A computational system processes the 5-word phrase 'deep learning models are powerful'. It generates a sequence of cumulative average values, where $\mathbf{\overline{y}}_i$ represents the average value after processing the first $i$ words. A function, denoted as $s(\cdot)$, is then applied to this sequence to perform a final calculation. Based on the notation $s(\mathbf{\overline{y}}_1...\mathbf{\overline{y}}_{k-1})$, what is the direct input to the function $s$ in this specific scenario?

Analyzing Information Flow in a System

Consider a system where a function s processes a series of k calculated average vectors, denoted $\bar{\mathbf{y}}_1, \bar{\mathbf{y}}_2, ..., \bar{\mathbf{y}}_k$. The notation $s(\bar{\mathbf{y}}_1...\bar{\mathbf{y}}_k)$ signifies that the function s is applied to each vector individually, producing a sequence of outputs $s(\bar{\mathbf{y}}_1), s(\bar{\mathbf{y}}_2), ..., s(\bar{\mathbf{y}}_k)$.