# Smooth Neural Point Processes via B-Splines

arXiv: https://arxiv.org/abs/2607.21098 · HTML: https://mlsanity.com/paper/2607.21098/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 21 references that are in the map.
- First posted on arXiv 23 Jul 2026.

## Builds on (most cited first, 4 of 4)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [Fully Neural Network based Model for General Temporal Point Processes](https://mlsanity.com/paper/1905.09690/) (2019)
- [Neural Likelihoods via Cumulative Distribution Functions](https://mlsanity.com/paper/1811.00974/) (2018)

## Abstract (arXiv)

Temporal point processes (TPPs) provide a general and flexible framework for modeling sequences of events in continuous time. Neural networks have been successfully employed to model TPPs in a highly expressive and data-driven way. Neural TPPs are typically trained via Maximum Likelihood Estimation (MLE) by minimizing the negative log-likelihood (NLL), which depends on both the conditional intensity function (CIF) and its integral over time, the compensator. Recent neural TPP approaches enable exact evaluation of the NLL without numerical integration. However, these methods typically model the compensator rather than the CIF directly, impose constraints on the neural network architecture, and are computationally expensive during training, as event contributions to the NLL are evaluated sequentially rather than in parallel. In this work, we propose a novel neural TPP model that directly parametrizes the CIF as a non-negative combination of B-spline basis functions, whose coefficients are predicted by a neural network. This formulation enables exact evaluation of the NLL, preserves full flexibility in the neural architecture, allows efficient parallelization during training, and naturally supports CIF smoothness regularization through the integrated squared second derivative. Experiments on both synthetic and real-world datasets show improved computational efficiency and predictive accuracy compared to the reference neural TPP baseline.