Transformers for Mixed-type Event Sequences
Authors: Felix Draxler
Yang Meng
Kai Nelson
Lukas Laskowski
Yibo Yang
Theofanis Karaletsos
Stephan Mandt
Venue: NeurIPS 2025 spotlight ()
Keywords: marked temporal point processes
generative modeling
autoregressive models
transformers
time series
Primary area: deep_learning
TL;DR: We propose a unified transformer framework to model mixed-type event sequences

Abstract: Event sequences appear widely in domains such as medicine, finance, and remote sensing, yet modeling them is challenging due to their heterogeneity: sequences often contain multiple event types with diverse structures—for example, electronic health records that mix discrete events like medical procedures with continuous lab measurements. Existing approaches either tokenize all entries, violating natural inductive biases, or ignore parts of the data to enforce a consistent structure. In this work, we propose a simple yet powerful Marked Temporal Point Process (MTPP) framework for modeling event sequences with flexible structure, using a single unified model. Our approach employs a single autoregressive transformer with discrete and continuous prediction heads, capable of modeling variable-length, mixed-type event sequences. The continuous head leverages an expressive normalizing flow to model continuous event attributes, avoiding the numerical integration required for inter-event times in most competing methods. Empirically, our model excels on both discrete-only and mixed-type sequences, improving prediction quality and enabling interpretable uncertainty quantification. We make our code public at https://github.com/czi-ai/FlexTPP.

Transformers for Mixed-type Event Sequences
Felix Draxler, Yang Meng, Kai Nelson University of California, Irvine {fdraxler, mengy13, {fdraxler,mengy13 ktnelson)@uui..edd
Lukas Laskowski Hasso Plattner Institute, University of Potsdam
lukas. laskowski @hpi
Yibo Yang, Theofanis Karaletsos
Stephan Mandt
Cyyang, Chan-Zuckerberg Initiative
University of California, Irvine mandt@uci. edu
com
Abstract
Event sequences appear widely in domains such as medicine, finance, and remote sensing, yet modeling them is challenging due to their heterogeneity: sequences often contain multiple event types with diverse structures- for example, electronic health records that mix discrete events like medical procedures with continuous lab measurements. Existing approaches either tokenize all entries, violating natural inductive biases, or ignore parts of the data to enforce a consistent structure. In this work, we propose simple yet powerful Marked Temporal Point Process (MTPP) framework for modeling event sequences with flexible structure, using single uni- fied model. Our approach employs a single autoregressive transformer with discrete and continuous prediction heads, capable of modeling variable-length. mixed-type event sequences. The continuous head leverages an expressive normalizing flow to model continuous event attributes, avoiding the numerical integration required for inter-event times most competing methods. Empirically, our model excels on both discrete-only and mixed-type sequences, improving prediction quality and enabling interpretable uncertainty quantification. We make our code public https: het::///tthuut thtb.bb.... com/ htt//czi-ai. czi-ai/FlexTP.
Introduction
Time series are a ubiquitous data modality, arising in a wide range of domains such as electronic health records [Wornow et al.. 2023], high-frequency trading [Bacry et al., 2015], click stream prediction [Gündüz and Özsu, 2003], hardware and access logs in cybersecurity [Fortino et al., 2023], and earthquake monitoring in remote sensing [Ogata, 1998]. Particularly common are time series with irregular time intervals between adjacent events (e.g., lab test times), where each event associated with metadata known as marks (e.g., test results). Such time series are known as Marked Temporal Point Processes (MTPPs) [Daley and Vere-Jones, 2008].
Despite their broad applicability, existing MTPP models typically handle only simplified forms of real- world event data. Prior work focuses on discrete marks such event types [Mei and Eisner, 2017] or sets of items [Chang et al., 2024], or on continuous marks such spatio-temporal features [Chen et al., 2021, Dong al., 2024]. contrast, many real datasets include mixed-type metadata that combines discrete attributes (e.g., diagnosis codes, transaction types) with structured continuous values (e.g.. measurements, durations). The length and structure of this metadata also vary across events for instance, due to different medical test panels or variable-length action logs in cybersecurity.
