An autoregressive language model is generating a sequence of tokens. The attention mechanism has already processed the first three tokens, resulting in the following Value matrix V stored in its cache, where each row corresponds to a token:

V = [[0.1, 0.8], [0.5, 0.2], [0.9, 0.3]]

For the fourth token, the model computes a new value vector:

v_new = [0.4, 0.6]

According to the standard update rule for the cache, what will the new Value matrix V be after this fourth token is processed?

Analysis of KV Cache Update Methods

During autoregressive inference, the Value matrix in the cache is updated by replacing the oldest value vector with the newly computed value vector for the current token.