  Standard Large Language Models (LLMs) struggle with handling dialogues with
long contexts due to efficiency and consistency issues. According to our
observation, dialogue contexts are highly structured, and the special token of
\textit{End-of-Utterance} (EoU) in dialogues has the potential to aggregate
information. We refer to the EoU tokens as ``conversational attention sinks''
(conv-attn sinks). Accordingly, we introduce StreamingDialogue, which
compresses long dialogue history into conv-attn sinks with minimal losses, and
thus reduces computational complexity quadratically with the number of sinks
(i.e., the number of utterances). Current LLMs already demonstrate the ability
to handle long context window, e.g., a window size of 200k or more. To this
end, by compressing utterances into EoUs, our method has the potential to
handle more than 200k of utterances, resulting in a prolonged dialogue
learning. In order to minimize information losses from reconstruction after
compression, we design two learning strategies of short-memory reconstruction
(SMR) and long-memory reactivation (LMR). Our method outperforms strong
baselines in dialogue tasks and achieves a 4 $\times$ speedup while reducing
memory usage by 18 $\times$ compared to dense attention recomputation.
