  Despite the significant success of large language models (LLMs), their
extensive memory requirements pose challenges for deploying them in
long-context token generation. The substantial memory footprint of LLM decoders
arises from the necessity to store all previous tokens in the attention module,
a requirement imposed by key-value (KV) caching. In this work, our focus is on
developing an efficient compression technique for the KV cache. Empirical
evidence indicates a significant clustering tendency within key embeddings in
the attention module. Building on this key insight, we have devised a novel
caching method with sublinear complexity, employing online clustering on key
tokens and online $\ell_2$ sampling on values. The result is a provably
accurate and efficient attention decoding algorithm, termed SubGen. Not only
does this algorithm ensure a sublinear memory footprint and sublinear time
complexity, but we also establish a tight error bound for our approach.
Empirical evaluations on long-context question-answering tasks demonstrate that
SubGen significantly outperforms existing and state-of-the-art KV cache
compression methods in terms of performance and efficiency.
