In word2vec I understand that selecting a vector size of lets say 100 would give me a word vector which has the correlation (kind of) between the word and 100 other words in corpus.
My question is are these 100 words same for each word?
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The vector size is the number of dimensions in the embedding space. Each word in the vocabulary is represented by a vector. The vector size is the same for each word. The values in the vector are different for each word.
In your example, 100 is the vector size. The number of words is far larger, typically thousands or millions.
No, the 100 words that are selected as context words for each word in word2vec are not the same for every word. The context words are chosen based on their proximity to the target word in the training corpus. The idea is to capture the local context of each word, so the context words will vary depending on the specific context in which each word appears. This allows the word vectors to capture different aspects of meaning and relationships between words.