Yes, word embeddings are capable of capturing word hierarchy to some extent. Word embeddings are vector representations of words in a high-dimensional semantic space, where words with similar meanings are expected to have similar vector representations. This allows us to capture the hierarchical semantic relationships between words.

  One popular method for generating word embeddings is Word2Vec, which uses either the Continuous Bag-of-Words (CBOW) model or the Skip-gram model. These models train on large corpora of text and learn to predict the context or surrounding words of a target word. In doing so, they are able to capture the semantic similarities between words.

  Word embeddings can capture different types of hierarchical relationships between words. For example, they can capture hyponymy (subtype) relationships, such as "cat" is a hyponym of "animal". This is because words that share similar hyponyms are likely to occur in similar contexts and thus have similar vector representations.

  Word embeddings can also capture hypernymy (supertype) relationships, such as "animal" is a hypernym of "cat". This is because the embedding for a hypernym word can be seen as an average or generalization of its hyponym words. For example, in the semantic space, the vector representation of "animal" would be expected to be closer to the vectors of "cat", "dog", "lion", etc., compared to non-animal words.

  Additionally, word embeddings can capture other types of hierarchical relationships like meronymy (part-whole), entailment, and synonymy. For example, "wheel" is a meronym of "car", and "king" entails "ruler".

  However, it's important to note that word embeddings are not perfect and may not capture all aspects of hierarchy accurately. They rely on the distributional hypothesis, which states that words that occur in similar contexts tend to have similar meanings. While this hypothesis holds true for many cases, it may not capture all nuances of word meanings, especially for words with multiple senses or ambiguous usage.