Mamba Hawkes Process

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.

RoTHP: Rotary Position Embedding-based Transformer Hawkes Process

Temporal Point Processes (TPPs), especially Hawkes Process are commonly used for modeling asynchronous event sequences data such as financial transactions and user behaviors in social networks. Due to the strong fitting ability of neural networks, various neural Temporal Point Processes are proposed, among which the Neural Hawkes Processes based on self-attention such as Transformer Hawkes Process (THP) achieve distinct performance improvement. Although the THP has gained increasing studies, it still suffers from the {sequence prediction issue}, i.e., training on history sequences and inferencing about the future, which is a prevalent paradigm in realistic sequence analysis tasks. What's more, conventional THP and its variants simply adopt initial sinusoid embedding in transformers, which shows performance sensitivity to temporal change or noise in sequence data analysis by our empirical study. To deal with the problems, we propose a new Rotary Position Embedding-based THP (RoTHP) architecture in this paper. Notably, we show the translation invariance property and {sequence prediction flexibility} of our RoTHP induced by the {relative time embeddings} when coupled with Hawkes process theoretically. Furthermore, we demonstrate empirically that our RoTHP can be better generalized in sequence data scenarios with timestamp translations and in sequence prediction tasks.