aiqbench analysis
This paper introduces Latent Jump Models (LJMs) to capture discrete shocks in irregular time series, replacing standard smooth dynamics with state-dependent instantaneous jumps. The authors propose Scan-Parallel Variational Inference (SPVI), a training method that samples latent event configurations in parallel to achieve logarithmic temporal depth and significantly faster convergence than sequential baselines. By combining closed-form deterministic dynamics with learned stochastic events, this approach offers a scalable framework for modeling complex systems where diffusive approximations are insufficient.
Scan-Parallel Variational Inference for event-driven Latent Jump Models
arXiv:2610.12986v1 Announce Type: cross Abstract: 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.
Abstract: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.
Machine Learning (stat.ML); Machine Learning (cs.LG)
arXiv:2610.12986 [stat.ML]
(or arXiv:2610.12986v1 [stat.ML] for this version)
https://doi.org/10.48550/arXiv.2610.12986 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
Full text under the publisher's open licence · 307 words
Related coverage
Runway’s WorldPrompt and the Engineering of Real-Time Worlds
Latent Space · Sep 25, 2026
[AINews] Meta Connect 2026: Muse glasses, voice, video, and Charm
Latent Space · Sep 24, 2026
Model Weight Profiles: Where Do the Parameters Go?
AMD · Sep 25, 2026
[AINews] Reality Checks on AI News (Yegge shuts down Gas Town, Databricks’ +60% Astra cost)
Latent Space · Sep 17, 2026