Set of Sequential Key-Value Pairs

Let a sequence of vectors be constructed where the first element is $a_1 = [0.1, 0.9]$ and the second element is $a_2 = [0.4, 0.6]$. The third element has multiple potential versions, and the 5th version is given as $a_3^{(5)} = [0.8, 0.2]$. According to the notational definition $\mathbf{a}_{\leq i+1} = (a_1, ..., a_i, a_{i+1}^{(j)})$, what is the specific sequence represented by $\mathbf{a}_{\leq 3}$ when using the 5th version of the 3rd element?

Key Matrix for Causal Attention (K_≤i)

Deconstructing Vector Prefix Notation

Key-Value Cache

Consider a sequence of vectors represented as $\mathbf{Z} = (\mathbf{z}_1, \mathbf{z}_2, \mathbf{z}_3, \mathbf{z}_4, \mathbf{z}_5)$. The notation $\mathbf{Z}_{\leq 3}$ represents the subsequence containing only the first two vectors, $(\mathbf{z}_1, \mathbf{z}_2)$.