Since modern word embeddings are motivated by a distributional hypothesis and
are, therefore, based on local co-occurrences of words, it is only to be
expected that synonyms and antonyms can have very similar embeddings. Contrary
to this widespread assumption, this paper shows that modern embeddings contain
information that distinguishes synonyms and antonyms despite small cosine
similarities between corresponding vectors. This information is encoded in the
geometry of the embeddings and could be extracted with a manifold learning
procedure or {\em contrasting map}. Such a map is trained on a small labeled
subset of the data and can produce new empeddings that explicitly highlight
specific semantic attributes of the word. The new embeddings produced by the
map are shown to improve the performance on downstream tasks