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Neural Jump-Diffusion Temporal Point Processes
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Reformulates TPP intensity processes as solutions of neural jump-diffusion SDEs (NJDTPP), proving classical TPPs are special cases and that the SDE has a unique solution under Lipschitz conditions.
Problem
Classical and neural TPPs usually fix a specific functional form for the intensity function, limiting expressiveness; neural jump SDE models for event sequences model hidden states and lack guarantees of existence and uniqueness.
Approach
Model the log-intensity as a neural jump-diffusion SDE whose drift, diffusion, and jump coefficients are MLPs, showing Poisson, Hawkes, and self-correcting intensities satisfy equivalent SDEs; trained by MLE with Euler-Maruyama discretization.
Key results
- NJDTPP achieves NLL of 1.305 on Earthquake and -0.440 on Taobao, versus best baseline NLL around 2.2 and 0.986 (NHP).
- Event time RMSE on Taobao drops to 0.130 from roughly 0.53 for baselines.
- On synthetic data NJDTPP achieves MAPE of 0.1, 0.2, and 0.1 for Poisson, Hawkes, and self-correcting processes, below NJSDE (1.3, 5.9, 9.3).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use NJDTPP instead of the strongest reported baseline | NJDTPP · Retweet | NLL: 4.137 -> 4.092 | Helped |
| Use NJDTPP instead of the strongest reported baseline | NJDTPP · Earthquake | NLL: 2.189 -> 1.305 | Helped |
| Use NJDTPP instead of the strongest reported baseline | NJDTPP · Taxi | NLL: 0.208 -> -0.293 | Helped |
| Use NJDTPP instead of the strongest reported baseline | NJDTPP · Taobao | NLL: 0.986 -> -0.440 | Helped |
| Use NJDTPP instead of the strongest reported baseline | NJDTPP · StackOverflow | NLL: 2.496 -> 2.347 | Helped |
| Use NJDTPP instead of the strongest reported baseline | NJDTPP · MIMIC-II | NLL: 1.515 -> 1.398 | Helped |
| Use NJDTPP instead of the strongest reported baseline | NJDTPP · Retweet, Earthquake, Taxi, Taobao, StackOverflow, and MIMIC-II | accuracy: 0.601 -> 0.608; 0.452 -> 0.472; 0.890 -> 0.908; 0.467 -> 0.486; 0.467 -> 0.469; 0.856 -> 0.861 | Helped |
| Add the Brownian-motion diffusion term (ablation) | NJDTPP · Earthquake | NLL: 1.594 -> 1.305 | Helped |
| Add the Brownian-motion diffusion term (ablation) | NJDTPP · Earthquake | RMSE: 1.507 -> 1.420 | Helped |
| Add the Brownian-motion diffusion term (ablation) | NJDTPP · Earthquake | accuracy: 0.470 -> 0.472 | Helped |
| Add the Brownian-motion diffusion term (ablation) | NJDTPP · Earthquake | F1: 0.306 -> 0.313 | Helped |
| Add the Brownian-motion diffusion term (ablation) | NJDTPP · Taxi | NLL: -0.290 -> -0.293 | Helped |
Surprising findings
- Removing the Brownian diffusion term changes Earthquake NLL only modestly in the ablation but worsens it from 1.305 to 1.594.
Limitations
- Diffusion term is Gaussian noise on log-intensity, and the paper's own ablation suggests modest gains from it in some settings
- Likelihood uses numerical integration via trapezoidal rule and Euler-Maruyama discretization, adding approximation error
- Existence and uniqueness guarantees require Lipschitz activations and assumptions on coefficients
Experimental setup
Datasets: Retweet Earthquake Taxi Taobao StackOverflow MIMIC-II Ogata thinning synthetic Poisson/Hawkes/self-correcting
Benchmarks: Retweet Earthquake Taxi Taobao StackOverflow MIMIC-II synthetic Poisson/Hawkes/self-correcting intensity recovery
Metrics: negative log-likelihood RMSE accuracy weighted F1 MAPE
Baselines: RMTPP NHP SAHP THP AttNHP NSTPP NJSDE RNN PP HP SC
Builds on: Neural Jump SDE Hawkes process neural ODE EasyTPP
Closest papers by meaning
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- Neural Stochastic Flows: Solver-Free Modelling and Inference for SDE Solutions (NeurIPS 2025 · similarity 0.86)
- Exact, Fast and Expressive Poisson Point Processes via Squared Neural Families (AAAI 2024 · similarity 0.86)
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