System Configuration

• OS: Linux Mint
• GPU: NVIDIA RTX 3090 (24GB)
• RAM: 16GB

TLDR:

• Mamba architecture was added to the DeepSTPP paper.
• The code was also GPU optimized.

Neural Point Process for Learning Spatiotemporal Event Dynamics (DeepSTPP) with Mamba Application

Mamba Abstract Spatiotemporal point processes (STPPs) provide a principled framework for modeling irregular event sequences over continuous space and time. DeepSTPP introduced a nonparametric kernel mixture approach with latent stochastic processes and amortized inference, using Transformer-based encoders to capture event history. However, Transformer encoders suffer from quadratic scaling with sequence length and may struggle to capture long-range dependencies efficiently. In this work, we propose DeepSTPP-Mamba, replacing the Transformer encoder with the recently developed Structured State Space Sequence Model, Mamba, which enables linear-time sequence modeling via selective state space dynamics. Extensive experiments on both synthetic and real-world continuous STPP datasets show that DeepSTPP-Mamba achieves comparable or superior forecasting accuracy while improving computational scalability. Our results suggest that structured state space models provide an effective alternative to attention-based architectures for continuous-time spatiotemporal event modeling.

Visual Represenations For MAMBA Results:

Covid NJ Dataset

Japanese Earthquake Dataset

Real-World Datasets

The table below presents results on COVID-19 NJ and Japan Earthquake datasets:

Table 1: Real-world dataset results.

Model	COVID-LL	COVID-Time	JPDS-LL	JPDS-HD
Mamba	-0.1158	2.4564	-4.3811	0.4393
LSTM	-0.1489	2.4468	-4.4488	0.3580
Separate Encoders	-0.1148	2.4559	-4.4011	0.4007
Shared Decoder	-0.1093	2.4570	-4.4018	0.4044
No Sample	-0.0892	2.4575	-4.4018	0.4044

Spatio Temporal Hawkes Process

Spatio Temporal Self-Correcting Process

Synthetic Datasets

The table below summarizes results on both synthetic processes:

Table 2: Synthetic dataset results.

Model	STHP-LL	STHP-HD	STSCP-LL	STSCP-HD
Mamba	-2.4772	-0.1985	-0.0949	-1.3956
LSTM	-2.3444	-0.2633	-0.1706	-1.3876
Separate Encoders	-2.4483	-0.3751	-0.1736	-1.3909
Shared Decoder	-3.7436	-0.6879	-1.0055	-1.8314
No Sample	-2.3037	-0.1947	-0.1173	-1.3674

On STSCP, DeepSTPP-Mamba achieves the best log-likelihood, outperforming both LSTM and ablations. On STHP, LSTM slightly outperforms Mamba in LL but Mamba yields lower HD, suggesting better intensity‐surface estimation.

Interpretation of Tables 1 and 2

For log-likelihood (LL), higher (less negative) values indicate better model fit. For Hellinger Distance (HD), lower values reflect improved intensity estimation. Mamba achieves its largest gains on STSCP and COVID-19, while remaining competitive with LSTM on Hawkes and JPDS datasets. Across both synthetic and real-world settings, Mamba demonstrates stable and robust performance.

Training Efficiency

While Mamba offers linear-time scaling theoretically, our datasets consist of relatively short event sequences where per-step computation cost dominates total runtime. Consequently, training throughput for Mamba is somewhat slower than LSTM due to the higher complexity of state-space updates; however, the linear-scaling benefits would emerge for longer sequences or larger datasets.

Original Deep Spatiotemporal Point Process [Paper]

Zihao Zhou, Adam Yang, Ryan Rossi, Handong Zhao, Rose Yu

In proceedings of Annual Conference on Learning for Dynamics and Control (L4DC), 2022