Ignoring these heterogeneities leads mismatch between model assumptions and real data. Re- cently, Event Stream GPT [McDermott et al., 2023] modeled heterogeneous event structures, but treats continuous marks with unimodal Gaussians, limiting expressivity and autoregressive sequence
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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Conditional Event Sequence
Mixec-tyyp Autoregressive Model
Diagnosia: Type
Diabates
Patient DOB 1951-13-50
YYYY-HN-DD
0.012
Day 11:19
0.423
A 4 (C)
LA3 RESULT
Mmm C.t))
Patient Record:
Elucose In serum 116.0 mg/di.
pilp C. 111
116.0
pim Colp "4
Day 1, 11:18 LAB RESOLT
bay 8, 06:46 EROCEDURE Blood collection
7.251
P & I.C...))
Serim Glucoses 1.6.0 mg/dr.
Day 8, 06:46 PROCBDURE
pirtiz Co C. 6.
Blood collection Day 8, 13:14 LAB RESOLT Whole
Day 8, 23:14
7.552
o is F. Mi
LA3 RESULF Glacose in whole 102.0 mg/di.
102.0 mg/db
pulli C... S.
102.0
pimns C.F. 2 (.lgg
Figure 1: propose a transformer-base MTPP model for event sequences of varying length and structure. (Left) The example shows how we model electronic health record series of events with variable-length and and mixed discrete and continuous variables, conditioned on demographic information. (Right) We fit the point process using conditional autoregressive model with separate output heads for discrete and continuous entries.
generation. To address this, propose streamlined MTPP architecture that leverages expressive distributions for all variable types, yielding unified and powerful joint probabilistic model. As illustrated in Figure 1, our approach converts each event sequence into single mixed-type vector and models it with a Transformer- based autoregressive network. Discrete event types act as "headers" that determine variable event structure, and separate continuous and discrete prediction heads capture heterogeneous mark attributes.
With this more expressive mark space, we can fully exploit conditioning MTPPs external input. While prior work considered limited forms of conditioning- as static covariates-with minimal impact on prediction (Šeputis al., 2022, Verheugd et al., 2020, Isik et al., 2023], we treat condi- tioning as central, addressing problems that cannot be solved without it. This broader perspective allows us use conditional MTPPs as a flexible probabilistic framework for structural mixed-type regression.
Together, our contributions are as follows:
We propose FLEXTPP, a flexible Transformer-base MTPP framework that supports variable-length, mixed-type marks, encompassing both discrete and continuous event at- tributes (section 1).. Beyond standard generative modeling, we treat MTPPs structured prediction framework, conditioning event sequences on auxiliary input solve regression and prediction tasks (section 4.2).
FLEEXTP is intensity-free, avoiding the numerical integration required by competing intensity- based approaches. Empirically, it also outperforms both intensity-free free and intensity- based methods the discrete-only TPs benchmark [Xue et al., 2024] (section 5.1).
We demonstrate how FLEXTPP's flexibility erogeneous events electronic health records, performing event-series annotation with uncertainty quantification and extracting event dependency structure (sections 5.2 to 5,4),
be leveraged in practice: modeling het-
Together, we propose simple and versatile framework to model heterogeneous event sequences.
2
Related Work
There is extensive literature on modeling marked temporal point processes (MTPPs); we summarize work in relation to existing methods in Table 1, and give
detailed discussion below.
The predominant line of work models MTPPs with so-called Hawkes processes [Hawkes, 1971], function that captures the rate at which the next event will occur. Several neural realizations have been proposed, first using recurrent neural networks [Du et al., 2016, Mei and Eisner, 2017] and later Transformers [Zhang et al., 2020, Zuo al., 2020, Yang et al., 2021].
parameterizing an functiin

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Table 1: Overview of related MTPP methods in the literature. To the best of our knowledge, we are the first to model expressive distributions events with mixed data types and varying dimensions. In addition, we consider conditional MTPPs, where the point process depends on auxiliary input. [*] collects [Du et al., 2016, Mei and Eisner, 2017, Zhang et al., 2020, Zuo al., 2020, Yang et al., 2021, Zhuzhel et al., 2024, Chang et al., 2025, Gao et al., 2024, Xu and Zha, 2017, 1, Liu and Quan, 2024, Isik et al., 2023].
