Given the task definition and input, reply with output. In this task, you will be presented with a context from an academic paper and a question separated with a 
. You have to answer the question based on the context.

Building on these results, we take a somewhat more systematic approach to looking for interpretable hidden state dimensions, by using decision trees to predict individual hidden state dimensions (Figure 2 ). We visualize the overall dynamics of the hidden states by coloring the training data with the k-means clusters on the state vectors (Figures 3 , 3 ). In Figures 3 and 3 , we color-code the training data with the 10 HMM states. In Figures 3 and 3 , we apply k-means clustering to the LSTM state vectors, and color-code the training data with the clusters. 
 Question: Which methods do the authors use to reach the conclusion that LSTMs and HMMs learn complementary information?

decision trees to predict individual hidden state dimensions apply k-means clustering to the LSTM state vectors, and color-code the training data with the clusters