Many natural and formal languages contain words or symbols that require a matching counterpart for making an expression well-formed. The combination of opening and closing brackets is a typical example of such a construction. Due to their commonness, the ability to follow such rules is important for language modeling. Currently, recurrent neural networks (RNNs) are extensively used for this task. We investigate whether they are capable of learning the rules of opening and closing brackets by applying them to synthetic Dyck languages that consist of different types of brackets. We provide an analysis of the statistical properties of these languages as a baseline and show strengths and limits of Elman-RNNs, GRUs and LSTMs in experiments on random samples of these languages. In terms of perplexity and prediction accuracy, the RNNs get close to the theoretical baseline in most cases.

Word embeddings are high-dimensional vector representations of words and are thus difficult to interpret. In order to deal with this, we introduce an unsupervised parameter free method for creating a hierarchical graphical clustering of the full ensemble of word vectors and show that this structure is a geometrically meaningful representation of the original relations between the words. This newly obtained representation can be used for better understanding and thus improving the embedding algorithm and exhibits semantic meaning, so it can also be utilized in a variety of language processing tasks like categorization or measuring similarity.