Consider two different functional approaches for processing a sequence of vectors $\bar{\mathbf{y}}_1, \bar{\mathbf{y}}_2, \dots, \bar{\mathbf{y}}_{k}$.

Approach A uses a function $s(\bar{\mathbf{y}}_1, \bar{\mathbf{y}}_2, \dots, \bar{\mathbf{y}}_{k})$ which takes the entire sequence as input and produces a single output.

Approach B applies a function $f(\cdot)$ to each vector individually, producing a sequence of outputs: $f(\bar{\mathbf{y}}_1), f(\bar{\mathbf{y}}_2), \dots, f(\bar{\mathbf{y}}_{k})$.

Explain the fundamental difference in the type of information these two approaches can capture from the input sequence.