  Irregular and asynchronous event sequences are prevalent in many domains,
such as social media, finance, and healthcare. Traditional temporal point
processes (TPPs), like Hawkes processes, often struggle to model mutual
inhibition and nonlinearity effectively. While recent neural network models,
including RNNs and Transformers, address some of these issues, they still face
challenges with long-term dependencies and computational efficiency. In this
paper, we introduce the Mamba Hawkes Process (MHP), which leverages the Mamba
state space architecture to capture long-range dependencies and dynamic event
interactions. Our results show that MHP outperforms existing models across
various datasets. Additionally, we propose the Mamba Hawkes Process Extension
(MHP-E), which combines Mamba and Transformer models to enhance predictive
capabilities. We present the novel application of the Mamba architecture to
Hawkes processes, a flexible and extensible model structure, and a theoretical
analysis of the synergy between state space models and Hawkes processes.
Experimental results demonstrate the superior performance of both MHP and
MHP-E, advancing the field of temporal point process modeling.
