  A lot of natural language processing problems need to encode the text
sequence as a fix-length vector, which usually involves aggregation process of
combining the representations of all the words, such as pooling or
self-attention. However, these widely used aggregation approaches did not take
higher-order relationship among the words into consideration. Hence we propose
a new way of obtaining aggregation weights, called eigen-centrality
self-attention. More specifically, we build a fully-connected graph for all the
words in a sentence, then compute the eigen-centrality as the attention score
of each word.
  The explicit modeling of relationships as a graph is able to capture some
higher-order dependency among words, which helps us achieve better results in 5
text classification tasks and one SNLI task than baseline models such as
pooling, self-attention and dynamic routing. Besides, in order to compute the
dominant eigenvector of the graph, we adopt power method algorithm to get the
eigen-centrality measure. Moreover, we also derive an iterative approach to get
the gradient for the power method process to reduce both memory consumption and
computation requirement.}
