x^{(t)}

Superscript in parentheses — a label

Read x^(t) as "x at step t". A raised number or letter in parentheses is a label, such as a time step. It is never a power.

$K^{(t)}_{\text{cache}}$ is the cache as it stands at step $t$ , not the cache raised to the power $t$ . The parentheses are there to make that clear.

The same convention appears in $\mathbf{x}_p^{(1)}$ (the first image patch) and $V^{(p)}$ (the set of tokens kept by nucleus sampling at threshold $p$ ).

Example

x^{(3)} \;\text{(the value at step 3)} \quad\text{vs}\quad x^3 = x \cdot x \cdot x

With parentheses it is a label; without, a power.

Where the course uses it

12.2 The KV Cache · Module 12, Generationfirst use

Related terms

The KV cacheRead "K cache" and "V cache". They store the keys and values of earlier tokens during generation, so each is computed once instead of again at every step.
Subscripts — picking one itemRead x_i as "x sub i" or "x i". A small lowered letter picks out one item: the i-th entry of a vector, or the i-th vector in a sequence.