Data types
Mark dimension Multiple
Conditional
Discrete Continuous
Variable
Classical Hawkes Process [Hawkes, 1971]
X
Neural Hawkes Process [+]
X
X
Instensity- Seees TPP [Omi et al., 2019, Shicuu el al., 2020]
x
X
X
X
Conditional event generators [Dong et al., 2024]
X
/
X
X
Set-valued MTPPs [Chang et al., 2024]
x
/
Neural spatio-temporal process [Chen al., 2021]
x
/
X
X
Event Streum GPT [McDermott al., 2023]
JIX
V
Ours
/
V
convolutional networks [Zhuzhel et al., 2024], and state-space models [Chang et al., 2025, Gao al., 2024]. Other notable directions model the next-time distribution instead of intensities [Omi et al., 2019, Shehur et al., 2020], consider mixtures of series [Xu and Zha, 2017], or leverage the inductive biases of pretrained language models Liu and Quan [2024]. While the aforementioned methods only consider MTPPs where each event is associated with one discrete mark (the event type), other kinds of marks have also been considered. Chen et al. [2021] model spatio-temporal point processes using Neural ODEs, where marks are purely continuous. Similarly, Dong et al. [2024) model multi-dimensional continuous marks using joint generative models such as diffusion models. Chang et al. [2024] model sets of discrete marks. Similar to our approach, McDermott et al. [2023] propose system to learn heterogeneous event structures, but they do not learn an expressive model for continuous event data, limiting performance. We generalize the previous work into one probabilistic framework that jointly handles variable-length and mixed-type mark spaces.
Some work has considered conditioning MTPPs on external input such as for predicting failures of water pipes [Verheugd et al., 2020] or in medical context [Šeputis et al., 2022, Isik et al., 2023]. Our Transformer-based architecture allows for natural conditioning. which we exploit both for feeding covariates and as the input to regression tasks.
In the context of the related work, model is Transformer-based, intensity-free, and allows for variable-length and mixed-type marks.
In generative modeling, autoregressively predicting variable-length sequences is at the core of language models such as GPT [Mikolov et al., 2010, Radford et al., 2018J. Mixed data types are often integrated in the input but cannot be generated, for example, in iision-unddesttnding models such as Flamingo [Alayrac et al., 2022]. Jointly modeling mixed modalities has been achieved by discretizing (tokenizing) continuous values fusing other generative models and language models. We refer to [Xu et al., 2023] for a comprehensive overview. Similar to our modeling approach, [Fakoor et al., 2020) propose and [Strauss and Oliva, 2021] perform joint modeling of discrete and continuous data with a transformer backbone, inspired by autoregressive models for continuous data [Germain al., 2015]. However, neither of these works exploit the full flexibility of modeling variable-length, mixed-type data.
3 Background: Marked Temporal Point Process
natural way to describe the distribution of event sequences over time is through a Marked Tem- poral Point Process (MTPP). An MTPP is a stochastic process describing sequence of events (ll, m) where each event is characterized by its occurrence time 4 E RR+, and an associated mark mi E -M. While M traditionally describes a single discrete continuous variable (see section and table 1), we generalize in section 4.1 to mixed discrete-comtinuuus spaces. Event sequences are inherently stochastic: both the timing and the mark of the next event are inherently
3

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uncertain. Their joint distribution can be factorized using the chain rule as:
p(1(tz, m)))
II
p(z, m; Hee);
i=1
where H, = mt)).))) It t. denotes the history of events up t, capturing both temporal and mark dependencies.
Ignoring the marks for minute (we will re-introduce them in section 4.1), key design choice is how to model the one-dimensional distribution of the next event time p(t; Hz.)-
First, intensity-based methods model the time distribution via learned intensity function A(t; He.). representing the instantaneous rate of events at a time [Daley and Vere-Jones, 2008]. Formally, the intensity function A(t H4) defines the infinitesimal expected event rate, linking the point process to its conditional likelihood via integration over time:
p(t. | H4.) X(te He. [m:]) exp (-/_", A(ta He.) dt 6--1
(2)
Since the intensity function can be any positive function, this formulation yields highly flexible time distributions. However, the numerical integration can be unstable and be expensive both at training (likelihood evaluation) and inference (sampling), depending on the modeling of the intensity function.
Second, intensity methods avoid numerical integration by directly modeling event times using parametric distributions (t; Hc,) ) conditioned on the history. Common choices are mixture models or one-dimensional normalizing flows, with parameters learned as a function of past events [Shchur al., 2020). This allows efficient evaluation and sampling.
Our proposed framework in section 4 is intensity-free. Outperforming previous models in section 5.1, it overcomes concerns about expressivity of intensity-free models [Chang et al., 2025].
