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A sequence of embedding vectors, indexed from a starting point $m$ to an ending point $len$, is represented as: $\mathbf{e}_m, \mathbf{e}_{m+1}, \mathbf{e}_{m+2}, \dots, \mathbf{e}_{len-1}, \mathbf{e}_{len}$. This notation serves as a specific application of indexed sequence representation for embedding vectors within sequence models.

Example of Indexed Embedding Sequence Notation

Consider the sentence 'Large language models are powerful tools', where the words are indexed starting from 1. The notation `e_3, e_4, e_5` represents the sequence of embedding vectors for the words 'models are powerful'.

A model is given the sentence 'Natural language processing is a subfield of AI.' The words are indexed starting from 1. Write the standard notation for the sequence of embedding vectors corresponding to the subsequence 'processing is a subfield'.

Representing a Subsequence with Embedding Notation

A model processes the sentence 'The quick brown fox jumps'. The sentence is tokenized, and each token is converted into a corresponding vector. The tokens are indexed starting from 1, so 'The' corresponds to index 1, 'quick' to index 2, and so on. Using the standard notation for a sequence of these vectors, how would you represent the vectors for the subsequence 'quick brown fox'?

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