  Similarity measures based purely on word embeddings are comfortably competing
with much more sophisticated deep learning and expert-engineered systems on
unsupervised semantic textual similarity (STS) tasks. In contrast to commonly
used geometric approaches, we treat a single word embedding as e.g. 300
observations from a scalar random variable. Using this paradigm, we first
illustrate that similarities derived from elementary pooling operations and
classic correlation coefficients yield excellent results on standard STS
benchmarks, outperforming many recently proposed methods while being much
faster and trivial to implement. Next, we demonstrate how to avoid pooling
operations altogether and compare sets of word embeddings directly via
correlation operators between reproducing kernel Hilbert spaces. Just like
cosine similarity is used to compare individual word vectors, we introduce a
novel application of the centered kernel alignment (CKA) as a natural
generalisation of squared cosine similarity for sets of word vectors. Likewise,
CKA is very easy to implement and enjoys very strong empirical results.
