  In this paper we delve deep in the Transformer architecture by investigating
two of its core components: self-attention and contextual embeddings. In
particular, we study the identifiability of attention weights and token
embeddings, and the aggregation of context into hidden tokens. We show that,
for sequences longer than the attention head dimension, attention weights are
not identifiable. We propose effective attention as a complementary tool for
improving explanatory interpretations based on attention. Furthermore, we show
that input tokens retain to a large degree their identity across the model. We
also find evidence suggesting that identity information is mainly encoded in
the angle of the embeddings and gradually decreases with depth. Finally, we
demonstrate strong mixing of input information in the generation of contextual
embeddings by means of a novel quantification method based on gradient
attribution. Overall, we show that self-attention distributions are not
directly interpretable and present tools to better understand and further
investigate Transformer models.
