Counting in Language with RNNs

In this paper we examine a possible reason for the LSTM outperforming the GRU on language modeling and more specifically machine translation. We hypothesize that this has to do with counting. This is a consistent theme across the literature of long term dependence, counting, and language modeling for RNNs. Using the simplified forms of language -- Context-Free and Context-Sensitive Languages -- we show how exactly the LSTM performs its counting based on their cell states during inference and why the GRU cannot perform as well.