# From Jumps to Signatures: a Generative Method for Temporal Point Processes

arXiv: https://arxiv.org/abs/2607.06652 · HTML: https://mlsanity.com/paper/2607.06652/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 30 of its 57 references that are in the map.
- First posted on arXiv 7 Jul 2026.

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

- [Chronos: Learning the Language of Time Series](https://mlsanity.com/paper/2403.07815/) (2024)
- [A decoder-only foundation model for time-series forecasting](https://mlsanity.com/paper/2310.10688/) (2023)
- [Large Language Models Are Zero-Shot Time Series Forecasters](https://mlsanity.com/paper/2310.07820/) (2023)
- [Towards Principled Methods for Training Generative Adversarial Networks](https://mlsanity.com/paper/1701.04862/) (2017)
- [On Wasserstein Two Sample Testing and Related Families of Nonparametric Tests](https://mlsanity.com/paper/1509.02237/) (2015)
- [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)
- [Deep Signature Transforms](https://mlsanity.com/paper/1905.08494/) (2019)
- [EasyTPP: Towards Open Benchmarking Temporal Point Processes](https://mlsanity.com/paper/2307.08097/) (2023)
- [Sig-Wasserstein GANs for Time Series Generation](https://mlsanity.com/paper/2111.01207/) (2021)
- [Signature moments to characterize laws of stochastic processes](https://mlsanity.com/paper/1810.10971/) (2018)
- [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)
- [Neural Point Process for Learning Spatiotemporal Event Dynamics](https://mlsanity.com/paper/2112.06351/) (2021)
- [Learning Temporal Point Processes via Reinforcement Learning](https://mlsanity.com/paper/1811.05016/) (2018)
- [Fast and Flexible Temporal Point Processes with Triangular Maps](https://mlsanity.com/paper/2006.12631/) (2020)
- [Exploring Generative Neural Temporal Point Process](https://mlsanity.com/paper/2208.01874/) (2022)
- [Learning to simulate realistic limit order book markets from data as a World Agent](https://mlsanity.com/paper/2210.09897/) (2022)
- [Deep Mixture Point Processes: Spatio-temporal Event Prediction with Rich Contextual Information](https://mlsanity.com/paper/1906.08952/) (2019)
- [Conditional Sig-Wasserstein GANs for Time Series Generation](https://mlsanity.com/paper/2006.05421/) (2020)
- [Add and Thin: Diffusion for Temporal Point Processes](https://mlsanity.com/paper/2311.01139/) (2023)
- [A signature-based machine learning model for bipolar disorder and borderline personality disorder](https://mlsanity.com/paper/1707.07124/) (2017)
- [Unlocking Point Processes through Point Set Diffusion](https://mlsanity.com/paper/2410.22493/) (2024)
- [Automatic Integration for Spatiotemporal Neural Point Processes](https://mlsanity.com/paper/2310.06179/) (2023)
- [Deep Continuous-Time State-Space Models for Marked Event Sequences](https://mlsanity.com/paper/2412.19634/) (2024)
- [Proper Scoring Rules for Multivariate Probabilistic Forecasts based on Aggregation and Transformation](https://mlsanity.com/paper/2407.00650/) (2024)
- [Time is of the Essence: a Joint Hierarchical RNN and Point Process Model for Time and Item Predictions](https://mlsanity.com/paper/1812.01276/) (2018)
- [EventFlow: Forecasting Temporal Point Processes with Flow Matching](https://mlsanity.com/paper/2410.07430/) (2024)
- [Edit-Based Flow Matching for Temporal Point Processes](https://mlsanity.com/paper/2510.06050/) (2025)
- [Neural Spatiotemporal Point Processes: Trends and Challenges](https://mlsanity.com/paper/2502.09341/) (2025)

## Abstract (arXiv)

Rough path signatures are a universal feature map for continuous paths and, via the expected signature, characterise path distributions. These guarantees do not directly extend to cadlag paths of Temporal Point Processes (TPPs), limiting the use of signature methods for event sequences. Furthermore, neural TPP models, including recent generative approaches, optimise per-event objectives with no global sequence-level loss, while evaluation of variable-length event sequences lacks distributional discrepancy measures. This paper proposes a common pathwise framework for addressing these limitations. We introduce the interarrival embedding, a stable, injective lift from jump paths to continuous paths of bounded variation, extending signature methods to discrete event sequences. Our theoretical contributions give rise to sigTPP, the first signature-based generative model for TPPs, trained using a path-level loss on complete trajectories. We further analyse the space of counting paths and derive three distributional discrepancies, providing mathematically justified tools for evaluating generative TPP models. Across synthetic and real-world datasets, sigTPP achieves the best average rank based on eight complementary metrics, outperforms or is within a standard error of the strongest baseline in 64% of the dataset-metric pairs, and according to a relative score, improves against every baseline by at least 19% on average.