Relating RNN layers with the spectral WFA ranks in sequence modelling

We analyse Recurrent Neural Networks (RNNs) to understand the significance of multiple LSTM layers. We argue that the Weighted Finite-state Automata (WFA) trained using a spectral learning algorithm are helpful to analyse RNNs. Our results suggest that multiple LSTM layers in RNNs help learning distributed hidden states, but have a smaller impact on the ability to learn long-term dependencies. The analysis is based on the empirical results, however relevant theory (whenever possible) was discussed to justify and support our conclusions.