cs.LGJul 7, 2024

Mamba Hawkes Process for Event Sequence Modeling

Authors: Shan Dai, Yuyang Shen, Yuyang Liang, Chenhao Ma, Anningzhe Gao

Organizations: Shenzhen Research Institute of Big Data

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Abstract

Modeling asynchronous event sequences is crucial in numerous real-world applications such as healthcare monitoring, financial transaction analysis, and so on. Traditional temporal point processes, including Hawkes Processes, often fail to capture complex dependencies due to their parametric limitations. While neural approaches like RNNs and Transformers have improved flexibility, they struggle with computational inefficiency, and attention saturation. In this paper, we introduce the Mamba Hawkes Process (MHP), the first framework to integrate selective state space model (Mamba) with temporal point processes. MHP leverages time-varying state transitions and input-dependent gating to efficiently encode event history and capture long-term dependencies with linear complexity. Importantly, we provide theoretical guarantees showing that MHP generalizes both classical multi-exponential Hawkes processes and exponential-decay gated RNNs, underscoring its expressive power and theoretical soundness. To address the inherent constraints of pure state space models in handling heterogeneous event interactions, we further develop Adaptive Mamba Hawkes Process (A-MHP) that incorporates two novel mechanisms: a Time-Scaling Mechanism that adaptively weights time intervals based on event type and history, and a Dual-Channel State Transition that adaptively processes event content and temporal dynamics for more refined state updates. Extensive experiments on synthetic and realworld datasets demonstrate that MHP and A-MHP consistently outperform state-of-the-art baselines in event prediction tasks, particularly in long-sequence scenarios. Our work establishes a scalable and theoretically grounded paradigm for event sequence modeling, with practical implications for predictive maintenance, anomaly detection, and dynamic system analysis.

Figures & tables

Figure 1. SSM is naturally aligned with the Hawkes Process
Figure 2. Accuracy comparison on three datasets.
Figure 3. RMSE comparison on three datasets.
Figure 4. Performance of MHP, THP, and A-MHP across different layer counts, evaluated by Log-Likelihood.
Appendix figures & tables4 assets

Supplementary material from the paper’s appendix.

Appendix

InfoFinancialSOSyntheticRetweetMIMIC-II
Len (Avg.)2074.072.460.3108.83.7
Len (Std.)1245.043.723.154.42.3
#Type2225375
Appendix
Table 3. Dataset Statistics
Parameterd_modelLearning RateBatch Sizeβ\betaγ\gamma
Financial1281e-411.01e-4
SO5121e-442.08e-5
Synthetic641e-441.01e-4
Retweet641e-3160.24e-4
Mimic-II645e-411.68e-5
Appendix
Table 4. Hyper-parameter settings of different datasets.
d_innerd_stated_convexpand factorn_layersdt_rankB_split
2 ×\times d_model16424d_model/16\text{d\_model}/162 : 1
Appendix
Table 5. Architecture details of proposed MHP.
DatasetTHPMHPSpeedup
Financial1167.405088.594.36 ×\times
SO20203.1321608.381.07 ×\times
Synthetic8064.1915562.601.93 ×\times
Retweet12733.8478983.226.20 ×\times
MIMIC-II302.12494.261.64 ×\times
Appendix
Table 6. Throughput (events/s) comparison and relative speedup between THP and MHP.
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