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Bitext mining: Given a sentence in one language, find its translation in a collection of sentences in another language using the cosine similarity of embeddings.
Classification: identify the kind of text you're dealing with using logistic regression on the embeddings.
Clustering: group similar texts together using k-means clustering on the embeddings.
Pair Classification: determine whether two texts are paraphrases of each other by using a binary threshold on the cosine similarity of the embeddings.
Reranking: given a query and a list of potential results, sort relevant results ahead of irrelevant ones by sorting according to the cosine similarity of embeddings.
Etc etc.
These are MTEB benchmark tasks https://arxiv.org/pdf/2210.07316.pdf . If you have no need for something like that, good for you, you don't need to care how well embeddings work for these tasks.
[1] https://web.stanford.edu/~jurafsky/slp3/
I tried to create a Kaggle (TensorFlow Hub, TensorFlow Quantum) competition for motivating alternative formalisms but was unable to publish it because all Kaggle competitions must be evaluated with information retrieval metrics. Talk about a one-track mindset!
Today work in NLP advances by ``leaderboards'' and dubious, language-specific evaluation datasets that the same authors stand to benefit from when their proprietary model is praised for doing well on the evaluation criteria they invented a few months back. It validates the price hike for access to their proprietary models.
These formalisms that do work are at odds with Firth Mode, the preferred representation for Google (Stanford, OpenAI), so I guess we should be thankful they're still in the book. If you're interested in language, though, I'd suggest picking up a different book.