This paper shows that modern word embeddings contain information that distinguishes synonyms and antonyms despite small cosine similarities between corresponding vectors. This information is implicitly encoded in the geometry of the embeddings and could be extracted with a straightforward manifold learning procedure or a contrasting map. Such a map is trained on a small labeled subset of the data and can produce new embeddings 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.