Word embeddings capture semantic relationships between words by representing words as dense vectors in a high-dimensional space. These vectors are learned through a process called word2vec or similar techniques, which typically use large amounts of unlabeled text to train the embeddings.

  Semantic relationships are captured in word embeddings through the distributional hypothesis, which states that words that appear in similar contexts tend to have similar meanings. In other words, words that have similar meanings tend to occur in similar contexts and are likely to be surrounded by similar words.

  The training process learns these relationships by considering the co-occurrence patterns of words in the training data. When two words appear frequently in similar contexts, their word embeddings will be closer together in the high-dimensional space.

  For example, if "king" and "queen" often appear in similar contexts, their word embeddings will be close to each other in the embedding space, capturing the semantic relationship of being related to royalty. Similarly, "man" and "woman" will have embeddings that are close, capturing the relationship of gender.

  These semantic relationships can be further explored using vector operations. For instance, by subtracting the vector representation of "man" from "king" and adding the vector representation of "woman," the resulting vector is close to the vector representation of "queen." This demonstrates that word embeddings can capture analogical relationships between words.

  Overall, word embeddings capture semantic relationships between words by representing them as dense vectors in a high-dimensional space, which are learned based on their co-occurrence patterns in text data. These embeddings enable the exploration and manipulation of semantic relationships through vector operations.