FlexTPP
4.1 Variable-length, mixxe--discrete-contnuuus events
Real-world events often carry heterogeneous information: some attributes are discrete (e.g., event type), others continuous (e.g., laboratory test results such glucose levels), and their number may vary depending on the event. To model such data, we introduce unified mixed-modality framework that extends MTPPs variable-length, mixed-type marks.
We are given events that consist of an arrival time 4 and an associated mark m, that may contain a variable number of discrete and continuous components. Instead of treating these parts separately, flatten the entire event sequence into a single sequence of scalar values X = (Xi...., XL), together with corresponding type vector D (D.....,I)) Dz) indicating whether each entry is continuous or discrete.
Figure illustrates this procedure. Formally, for each event i, the first mark m type denotes its type (always discrete). The remaining components add mi..,, contain additional attributes whose number N; and data types dı E {cont, disc) depend on the event type. Formally,
X (t1, mi type mil mIN, .2....), D (cont, disc, dii..... dIN, cont....). (3)
This vectorization yields single sequence of length L 2T - No
Modeling this vectorized event sequence straightforward with an autoregressive model: The joint distribution of the sequence is (X1,..,XX,, Xx.) = ID distribution matches the data type:
X where each conditional
PD, (X, X2i) = Cat(Xi (xx)
if D: = disc,
Pdeesityy (Xi Xei)
if D; = cont.
Here, Cat is a categorical distribution and Pdensity continuous density.

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Algorithm Sampling from Mixed-Typp Autoregressive Model
Input: Lengths N (mbbp) and types d(m for each event type m ...., M.
2: Initialize empty sequence X = 0, 1, 1,1=1.
3: while true do
4: Sample time X; = t Paeesityy 1,.,,,X(-11
5: Sample event type X1+1 m,
6: if mi = EDS then
7: break.
8: end if
9: for j j= j. 1..... NNm, type do
X14j+1 magus Cat(X XI,..., X(ts) if d(m)")) disc
10:
Pddenstty X14s+1[X1,--.. X(+s)
else.
11: end for
12: Update indices: 1 = 1 + (mmal and =id==
13:
end while
14:
return (li, mm
The above approach is unified autoregressive model of variable-length, mixed-type MTPPs with parameters We train it by minimizing the negative loglikelihood of a dataset 'D of time series:
min
Σ
logPD.e(X).
(X.D)ED
Algorithm shows how sample from this model. Each event begins by sampling continuous value for the arrival time, followed by an event type that determines the structure of the remaining entries. Sampling special end-of-sequence token EOS terminates the sampling.
4.2 Conditional Marked Temporal Point Processes
The general-purposs structure of our extension of MTPPs to variable data types makes them a natural choice for the output format in supervised prediction tasks. For example, we will later formulate the detection of events time series as a conditional marked time point process (see section 5.3). Similarly, for health records, feeding demographic information can increase modeling accuracy (see section 5.2). To this end, we modify the setup in section 4.1 to include conditional input C, so that the likelihood of each sequence is conditioned on C: pn pn (X(C) = -I PD, (X₂ , XI-1).
Now that have generalized MTPPs to handle heterogencous mark data and condition auxiliary information, we next instantiate this modeling approach with a Transformer architecture.
4.3 Flexible Marked Temporal Point Process (FLEXTPP)
We implement the the conditional likelihood pD, (X, X²1) in eq. (4) with an autoregressive model. The idea is map the history X X to -ied-dimensiooal representation:
Φ = (D; C, ......,, E Rdm..
(6)
which is then used to parameterize the conditional distribution of X,. As illustrated in Figure 2, we implement the autoregressive computation with a Transformer [Vaswani al., 2017]. This architecture captures long-range dependencies between events [Zhang et al., 2020, Yang et al., 2021, Zuo et al., 2020], and lets the size of intermediate representations grow naturally with the dimensionality of the marks.
For predicting discrete dimensions, map into a categorical distribution in language modeling,
Cat(2; Φt) (ofttmax((Ptiee(0r))))
(7)
where we turn di into logits ( ( with small fully-connected neural network.
