Neural Temporal Point Processes (TPPs) are the prevalent paradigm for modeling continuous-time event sequences, such as user activities on the web and financial transactions. In real-world applications, event data is typically received in a \emph{streaming} manner, where the distribution of patterns may shift over time. Additionally, \emph{privacy and memory constraints} are commonly observed in practical scenarios, further compounding the challenges. Therefore, the continuous monitoring of a TPP to learn the streaming event sequence is an important yet under-explored problem. Our work paper addresses this challenge by adopting Continual Learning (CL), which makes the model capable of continuously learning a sequence of tasks without catastrophic forgetting under realistic constraints. Correspondingly, we propose a simple yet effective framework, PromptTPP\footnote{Our code is available at {\small \url{ https://github.com/yanyanSann/PromptTPP}}}, by integrating the base TPP with a continuous-time retrieval prompt pool. The prompts, small learnable parameters, are stored in a memory space and jointly optimized with the base TPP, ensuring that the model learns event streams sequentially without buffering past examples or task-specific attributes. We present a novel and realistic experimental setup for modeling event streams, where PromptTPP consistently achieves state-of-the-art performance across three real user behavior datasets.

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