A development team is using a large, pre-trained language model for a real-time, multi-turn conversational agent. They observe that while the initial response to a user's first message is fast, the time it takes to generate each subsequent response in the same conversation increases progressively. System monitoring reveals that the memory allocated for the ongoing conversation grows linearly with the length of the conversation history. The team has confirmed this is not a network or server load issue. Based on the typical step-by-step (autoregressive) generation process, what specific data structure associated with the self-attention mechanism is the most likely cause of both the increasing latency and growing memory footprint? Explain the connection.