For the continuous distributions, we map o; to the parameters (Pcot((s)) of one-dimensional normalizing flow, is common for continuous autoregressive models [Germain al., 2015]. We use
5

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Conditioning Network
0.012
0 0.423
Ploee
Autoregressive Transformer
Fise
Embedding
P1
Paa
116.0
P4
Poas
EOS
Figure 2: Our Transformer backbone naturally encompasses mixed-type marks and conditions. The vectorized input data (see fig. 1) is shifted by one position so that the embedding Φi for predicting X; depends only the history X and the condition. The Transformer is equipped with causal mask. We use classification head for discrete dimensions, and oie-dimensional normalizing flow for continuous dimensions.
rational- aational-quadratic spline frcmm (x) [Durkan al., 2019]. The flow defines one-dimensional (conditional) density via the change variables equation:
Pdensity (z;; Φ1) = =====Jpunatte (r); m = 0, (z)]
(8)
Note that for simplicity, we use eq. (8) both for the time and continuous mark dimensions ("intensity- free", section 3). We call the above model Flexible Marked Temporal Point Process FLEXTPP when no condition is present, and we refer to FLEXTPP-C whenever it is conditioned.
5 Experiments
We evaluate our generalized MTPP framework in practice. We first confirm that FLEXTPP(-C)
reliably works with discrete mark spaces on the EasyTPP benchmark [Xue al., 2024] in section 5.1. We then demonstrate in section 5.2 how our generalized mark structure improves predicting medical procedures electronic health records extracted from the EHRSHOT dataset [Wornow et al., 2023]. Finally, we propose to use MTPPs to make structured predictions in annotating time series in section 5.3. This MTPP heavily relies on its condition and can predict several types of annotations together with their structurally different properties.
For the experiments that concern generalized mark spaces, compare the following versions of our model:
Conditional + discrete event type mark:
type adl C)) p(t1, mine _paa tr, m .p89
(9)
Unconditional full mark (FLEXTPP): p(t1, mipe .m add
..... tr m type add
mmT
(10)
Conditional full mark (FLEXTPP-C): p(1 mire mi tr, mT m²T (C),
(11)
The first model in eq. (9) only models time and discrete event type as a mark, corresponding to how the bulk of the literature MTPPs would model the data. We give these models access to the condition to allow for fair comparison the most general variant, FLEXTPP-C. The second model in eq. (10), in contrast, does not have access to the condition and only models the marginal marked time point process. Here, we measure how much the condition helps in making a prediction. Finally, model in eq. (11) accepts condition and jointly models all discrete and continuous marks.
We evaluate all models on a held-out test set terms of negative lig-likelihood (NLL), capturing the generative quality and the uncertainty in making predictions.
To compare conditional model the unconditional variant, compute the negative logarithms of eqs. (10) and (11). Intuitively, a lower value means that the conditional model can make use the condition more accurately model the MTPP.
Comparing these likelihoods to the ones of the model that only captures discrete event types not directly possible, eq. (9) does not model the additional mark dimensions. We therefore also report

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Table 2: Our model sets a new SOTA in four out of five datasets in terms of Negative Log-Likelihoods (lower better, 4) on EasyTPP Datasets [Xue al., 2024], notably outperforming both intensity-fiee
TPP [Shchur et al., 2020] and intensity-based methods. Marks are single discrete event type. Baseline values are due to [Chang et al., 2025].
Model
Amazon
Retweet
Taxi
Taobao
StackOverflww
RMTPP [Du al., 2016]
2.136 (0.003)
7.098 (0.217)
-0.346 (0.002)
-1.003 (0.004)
2.480 (0.019)
NHP [Mci and Eisner, 2017]
-0.129 (0.012)
6.348 (0.000)
-0.514 (0.004)
-1.157 (0.004)
2.241 (0.002)
SAHP [Zhang et al. 2020]
2.074 (0.029)
6.708 (0.029)
-0.298 (0.057)
1,646 (0.083)
2.341 (0.058)
THP [Zuo et al., 2020]
2.096 (0.002)
6.659 (0.007)
-0.372 (0.002)
(0.01))
2.338 (0.014)
Aung et al., 2021]
0..8470.0077
6,499 (0.028)
-0.493 (0.009)
1.259900.02)
2.194 (0.016)
IFTPP [Shchur al., 2020]
-0.496 (0.002)
10.344 (0.016)
-0.453 (0.002)
(0.017)
2.233 (0.009)
MHP [Gao et al., 2024]
-0,4% (0.002)
10.344 (0.016)
-0,453 (0.002)
-1.318 (0.017)
2.233 (0.009)
S2P2 [Chang ct al., 2025]
-0,781 (0.011)
6,365 (0.003)
-0.522 (0.004)
-1.304 (0.039)
2.163 (0.009)
FLEXTPP (Ours)
-0.633 (0.039)
5,646 (0.070)
-0.763 (0.005) -1.402 (0.013)
2,133 (0.004)
the negative log-likelihood of the time and the event type mark dimensions under each model:
m! p(t, m. [[),, m 1..-11 [m (...11))
1ype
add
(12)
We pass in the additional mark dimensions and the condition only if the model version accepts them. A smaller loss means that the model can better estimate the arrival time and type of the next event when it has seen all marks of the previous event instead of just arrival times and marks. For example, in the clinical settings, it measures whether the next medical procedure prediction improves if know the continuous lab results.
