vector. The decoder is a stacked bidirectional long short-term memory 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 likelihood estimation as the objective function. At completion 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 also overcomes the exposure bias problem by closing the feedback loop in the decoder during sequence-level training, i.e., feeding in the predicted token instead of the ground truth token at every time step. The model is trained and evaluated on the IM2LATEX-100 K dataset and shows state-of-the-art performance on both sequence-based and image-based evaluation metrics.