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Deep Continuous-Time State-Space Models for Marked Event Sequences
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Proposes S2P2, a deep stack of latent linear Hawkes layers (diagonalized, ZOH-discretized continuous-time SSM layers with jumps at events) that yields an expressive, parallel-scan-trainable intensity-based marked TPP, outperforming baselines on eight datasets.
Problem
Neural marked temporal point process models are limited in expressivity, lack long-range dependency handling, or scale poorly (quadratic for transformers, serial for RNNs) with sequence length.
Approach
Combines linear Hawkes process dynamics with deep SSM machinery: a stochastic jump differential equation (latent linear Hawkes layer) with diagonalized, zero-order-hold discretized dynamics, stacked with GELU and LayerNorm, evaluated via parallel scans and with intensities decoded continuously from evolving latent states rather than a parametric head.
Key results
- S2P2 achieves best or second-best per-event log-likelihood on all eight datasets, with a composite rank of 1.4 among models for log-likelihood (vs 3.0 for next best NHP/IFTPP).
- Geometric mean likelihood ratio of 1.33 (33% higher likelihood of true events) over baselines, as stated in the abstract.
- On the long-range dependency synthetic task S2P2 recovers 98% of the true data likelihood while NHP achieves 88%.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use S2P2 instead of existing baselines | MTPP models · Eight real-world datasets | per-event total log-likelihood: 1.33 | Helped |
| Use S2P2 instead of the strongest baseline | MTPP models · Real-world datasets, overall | next event time RMSE | Mixed |
| Use S2P2 instead of the strongest baseline | MTPP models · Real-world datasets, overall | next mark classification accuracy | Mixed |
| Use S2P2 rather than NHP | Synthetic long-range dependency task · Synthetic long-range dependencies | true data likelihood recovered: 88% -> 98% | Helped |
| Add input-dependent dynamics (ablation) | S2P2 · Real-world ablation experiments | performance | Helped |
| Use backwards rather than forwards zero-order hold (ablation) | S2P2 · Real-world ablation experiments | performance | No clear effect |
Limitations
- Forgoes the interpretability of linear Hawkes process parameters and latent states
- Intensity-based, requires numerical integration for expected next event times and cannot model point masses in time (no concurrent events)
- PyTorch implementation less optimized than baselines such as IFTPP's GPU-optimized GRU
Experimental setup
Datasets: Amazon Retweet Taxi Taobao StackOverflow Last.fm MIMIC-II EHRSHOT
Benchmarks: Amazon Retweet Taxi Taobao StackOverflow Last.fm MIMIC-II EHRSHOT
Metrics: per-event log-likelihood next event time RMSE next mark accuracy calibration
Baselines: RMTPP SAHP THP IFTPP MHP NHP AttNHP
Builds on: linear Hawkes process S5 Mamba EasyTPP Neural Hawkes process
Closest papers by meaning
- EasyTPP: Towards Open Benchmarking Temporal Point Processes (ICLR 2024 · similarity 0.90)
- Decoupled Marked Temporal Point Process using Neural Ordinary Differential Equations (ICLR 2024 · similarity 0.89)
- Interacting Diffusion Processes for Event Sequence Forecasting (ICML 2024 · similarity 0.87)
- Hyper Hawkes Processes: Interpretable Models of Marked Temporal Point Processes (NeurIPS 2026 · similarity 0.87)
- Seahorse: A Unified Benchmarking Framework for Spatiotemporal Event Modeling (NeurIPS 2026 · similarity 0.86)
- ExPERT: Modeling Human Behavior Under External Stimuli Aware Personalized MTPP (AAAI 2025 · similarity 0.85)
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