We give all details to replicate our experiments in appendix A.
5.1 EasyTPP Datasets
The EasyTPP benchmark [Xue al., 2024] collects five datasets to compare models fitting MTPPs. All datasets have discrete mark space modeling event types only, see appendix A.1. Table 2 shows that our intensity-free, Transformer-baas based MTPP outperforms both antensity-based and previous intensity-free methods.
This is important data point in the MTPP modeling space, it shows that intensity-free methods can perform well, all while avoiding numerical integration at training and inference time. In the next sections, we generalize the mark space beyond discrete marks.
5.2 Patient Record Data
As a first generalized experiment, we model a subset of EHR data from the EHRSHOT bench- mark [Wornow et al., 2023]. Unlike standard EHR setups that capture only discrete events like procedures [Chang et al., 2025], our construction also includes continuous lab results, enabling a richer, mixed-modalit representation of patient trajectories. This structure improves next-event prediction and enhances uncertainty quantification by integrating diverse clinical signals. See ap- pendix A.2 for details.
To compile the dataset, we subset the patients diagnosed with 20 different diseases such as type diabetes, dyspnea, atrial fibrillation, etc., to create disease-specific longitudinal analyses. For each disease, we capture the most used Current Procedural Terminology (CPT-4) codes that denote medical services and the most common procedures as discrete events, and model discasc-related lab results as continuous events. Additionally, demographic data are incorporated as conditional inputs, enabling a better modeling of patient-specifie dynamics.
Table demonstrates the effectiveness of our proposed method. Besides the baseline in eq. (9) ("Procedures") which only models procedures as discrete events, we also compare FLEXTPP and FLEXTPP-CG to another baseline ("+ Lab Tests") which additionally measures discrete lab test types but without their corresponding continuous results. By jointly modeling continuous lab results alongside discrete procedure types and conditioning on demographie information, our FLEXTPP-C approach achieves the best performance on both measures of negative likeliold ("Full" and
7

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Table 3: By incorporating continuous lab results via eq. (1I), our flexible models outperform baselines in predicting time and type of medical procedures: An MTPP with discrete marks would either not model lab events at all [Chang et al., 2025] ("Procedures"), or model that a lab test exists, but ignore its value ("+ Lab Tests"). Conditioning on demographic covariates (our FLEXTPP-CI always improves prediction quality for procedures and in the majority of cases for all events. Standard deviations tables 9 and 10.
Time Discrete Procedure (LL ESGPT
Full NLL PLEXTPP
Duttsse
Procedures
e LLab Tests
ESGPTE
FLEXTPP
PLEXTPP:C
ESGPT
ESGPEC
PLEXTPP-C
Type 2 diabetes mellitus
0
0.202
0.186
0.180
0.147
0.143
0.754
0.758
0.641
0,638
Transplanted kidsey
0,755
0,177
0.399
0.192
0.134
0.130
0.859
0.363
0.670
0.668
Transplanted lung
0:912
0.089
0,078
0:075
0.068
01063
0.51
0.857
0.581
0,546
Dyspnea
0.581
0.162
0.162
0.155
0.121
0.117
0.560
0.549
0.053
0.436
libiilittion
0.005
0.171
0,059
0.388
Carliac transplant discecker
0.552
0.504
sage discase
0.117
0.257
Transplanted
0,028
0.701
Congestive heart failure
0.134
0.330
0.128
0.100
0.846
0.361
Chrenic pain
0.735
0.099
0.085
0.091
0.073
0.765
0.743
0.162
Neoplasm of female breust
0.716
0,043
0.040
0.038
0.002
0,030
0.608
0.508
0.516
0.461
Obstructive sleep sprici Diabetes with complicaton
0.695
0,023
11.090
0.0897
0.061
11A89
0.710
0.676
0.195
0L187
0.718
0.176
0.164
0.150
0.133
0.129
0.694
0.703
0.579
0.582
Anemia
0.655
0.164
1.365
0.158
0.127
0.126
0.322
0.296
0.238
0.245
Corcuury artery discasc
0.692
0.144
0.138
0.134
0.108
I1105
0.965
0.986
0.636
R.625
Hypollyyoidion
0.735
0.234
0..112
0.208
0.166
111199
0.665
0.564
0.524
0.528
Acule mycloid leukemia
0.729
0.182
0.160
0.154
0.124
0.117
0.727
0.735
0.567
0.561
Depressive disorder
0.105
0.545
Traesphanial liver
0.142
kidney injury
0.191
0.706
0.711
0.621
"Time Discrete Procedure"). ESGPT and ESGPT-C (McDermott et al. [2023]) are also implemented as additional baselines, where continuous lab results and arrival times are modeled by Gaussian and Log- mixture heads, respectively, instead of the normalizing flow head used in our proposed methods. These results validate the advantage of incorporating continuous event types, patient- specific conditioning, and the expressiveness in modeling continuous attributes using normalizing flow in multimodal health record modeling.
