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Bridging Discrete Marks and Continuous Dynamics: Dual-Path Cross-Interaction for Marked Temporal Point Processes

Yuxiang Liu, Qiao Liu, Tong Luo, Yanglei Gan, Peng He, Yao LIu

Abstract

Predicting irregularly spaced event sequences with discrete marks poses significant challenges due to the complex, asynchronous dependencies embedded within continuous-time data streams.Existing sequential approaches capture dependencies among event tokens but ignore the continuous evolution between events, while Neural Ordinary Differential Equation (Neural ODE) methods model smooth dynamics yet fail to account for how event types influence future timing.To overcome these limitations, we propose NEXTPP, a dual-channel framework that unifies discrete and continuous representations via Event-granular Neural Evolution with Cross-Interaction for Marked Temporal Point Processes. Specifically, NEXTPP encodes discrete event marks via a self-attention mechanism, simultaneously evolving a latent continuous-time state using a Neural ODE. These parallel streams are then fused through a crossattention module to enable explicit bidirectional interaction between continuous and discrete representations. The fused representations drive the conditional intensity function of the neural Hawkes process, while an iterative thinning sampler is employed to generate future events. Extensive evaluations on five real-world datasets demonstrate that NEXTPP consistently outperforms state-of-the-art models. The source code can be found at https://github.com/AONE-NLP/NEXTPP.

Bridging Discrete Marks and Continuous Dynamics: Dual-Path Cross-Interaction for Marked Temporal Point Processes

Abstract

Predicting irregularly spaced event sequences with discrete marks poses significant challenges due to the complex, asynchronous dependencies embedded within continuous-time data streams.Existing sequential approaches capture dependencies among event tokens but ignore the continuous evolution between events, while Neural Ordinary Differential Equation (Neural ODE) methods model smooth dynamics yet fail to account for how event types influence future timing.To overcome these limitations, we propose NEXTPP, a dual-channel framework that unifies discrete and continuous representations via Event-granular Neural Evolution with Cross-Interaction for Marked Temporal Point Processes. Specifically, NEXTPP encodes discrete event marks via a self-attention mechanism, simultaneously evolving a latent continuous-time state using a Neural ODE. These parallel streams are then fused through a crossattention module to enable explicit bidirectional interaction between continuous and discrete representations. The fused representations drive the conditional intensity function of the neural Hawkes process, while an iterative thinning sampler is employed to generate future events. Extensive evaluations on five real-world datasets demonstrate that NEXTPP consistently outperforms state-of-the-art models. The source code can be found at https://github.com/AONE-NLP/NEXTPP.
Paper Structure (21 sections, 16 equations, 6 figures, 4 tables)

This paper contains 21 sections, 16 equations, 6 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Preliminaries and Related Works
  3. Marked Temporal Point Processes
  4. Neural Ordinary Differential Equations
  5. Methodology
  6. Sequence Representations
  7. Training
  8. Thinning Sampler for NEXTPP
  9. Experiments
  10. Experimental Settings
  11. Datasets
  12. Baselines
  13. Evaluation Metrics
  14. Implementation Details
  15. Overall Performance
  16. ...and 6 more sections

Figures (6)

  • Figure 1: Seismic timeline for the August 30, 2009 sequence, showing 18 events within 12.3 s. A magnitude 5.2 mainshock at 11.56s marks the transition from foreshocks to aftershocks, illustrating the classic three-phase seismic cycle.
  • Figure 2: The overall framework NEXTPP. Left(SA): Discrete event sequence processing through embedding and self-attention layers. Right(NE): Continuous representation via latent space. X-Interaction(CA): Continuous-Discrete Interaction.
  • Figure 3: Block-wise test results: The sequence is divided into several blocks according to partition ratio $\alpha$, with each block evolving in its corresponding latent space, where X indicates one block per event.(Lower scores are better)
  • Figure 4: Heatmap comparison of the seismic sequences (shown in Figure \ref{['intro']}) during model training. (a) The first row shows our Continuous-Discrete Interaction($\mathbf{X}\text{-}Interaction$); (b) The second row displays the conventional Attention($Self\text{-}Attention$).
  • Figure 5: Training curves with varying event counts (Percentage of the total training dataset) for Earthquake and Retweet datasets.
  • ...and 1 more figures