Processing symbolic mathematics algorithmically is an important field of research. It has applications in computer algebra systems and supports researchers as well as applied mathematicians in their daily work. Recently, exploring the ability of neural networks to grasp mathematical concepts has received special attention. One complex task for neural networks is to understand the relation of two mathematical expressions to each other. Despite the advances in learning mathematical relationships, previous studies are limited by small-scale datasets, relatively simple formula construction by few axiomatic rules and even artifacts in the data. With this work, we aim at overcoming these limitations and provide a deeper insight into the representation power of neural networks for classifying mathematical relations. We introduce a novel data generation algorithm to allow for more complex formula compositions and fully include mathematical fields up to high-school level. We research several tree-based and sequential neural architectures for classifying mathematical relations and conduct a systematic analysis of the models against rule-based as well as neural baselines with a focus on varying dataset complexity, generalization abilities, and understanding of syntactical patterns. Our findings show the potential of deep learning models to distinguish high-school level mathematical concepts.

To the present day, computer algebra systems used for calculating mathematical relations on a symbolic level are mainly rule-based systems. Only recently, deep learning has been applied to the task of symbolic mathematics. Researchers succeeded in developing neural networks which can do symbolic calculations of the equivalence of multiple pairing of equations. However, the generator used to create mathematical terms in previous research has several drawbacks and as with all deep learning tasks, the quality of the data used for training the models has a significant impact on the quality of the results. In this work, we propose a new generator for polynomials. We use it to train several recursive neural networks to recognize the equivalence, derivative, or variable substitution between pairs of polynomials for the first time. Our results indicate that these mathematical relations are identifiable with the help of deep learning.

The appropriate tagging of questions on Q&A networks like StackExchange is important for organizing the content of these platforms. Accordingly, recommender systems can help the users by suggesting relevant tags for their questions. The data used as input to these recommender systems can be manifold like headlines of the questions or their entire content. In this work, we explore whether mathematical formulas alone are sufficient for predicting tags of mathematical questions. To achieve this goal, we employ and compare well established methods on both textual and visual representations of formulas. To the best of our knowledge, we are the first to use this kind of limited content as input. Our results show that formulas are helpful for finding proper tags while visual representations outperform textual ones.

In today's aging society, the number of neurodegenerative diseases such as Alzheimer's disease (AD) increases. Reliable tools for automatic early screening as well as monitoring of AD patients are necessary. For that, semantic deficits have been shown to be useful indicators. We present a way to significantly improve the method introduced by Wankerl et al. [1]. The purely statistical approach of n-gram language models (LMs) is enhanced by using the rwthlm toolkit to create neural network language models (NNLMs) with Long Short Term-Memory (LSTM) cells. The prediction is solely based on evaluating the perplexity of transliterations of descriptions of the Cookie Theft picture from DementiaBank's Pitt Corpus. Each transliteration is evaluated on LMs of both control and Alzheimer speakers in a leave-one-speaker-out cross-validation scheme. The resulting perplexity values reveal enough discrepancy to classify patients on just those two values with an accuracy of 85.6% at equal-error-rate.