1Cademy - Function of a Sequence of Averaged Vectors Notation ($$s(\bar{\mathbf{y}}_1 \dots \bar{\mathbf{y}}

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Function of a Sequence of Averaged Vectors Notation ( $s(\bar{\mathbf{y}}_1 \dots \bar{\mathbf{y}}_{k-1})$ )

The expression $s(\bar{\mathbf{y}}_1 \dots \bar{\mathbf{y}}_{k-1})$ represents a function, denoted by $s$ , that takes a sequence of averaged vectors as its input. The sequence consists of terms from the first vector, $\bar{\mathbf{y}}_1$ , up to the $(k-1)$ -th vector, $\bar{\mathbf{y}}_{k-1}$ .

Updated 2026-07-03

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Reference of Foundations of Large Language Models Course

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Input for Next-Token Prediction
Consider the expression $s(\bar{\mathbf{y}}_1...\bar{\mathbf{y}}_{k-1})$ , where 's' is a function that operates on a sequence of averaged vectors. What does this notation imply about the information used to compute an outcome for a given step 'k'?
Consider a process where the outcome at step k is determined by a function s(ȳ₁...ȳₖ₋₁). This function takes a sequence of averaged vectors from step 1 to k-1 as input. Based on this definition, the outcome at step 10 is completely independent of the vector ȳ₂.