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

cs.LGMar 12, 2026

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

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

Organizations: University of Electronic Science and Technology of China, Chengdu, Sichuan, China

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.

Figures & tables

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.

Dataset	M	Event Tokens			Sequence Length
Dataset	M	Train	Dev	Test	Min	Mean	Max
RETWEET	3	369731	62823	61154	10	41	97
AMAZON	16	288377	40995	84048	14	44	94
TAXI	10	51854	7404	14820	36	37	38
STACKOVERFLOW	22	90497	25762	26518	41	65	101
EARTHQUAKE	7	49363	6612	14748	15	16	18

Table 1: Dataset statistics with number of marks (M), event tokens distribution across splits, and sequence length characteristics.

Method	Taxi		Amazon		S.O.		EQ		Retweet
Method	R	E	R	E	R	E	R	E	R	E
MHP	0.382	9.53	0.635	75.9	1.388	65.0	4.128	54.9	22.920	55.7
RMTPP	0.374	10.4	0.474	68.1	1.392	56.3	2.097	54.9	26.508	45.8
NHP	0.373	10.0	0.513	68.5	1.431	53.3	2.347	54.7	22.410	39.9
THP	0.370	10.1	0.471	66.6	1.343	53.3	2.160	55.1	24.491	39.9
SAHP	0.334	10.0	0.549	68.9	1.331	56.5	1.864	54.9	21.673	40.6

Table 2: Results of all model reproductions across five real datasets. The performance of our NEXTPP model represents the average of five training runs with different random seeds. Lower scores indicate better performance. The best results are indicated in bold and suboptimal results are underlined .(R = RMSE (

\downarrow

), E = Error Rate % (

\downarrow

), S.O. = StackOverflow, EQ = Earthquake)

MODEL	Log-Likelihood
MODEL	Taxi	Amazon	Stack Overflow	Earthquake	Retweet
RMTPP	$\text{0.219}_{\pm\text{0.033}}$	$\text{-2.258}_{\pm\text{0.009}}$	$\text{-2.820}_{\pm\text{0.025}}$	$\text{-2.313}_{\pm\text{0.272}}$	$\text{-5.754}_{\pm\text{1.785}}$
NHP	$\text{0.440}_{\pm\text{0.007}}$	$\text{-2.036}_{\pm\text{0.066}}$	$\text{-2.440}_{\pm\text{0.103}}$	$\text{-2.155}_{\pm\text{0.056}}$	$\text{-4.020}_{\pm\text{0.133}}$
THP	$\text{0.217}_{\pm\text{0.034}}$	$\text{-2.215}_{\pm\text{0.016}}$	$\text{-2.478}_{\pm\text{0.031}}$	$\text{-2.353}_{\pm\text{0.040}}$	$\text{-4.143}_{\pm\text{0.005}}$
SAHP	$\text{-0.295}_{\pm\text{0.266}}$	$\text{-2.417}_{\pm\text{0.207}}$	$\text{-6.930}_{\pm\text{0.007}}$	$\text{-3.136}_{\pm\text{0.610}}$	$\text{-4.798}_{\pm\text{0.637}}$
AttNHP	$\text{0.164}_{\pm\text{0.031}}$	$\text{-1.364}_{\pm\text{0.195}}$	$\text{-2.560}_{\pm\text{0.004}}$	$\text{-2.359}_{\pm\text{0.026}}$	$\text{-4.128}_{\pm\text{0.002}}$

Table 3: Log-Likelihood Performance Comparison. Reported values are the mean log-likelihood over five independent runs, with the corresponding standard deviation indicating experimental variability.

Settings	Amazon			StackOverflow			Retweet
Settings	LL( $\uparrow$ )	RMSE( $\downarrow$ )	ErrRt( $\downarrow$ )	LL( $\uparrow$ )	RMSE( $\downarrow$ )	ErrRt( $\downarrow$ )	LL( $\uparrow$ )	RMSE( $\downarrow$ )	ErrRt( $\downarrow$ )
w/o NE	-2.178	0.468	66.8%	-2.474	1.338	53.3%	-4.180	20.541	40.2%
w/o CA	-1.530	0.438	71.1%	-2.657	2.199	56.4%	-4.122	20.108	47.3%
NE $\rightarrow$ GRU	-2.235	0.481	67.7%	-2.369	1.366	53.2%	-4.166	21.145	40.7%
NE $\rightarrow$ LSTM	-2.263	0.495	68.2%	-2.403	1.389	53.3%	-4.177	20.795	40.6%
NEXTPP	-1.246	0.377	66.5%	-1.971	1.152	52.2%	-3.993	19.340	35.5%

Table 4: Ablation results on Amazon, StackOverflow and Retweet.

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)

Panel of Figure 4 — Figure 4: Heatmap comparison of the seismic sequences (shown in Figure 1 ) during model training. (a) The first row shows our Continuous-Discrete Interaction( $\mathbf{X}\text{-}Interaction$ ); (b) The second row displays the conventional Attention( $Self\text{-}Attention$ ).

Panel of Figure 5 — Figure 5: Training curves with varying event counts (Percentage of the total training dataset) for Earthquake and Retweet datasets.

Panel of Figure 6 — Figure 6: Training Stability and Efficiency.

Temporal Point Processes

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Multi-class event streams arise in numerous real-world applications, where uncovering structured, interpretable inter-event relationships, together with accurate prediction, remains a central challenge. Existing neural point process models are highly expressive but encode event interactions in a black-box manner, preventing explicit discovery of structured dependencies. In this paper, we propose a structured neural marked point process (SNMPP) that achieves high modeling flexibility while enabling explicit event-wise and class-wise relationship discovery from data. Our model constructs a product-form neural influence kernel composed of a signed interaction network over event types and a delay-aware monotonic temporal network. This design enables explicit characterization of inter-class influence topology -- including excitation, inhibition, and neutrality -- while flexibly capturing diverse temporal decay patterns and potential influence delays. For efficient learning, we develop a stratified Monte Carlo estimator for stochastic training. Extensive experiments on synthetic and real-world benchmark datasets validate the ability of our approach to uncover structured relationships and deliver strong predictive performance.

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