# Advances in Temporal Point Processes: Bayesian, Neural, and LLM Approaches

arXiv: https://arxiv.org/abs/2501.14291 · HTML: https://mlsanity.com/paper/2501.14291/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 72 of its 175 references that are in the map.
- First posted on arXiv 24 Jan 2025.

## Builds on (most cited first, 30 of 72)

- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [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)
- [Detecting causal associations in large nonlinear time series datasets](https://mlsanity.com/paper/1702.07007/) (2017)
- [Transformer Hawkes Process](https://mlsanity.com/paper/2002.09291/) (2020)
- [Exploring the Limits of Language Modeling](https://mlsanity.com/paper/1602.02410/) (2016)
- [Neural Jump Stochastic Differential Equations](https://mlsanity.com/paper/1905.10403/) (2019)
- [Intensity-Free Learning of Temporal Point Processes](https://mlsanity.com/paper/1909.12127/) (2019)
- [Fully Neural Network based Model for General Temporal Point Processes](https://mlsanity.com/paper/1905.09690/) (2019)
- [Neural Temporal Point Processes: A Review](https://mlsanity.com/paper/2104.03528/) (2021)
- [Modeling The Intensity Function Of Point Process Via Recurrent Neural Networks](https://mlsanity.com/paper/1705.08982/) (2017)
- [Neural Spatio-Temporal Point Processes](https://mlsanity.com/paper/2011.04583/) (2020)
- [Transformer Embeddings of Irregularly Spaced Events and Their Participants](https://mlsanity.com/paper/2201.00044/) (2021)
- [Learning Granger Causality for Hawkes Processes](https://mlsanity.com/paper/1602.04511/) (2016)
- [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)
- [Spatio-temporal Diffusion Point Processes](https://mlsanity.com/paper/2305.12403/) (2023)
- [Wasserstein Learning of Deep Generative Point Process Models](https://mlsanity.com/paper/1705.08051/) (2017)
- [Language Models Can Improve Event Prediction by Few-Shot Abductive Reasoning](https://mlsanity.com/paper/2305.16646/) (2023)
- [Neural Point Process for Learning Spatiotemporal Event Dynamics](https://mlsanity.com/paper/2112.06351/) (2021)
- [Lecture Notes: Temporal Point Processes and the Conditional Intensity Function](https://mlsanity.com/paper/1806.00221/) (2018)
- [Uncovering Causality from Multivariate Hawkes Integrated Cumulants](https://mlsanity.com/paper/1607.06333/) (2016)
- [CAUSE: Learning Granger Causality from Event Sequences using Attribution Methods](https://mlsanity.com/paper/2002.07906/) (2020)
- [Fast and Flexible Temporal Point Processes with Triangular Maps](https://mlsanity.com/paper/2006.12631/) (2020)
- [Variational Inference for Gaussian Process Modulated Poisson Processes](https://mlsanity.com/paper/1411.0254/) (2014)
- [Prompt-augmented Temporal Point Process for Streaming Event Sequence](https://mlsanity.com/paper/2310.04993/) (2023)
- [Add and Thin: Diffusion for Temporal Point Processes](https://mlsanity.com/paper/2311.01139/) (2023)

## Built on by (most cited first, 3 of 3)

- [HawkesLLM: Semantic Uncertainty Propagation in Agentic Text Simulation](https://mlsanity.com/paper/2605.23043/) (2026)
- [Latent Block-Diffusion Temporal Point Processes: A Semi-Autoregressive Framework for Asynchronous Event Sequence Generation](https://mlsanity.com/paper/2606.24982/) (2026)
- [Exact Phase-Type Point Processes for Certified Measurement and Prediction of Event Streams](https://mlsanity.com/paper/2610.14948/) (2026)

## Abstract (arXiv)

Temporal point processes (TPPs) are stochastic process models used to characterize event sequences occurring in continuous time. Traditional statistical TPPs have a long-standing history, with numerous models proposed and successfully applied across diverse domains. In recent years, advances in deep learning have spurred the development of neural TPPs, enabling greater flexibility and expressiveness in capturing complex temporal dynamics. The emergence of large language models (LLMs) has further sparked excitement, offering new possibilities for modeling and analyzing event sequences by leveraging their rich contextual understanding. This survey presents a comprehensive review of recent research on TPPs from three perspectives: Bayesian, deep learning, and LLM approaches. We begin with a review of the fundamental concepts of TPPs, followed by an in-depth discussion of model design and parameter estimation techniques in these three frameworks. We also revisit classic application areas of TPPs to highlight their practical relevance. Finally, we outline challenges and promising directions for future research.