For LLM decoder, how exactly is the K, Q, V for each decoding step?

Say my input prompt is "today is a" (good day).

At t= 0 (generation step 0): K, Q, V are the projections of the sequence ("today is a") Then say the next token generated is "good"

At t= 1(generation step 1): Which one is true:

• K, Q, V are the projections of the sequence ("today is a good")

OR

• K, Q, are the projections of the sequence ("today is a") , V is the projection of sequence ("good")?

For a transformer decoder, how exactly are K, Q, and V for each decoding step?

Assume my input prompt is "today is a" (good day).

At t= 0 (generation step 0): K, Q, and V are the projections of the sequence ("today is a") Then say the next token generated is "good".

At t=1 (generation step 1): Which one is true:

1. K, Q, and V are the projections of the sequence ("today is a good")
2. K, Q, are the projections of the sequence ("today is a"), and V is the projection of the sequence ("good")?