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Definition

Vector Prefix Notation

Vector prefix notation, commonly denoted as Xi\mathbf{X}_{\leq i}, represents the sequence of all vectors from the beginning of a sequence up to and including the ii-th position. For example, if X\mathbf{X} is a sequence of vectors, then Xi=(x1,x2,,xi)\mathbf{X}_{\leq i} = (\mathbf{x}_1, \mathbf{x}_2, \dots, \mathbf{x}_i). This notation is frequently used in autoregressive models to refer to the prefixes of key (Ki\mathbf{K}_{\leq i}) and value (Vi\mathbf{V}_{\leq i}) sequences that have been processed so far.

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Updated 2026-05-02

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