# Mamba Hawkes Process

arXiv: https://arxiv.org/abs/2407.05302 · HTML: https://mlsanity.com/paper/2407.05302/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Placed in Time series forecasting with SSMs, one of 10 directions in State-space sequence models (S4, Mamba).
- Builds on 21 of its 38 references that are in the map.
- First posted on arXiv 7 Jul 2024.

## Placed in

- State-space sequence models (S4, Mamba) / [Time series forecasting with SSMs](https://mlsanity.com/ssm/time-series-forecasting-with-ssms/)

## Builds on (most cited first, 21 of 21)

- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling](https://mlsanity.com/paper/1412.3555/) (2014)
- [RWKV: Reinventing RNNs for the Transformer Era](https://mlsanity.com/paper/2305.13048/) (2023)
- [Combining Recurrent, Convolutional, and Continuous-time Models with Linear State-Space Layers](https://mlsanity.com/paper/2110.13985/) (2021)
- [HiPPO: Recurrent Memory with Optimal Polynomial Projections](https://mlsanity.com/paper/2008.07669/) (2020)
- [Hungry Hungry Hippos: Towards Language Modeling with State Space Models](https://mlsanity.com/paper/2212.14052/) (2022)
- [Jamba: A Hybrid Transformer-Mamba Language Model](https://mlsanity.com/paper/2403.19887/) (2024)
- [Long Range Language Modeling via Gated State Spaces](https://mlsanity.com/paper/2206.13947/) (2022)
- [Transformer Hawkes Process](https://mlsanity.com/paper/2002.09291/) (2020)
- [HyenaDNA: Long-Range Genomic Sequence Modeling at Single Nucleotide Resolution](https://mlsanity.com/paper/2306.15794/) (2023)
- [Supervised Reinforcement Learning with Recurrent Neural Network for Dynamic Treatment Recommendation](https://mlsanity.com/paper/1807.01473/) (2018)
- [Modeling The Intensity Function Of Point Process Via Recurrent Neural Networks](https://mlsanity.com/paper/1705.08982/) (2017)
- [SEISMIC: A Self-Exciting Point Process Model for Predicting Tweet Popularity](https://mlsanity.com/paper/1506.02594/) (2015)
- [SNAP: A General Purpose Network Analysis and Graph Mining Library](https://mlsanity.com/paper/1606.07550/) (2016)
- [Wasserstein Learning of Deep Generative Point Process Models](https://mlsanity.com/paper/1705.08051/) (2017)
- [Learning Temporal Point Processes via Reinforcement Learning](https://mlsanity.com/paper/1811.05016/) (2018)
- [Group Network Hawkes Process](https://mlsanity.com/paper/2002.08521/) (2020)
- [Temporal Attention Augmented Transformer Hawkes Process](https://mlsanity.com/paper/2112.14472/) (2021)
- [Universal Transformer Hawkes Process with Adaptive Recursive Iteration](https://mlsanity.com/paper/2112.14479/) (2021)
- [RoTHP: Rotary Position Embedding-based Transformer Hawkes Process](https://mlsanity.com/paper/2405.06985/) (2024)

## Built on by (most cited first, 5 of 5)

- [Deep Continuous-Time State-Space Models for Marked Event Sequences](https://mlsanity.com/paper/2412.19634/) (2024)
- [TPP-LLM: Modeling Temporal Point Processes by Efficiently Fine-Tuning Large Language Models](https://mlsanity.com/paper/2410.02062/) (2024)
- [Advances in Temporal Point Processes: Bayesian, Neural, and LLM Approaches](https://mlsanity.com/paper/2501.14291/) (2025)
- [Hyper Hawkes Processes: Interpretable Models of Marked Temporal Point Processes](https://mlsanity.com/paper/2511.01096/) (2025)
- [Exact Phase-Type Point Processes for Certified Measurement and Prediction of Event Streams](https://mlsanity.com/paper/2610.14948/) (2026)

## Abstract (arXiv)

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.