# Neural Markov Jump Processes

arXiv: https://arxiv.org/abs/2305.19744 · HTML: https://mlsanity.com/paper/2305.19744/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 77 references that are in the map.
- First posted on arXiv 31 May 2023.

## Builds on (most cited first, 24 of 24)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [On the Properties of Neural Machine Translation: Encoder-Decoder Approaches](https://mlsanity.com/paper/1409.1259/) (2014)
- [On Neural Differential Equations](https://mlsanity.com/paper/2202.02435/) (2022)
- [Conditional Computation in Neural Networks for faster models](https://mlsanity.com/paper/1511.06297/) (2015)
- [Neural Jump Stochastic Differential Equations](https://mlsanity.com/paper/1905.10403/) (2019)
- [VAMPnets: Deep learning of molecular kinetics](https://mlsanity.com/paper/1710.06012/) (2017)
- [Learning in Implicit Generative Models](https://mlsanity.com/paper/1610.03483/) (2016)
- [Fast Decoding in Sequence Models using Discrete Latent Variables](https://mlsanity.com/paper/1803.03382/) (2018)
- [Neural Spatio-Temporal Point Processes](https://mlsanity.com/paper/2011.04583/) (2020)
- [Machine Learning of coarse-grained Molecular Dynamics Force Fields](https://mlsanity.com/paper/1812.01736/) (2018)
- [STEER: Simple Temporal Regularization For Neural ODEs](https://mlsanity.com/paper/2006.10711/) (2020)
- [Semi-Implicit Variational Inference](https://mlsanity.com/paper/1805.11183/) (2018)
- [Self-attention with Functional Time Representation Learning](https://mlsanity.com/paper/1911.12864/) (2019)
- [Variational Inference using Implicit Distributions](https://mlsanity.com/paper/1702.08235/) (2017)
- [Granger-causal Attentive Mixtures of Experts: Learning Important Features with Neural Networks](https://mlsanity.com/paper/1802.02195/) (2018)
- [Interpretable Embeddings From Molecular Simulations Using Gaussian Mixture Variational Autoencoders](https://mlsanity.com/paper/1912.12175/) (2019)
- [Variational Inference for Continuous-Time Switching Dynamical Systems](https://mlsanity.com/paper/2109.14492/) (2021)
- [Moment-Based Variational Inference for Markov Jump Processes](https://mlsanity.com/paper/1905.05451/) (2019)
- [JUMP-Means: Small-Variance Asymptotics for Markov Jump Processes](https://mlsanity.com/paper/1503.00332/) (2015)

## Built on by (most cited first, 12 of 12)

- [Zero-shot Imputation with Foundation Inference Models for Dynamical Systems](https://mlsanity.com/paper/2402.07594/) (2024)
- [Foundation Inference Models for Markov Jump Processes](https://mlsanity.com/paper/2406.06419/) (2024)
- [When to Sense and Control? A Time-adaptive Approach for Continuous-Time RL](https://mlsanity.com/paper/2406.01163/) (2024)
- [Entropic Matching for Expectation Propagation of Markov Jump Processes](https://mlsanity.com/paper/2309.15604/) (2023)
- [Neural MJD: Neural Non-Stationary Merton Jump Diffusion for Time Series Prediction](https://mlsanity.com/paper/2506.04542/) (2025)
- [Towards Fast Coarse-graining and Equation Discovery with Foundation Inference Models](https://mlsanity.com/paper/2510.12618/) (2025)
- [Predicting the Energy Landscape of Stochastic Dynamical System via Physics-informed Self-supervised Learning](https://mlsanity.com/paper/2502.16828/) (2025)
- [On Foundation Models for Temporal Point Processes to Accelerate Scientific Discovery](https://mlsanity.com/paper/2510.12640/) (2025)
- [Efficient Inference for Coupled Hidden Markov Models in Continuous Time and Discrete Space](https://mlsanity.com/paper/2510.12916/) (2025)
- [EVIL: Evolving Interpretable Algorithms for Zero-Shot Inference on Event Sequences and Time Series with LLMs](https://mlsanity.com/paper/2604.15787/) (2026)
- [Variational Inference for L'evy Process-Driven SDEs via Neural Tilting](https://mlsanity.com/paper/2605.10934/) (2026)
- [Scan-Parallel Variational Inference for event-driven Latent Jump Models](https://mlsanity.com/paper/2610.12986/) (2026)

## Abstract (arXiv)

Markov jump processes are continuous-time stochastic processes with a wide range of applications in both natural and social sciences. Despite their widespread use, inference in these models is highly non-trivial and typically proceeds via either Monte Carlo or expectation-maximization methods. In this work we introduce an alternative, variational inference algorithm for Markov jump processes which relies on neural ordinary differential equations, and is trainable via back-propagation. Our methodology learns neural, continuous-time representations of the observed data, that are used to approximate the initial distribution and time-dependent transition probability rates of the posterior Markov jump process. The time-independent rates of the prior process are in contrast trained akin to generative adversarial networks. We test our approach on synthetic data sampled from ground-truth Markov jump processes, experimental switching ion channel data and molecular dynamics simulations. Source code to reproduce our experiments is available online.