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The question is pretty clear from the Title itself, why the Continuous Bag of Words (CBOW) model is called continuous.

I also don't know what exactly "distributed representation" of word vectors mean? Is there any relation between "Continuous" of CBOW and distributed words? Thanks!

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I'm assuming you're referring to the word2vec models, in which case the the original paper here references the usage of the word "continuous" in the model name:

"We denote this model further as CBOW, as unlike standard bag-of-words model, it uses continuous distributed representation of the context".

Since word vectors are elements in $\mathbb{R}^n$, they are inherently continuous, as opposed to the discrete one-hot representations previously used in NLP.

The distributed part of the word vector representations comes from the fact that each word is represented by an array of numbers, meaning that the word meaning is "distributed" among each element of the word vector.

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In cbow, Continuous means that all the values in the array are continuous decimal values. Distributed means they are separated as array elements.

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