# Deep Continuous-Time State-Space Models for Marked Event Sequences

arXiv: https://arxiv.org/abs/2412.19634 · HTML: https://mlsanity.com/paper/2412.19634/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 65 references that are in the map.
- First posted on arXiv 27 Dec 2024.

## Builds on (most cited first, 30 of 35)

- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [Vision Mamba: Efficient Visual Representation Learning with Bidirectional State Space Model](https://mlsanity.com/paper/2401.09417/) (2024)
- [Simplified State Space Layers for Sequence Modeling](https://mlsanity.com/paper/2208.04933/) (2022)
- [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)
- [Predicting Dynamic Embedding Trajectory in Temporal Interaction Networks](https://mlsanity.com/paper/1908.01207/) (2019)
- [On the Parameterization and Initialization of Diagonal State Space Models](https://mlsanity.com/paper/2206.11893/) (2022)
- [Diagonal State Spaces are as Effective as Structured State Spaces](https://mlsanity.com/paper/2203.14343/) (2022)
- [Transformer Hawkes Process](https://mlsanity.com/paper/2002.09291/) (2020)
- [The Illusion of State in State-Space Models](https://mlsanity.com/paper/2404.08819/) (2024)
- [It's Raw! Audio Generation with State-Space Models](https://mlsanity.com/paper/2202.09729/) (2022)
- [Intensity-Free Learning of Temporal Point Processes](https://mlsanity.com/paper/1909.12127/) (2019)
- [Selective Structured State-Spaces for Long-Form Video Understanding](https://mlsanity.com/paper/2303.14526/) (2023)
- [EHRSHOT: An EHR Benchmark for Few-Shot Evaluation of Foundation Models](https://mlsanity.com/paper/2307.02028/) (2023)
- [Transformer Embeddings of Irregularly Spaced Events and Their Participants](https://mlsanity.com/paper/2201.00044/) (2021)
- [The Hidden Attention of Mamba Models](https://mlsanity.com/paper/2403.01590/) (2024)
- [SEISMIC: A Self-Exciting Point Process Model for Predicting Tweet Popularity](https://mlsanity.com/paper/1506.02594/) (2015)
- [Theoretical Foundations of Deep Selective State-Space Models](https://mlsanity.com/paper/2402.19047/) (2024)
- [EasyTPP: Towards Open Benchmarking Temporal Point Processes](https://mlsanity.com/paper/2307.08097/) (2023)
- [HYPRO: A Hybridly Normalized Probabilistic Model for Long-Horizon Prediction of Event Sequences](https://mlsanity.com/paper/2210.01753/) (2022)
- [Imputing Missing Events in Continuous-Time Event Streams](https://mlsanity.com/paper/1905.05570/) (2019)
- [Facing Off World Model Backbones: RNNs, Transformers, and S4](https://mlsanity.com/paper/2307.02064/) (2023)
- [Fast and Flexible Temporal Point Processes with Triangular Maps](https://mlsanity.com/paper/2006.12631/) (2020)
- [User-Dependent Neural Sequence Models for Continuous-Time Event Data](https://mlsanity.com/paper/2011.03231/) (2020)
- [Meta Temporal Point Processes](https://mlsanity.com/paper/2301.12023/) (2023)
- [On the Predictive Accuracy of Neural Temporal Point Process Models for Continuous-time Event Data](https://mlsanity.com/paper/2306.17066/) (2023)
- [Point process models for sequence detection in high-dimensional neural spike trains](https://mlsanity.com/paper/2010.04875/) (2020)

## Built on by (most cited first, 11 of 11)

- [One Loss to Rule Them All: Marked Time-to-Event for Structured EHR Foundation Models](https://mlsanity.com/paper/2602.00541/) (2026)
- [Advances in Temporal Point Processes: Bayesian, Neural, and LLM Approaches](https://mlsanity.com/paper/2501.14291/) (2025)
- [NetBurst: Event-Centric Forecasting of Bursty, Intermittent Time Series](https://mlsanity.com/paper/2510.22397/) (2025)
- [Hyper Hawkes Processes: Interpretable Models of Marked Temporal Point Processes](https://mlsanity.com/paper/2511.01096/) (2025)
- [Towards Unified Approaches in Self-Supervised Event Stream Modeling: Progress and Prospects](https://mlsanity.com/paper/2502.04899/) (2025)
- [Long-range Modeling and Processing of Multimodal Event Sequences](https://mlsanity.com/paper/2602.01125/) (2026)
- [Latent Block-Diffusion Temporal Point Processes: A Semi-Autoregressive Framework for Asynchronous Event Sequence Generation](https://mlsanity.com/paper/2606.24982/) (2026)
- [From Jumps to Signatures: a Generative Method for Temporal Point Processes](https://mlsanity.com/paper/2607.06652/) (2026)
- [Model-Based Reinforcement Learning for Heterogeneous Multi-Robot Task Assignment Under Distribution Shifts](https://mlsanity.com/paper/2608.21554/) (2026)
- [Scan-Parallel Variational Inference for event-driven Latent Jump Models](https://mlsanity.com/paper/2610.12986/) (2026)
- [Exact Phase-Type Point Processes for Certified Measurement and Prediction of Event Streams](https://mlsanity.com/paper/2610.14948/) (2026)

## Abstract (arXiv)

Marked temporal point processes (MTPPs) model sequences of events occurring at irregular time intervals, with wide-ranging applications in fields such as healthcare, finance and social networks. We propose the state-space point process (S2P2) model, a novel and performant model that leverages techniques derived for modern deep state-space models (SSMs) to overcome limitations of existing MTPP models, while simultaneously imbuing strong inductive biases for continuous-time event sequences that other discrete sequence models (i.e., RNNs, transformers) do not capture. Inspired by the classical linear Hawkes processes, we propose an architecture that interleaves stochastic jump differential equations with nonlinearities to create a highly expressive intensity-based MTPP model, without the need for restrictive parametric assumptions for the intensity. Our approach enables efficient training and inference with a parallel scan, bringing linear complexity and sublinear scaling while retaining expressivity to MTPPs. Empirically, S2P2 achieves state-of-the-art predictive likelihoods across eight real-world datasets, delivering an average improvement of 33% over the best existing approaches.