# Efficient Temporal Point Processes via Monotone Alternating Splines

arXiv: https://arxiv.org/abs/2607.01752 · HTML: https://mlsanity.com/paper/2607.01752/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 46 references that are in the map.
- First posted on arXiv 2 Jul 2026.

## Builds on (most cited first, 16 of 16)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [Intensity-Free Learning of Temporal Point Processes](https://mlsanity.com/paper/1909.12127/) (2019)
- [Improving Generalization Performance by Switching from Adam to SGD](https://mlsanity.com/paper/1712.07628/) (2017)
- [Fully Neural Network based Model for General Temporal Point Processes](https://mlsanity.com/paper/1905.09690/) (2019)
- [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)
- [Invertible Generative Modeling using Linear Rational Splines](https://mlsanity.com/paper/2001.05168/) (2020)
- [Fast and Flexible Temporal Point Processes with Triangular Maps](https://mlsanity.com/paper/2006.12631/) (2020)
- [Decomposable Transformer Point Processes](https://mlsanity.com/paper/2409.18158/) (2024)
- [Interpretable Transformer Hawkes Processes: Unveiling Complex Interactions in Social Networks](https://mlsanity.com/paper/2405.16059/) (2024)
- [SMURF-THP: Score Matching-based UnceRtainty quantiFication for Transformer Hawkes Process](https://mlsanity.com/paper/2310.16336/) (2023)
- [Is Score Matching Suitable for Estimating Point Processes?](https://mlsanity.com/paper/2410.04037/) (2024)
- [Cumulative Hazard Function Based Efficient Multivariate Temporal Point Process Learning](https://mlsanity.com/paper/2404.13663/) (2024)
- [Cumulative Distribution Function based General Temporal Point Processes](https://mlsanity.com/paper/2402.00388/) (2024)

## Abstract (arXiv)

Temporal point processes (TPPs) have widespread applications across various domains. Compared to modeling the conditional intensity of a TPP, modeling its cumulative conditional intensity function (CCIF) improves computational efficiency and eliminates numerical approximation errors. However, current CCIF parameterizations uniformly rely on Monotone Neural Networks (MNNs), which we identify as suffering from three structural deadlocks--convexity restrictions, saturation limits, and violations of CCIF modeling requirements--that fundamentally restrict their representational capacity for complex temporal dynamics. To resolve these bottlenecks, this paper proposes a novel framework called Monotone Alternating Splines (MAS). By leveraging distinct interpolation and extrapolation components, MAS provides a flexible and efficient framework for modeling CCIFs. Theoretically, MAS's interpolation provides strong fitting accuracy, while its extrapolation supports robust generalization, reducing the irreducible approximation gaps of MNNs. Extensive experiments show that MAS achieves superior performance on both synthetic and real-world datasets.