how it the embedding model trained? Are the embeddings simply extracted from chatGPT4 or are they trained differently from the beginning (pre-training stage)?
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OpenAI embeddings are not extracted from chatGPT. They are trained independently.
According to the original article OpenAI used to present their embeddings, the model used to obtain the embeddings is a Transformer encoder (like BERT or RoBERTa) trained on the task to distinguish if 2 pieces of text where consecutive in the original source text/code.
Also, as described in their last announcement, their embeddings now are also trained with a technique called "Matrioska representation learning" (see the article) that enables them to have their dimensionality reduced to take less storage space if needed.
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