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.