Towards Formula Translation using Recursive Neural Networks

Abstract

While it has become common to perform automated translations on natural language, performing translations between different representations of mathematical formulae has thus far not been possible. We implemented the first translator for mathematical formulae based on recursive neural networks. We chose recursive neural networks because mathematical formulae inherently include a structural encoding. In our implementation, we developed new techniques and topologies for recursive tree-to-tree neural networks based on multi-variate multi-valued Long Short-Term Memory cells. We propose a novel approach for mini-batch training that utilizes clustering and tree traversal. We evaluate our translator and analyze the behavior of our proposed topologies and techniques based on a translation from generic LaTeX to the semantic LaTeX notation. We use the semantic LaTeX notation from the Digital Library for Mathematical Formulae and the Digital Repository for Mathematical Formulae at the National Institute for Standards and Technology. We find that a simple heuristics-based clustering algorithm outperforms the conventional clustering algorithms on the task of clustering binary trees of mathematical formulae with respect to their topology. Furthermore, we find a mask for the loss function, which can prevent the neural network from finding a local minimum of the loss function. Given our preliminary results, a complete translation from formula to formula is not yet possible. However, we achieved a prediction accuracy of 47.05% for predicting symbols at the correct position and an accuracy of 92.3% when ignoring the predicted position. Concluding, our work advances the field of recursive neural networks by improving the training speed and quality of training. In the future, we will work towards a complete translation allowing a machine-interpretation of LaTeX formulae.