# Scan-Parallel Variational Inference for event-driven Latent Jump Models

arXiv: https://arxiv.org/abs/2610.12986 · HTML: https://mlsanity.com/paper/2610.12986/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 31 references that are in the map.
- First posted on arXiv 9 Oct 2026.

## Builds on (most cited first, 21 of 21)

- [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)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Simplified State Space Layers for Sequence Modeling](https://mlsanity.com/paper/2208.04933/) (2022)
- [On the Parameterization and Initialization of Diagonal State Space Models](https://mlsanity.com/paper/2206.11893/) (2022)
- [Resurrecting Recurrent Neural Networks for Long Sequences](https://mlsanity.com/paper/2303.06349/) (2023)
- [GRU-ODE-Bayes: Continuous modeling of sporadically-observed time series](https://mlsanity.com/paper/1905.12374/) (2019)
- [Neural Jump Stochastic Differential Equations](https://mlsanity.com/paper/1905.10403/) (2019)
- [Modeling Irregular Time Series with Continuous Recurrent Units](https://mlsanity.com/paper/2111.11344/) (2021)
- [Neural Flows: Efficient Alternative to Neural ODEs](https://mlsanity.com/paper/2110.13040/) (2021)
- [Neural Jump Ordinary Differential Equations: Consistent Continuous-Time Prediction and Filtering](https://mlsanity.com/paper/2006.04727/) (2020)
- [Temporal Parallelization of Bayesian Smoothers](https://mlsanity.com/paper/1905.13002/) (2019)
- [Fast and Flexible Temporal Point Processes with Triangular Maps](https://mlsanity.com/paper/2006.12631/) (2020)
- [Neural Continuous-Discrete State Space Models for Irregularly-Sampled Time Series](https://mlsanity.com/paper/2301.11308/) (2023)
- [SDE Matching: Scalable and Simulation-Free Training of Latent Stochastic Differential Equations](https://mlsanity.com/paper/2502.02472/) (2025)
- [Amortized Reparametrization: Efficient and Scalable Variational Inference for Latent SDEs](https://mlsanity.com/paper/2312.10550/) (2023)
- [Neural Markov Jump Processes](https://mlsanity.com/paper/2305.19744/) (2023)
- [Deep Continuous-Time State-Space Models for Marked Event Sequences](https://mlsanity.com/paper/2412.19634/) (2024)
- [Moment-Based Variational Inference for Markov Jump Processes](https://mlsanity.com/paper/1905.05451/) (2019)
- [Neural Stochastic Flows: Solver-Free Modelling and Inference for SDE Solutions](https://mlsanity.com/paper/2510.25769/) (2025)
- [Closing the Approximation Gap in Simulation-free Latent SDEs](https://mlsanity.com/paper/2606.16138/) (2026)

## Abstract (arXiv)

Continuous-time latent state-space models are widely used for irregularly observed time series, typically representing uncertainty through a random initial state followed by smooth ordinary differential equation (ODE) dynamics, or Brownian perturbations accumulated by a stochastic differential equation (SDE). While these constructions are natural for smooth or diffusive systems, they do not directly encode a finite set of unobserved shocks whose timing, magnitude, and effect on memory are themselves uncertain. We instead introduce latent jump models (LJMs): the latent state follows closed-form deterministic dynamics between Poisson-driven event times and undergoes a learned instantaneous jump at each event, with state-dependent intensity and mark distributions. This defines a time-homogeneous Markov process whose jumps are intrinsic state transitions rather than numerical integration steps. For training, we derive a tractable event-augmented path-space evidence lower bound (ELBO) and introduce Scan-Parallel Variational Inference (SPVI): an observation-conditioned variational posterior samples the complete latent event configuration before the state recurrence is evaluated using triangular affine scans. This enables fast and scalable training for LJMs in logarithmic temporal depth. Across synthetic stochastic systems and real irregular time series, LJMs remain competitive with continuous-time latent baselines in forecast accuracy, often with fewer latent updates than numerical solver evaluations, while training one to two orders of magnitude faster than the sequential baselines.