5.3 Time Series Annotation
Finding eventful subsequences in time series data is crucial in many real-world applications. For example, in healthcare, timely and accurate identification of critical events can significantly impact diagnosis and treatment, and in audio annotation, where a continuous time series is transformed into an interpretable description.
traditional approach to have a classifier p(m |t, C)) predict the presence of an event type mre at given time L in an input sequence C' [Zhao et al., 2017]. However, fig. 3 (top right) illustrates how this is fundamentally limited when several events are present at the same time: It expresses uncertainty in the event class instead of predicting both classes to be present. Another restriction is that classifiers are often evaluated on small windows to save compute for long input time series.
We lift these restrictions by directly predicting the target sequence of events as a MTPP under our flexible framework FLEXTPP-C. This allows for parallel events, and compute is naturally bounded by the number of events. In this setting, each event is characterized by start timestamp (continuous). a type label (diserete), a duration (continuous), and additional event data (mixed length, mixed type). Because our framework is fully probabilistic, we get uncertainties for all these quantities.
We evaluate our model on set of synthetic input time series. Our dataset is based on noisy harmonic oscillator, a common model in biology, physics, acoustic and mechanical systems. It is given by the following system of stochastic differential equations:
(13) For each time series in our dataset, we first choose base values for the constants w, 7, oz, T. We then randomly sample a list of events that alter the dynamics over some amount of time by changing one or several of the constants, or add an external force f()). See appendix A.3 for details.
dx vdt + o,,, de (-y0 - w2x ff f()) + o,dw,,
Figure shows a typical example time series with annotated events. Our FLEXTPP-C predicts event times and properties, together with uncertainty intervals. Note how an MTPP with discrete marks only captures the start times and type of events. Table evaluates eqs. (9) and (11) to compare negative likeliiissssss. We also train sliding window classifier [Zhao al., 2017] with a finite
8

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Iripus Lime baries
Sliding window cissiffer
Tar For Cor Plapy
50%
Input
Rn.
disrmtee marks
B.tc
km..
Ground teuch annocations
71 toars)
B.
B.tc.
E(-
Time
Time
Figure 3: Our FLEXTPP-C framework allows structured prediction tasks such annotating events in an input time series with full uncertainty quantification. (a) Example input time series from our synthetic dataset. (b) Ground truth events including per-event-type properties, one row per event type, see legend on top right for abbreviations. (c) Predicting the event type p pm (c, C.) at given time I cannot properly describe several events happening at the same time, it instead expresses uncertainty in the event class. (d) A discrete-mant MTPP only predicts start times and event types. (c) Our model samples meaningful sequences detailed as the ground truth. Error bars are the standard deviation from 256 model samples.
Table 4: We formulate probabilistic time series annotation conditional MTPP. Our FLEXTPP-C achieves the best AUC ROC scores by jointly sampling events, event types and durations. FLEXTPP without condition naturally achieves random AUC ROC (0.5), but yields useful baseline for negative log-likelihoods (NLL). A conditional MTPP with only discrete marks does not predict event durations, but achieves decent AUC ROC when assuming the average duration for each event. As an additional baseline, we compare to a CNN-based time series classifier [Zhao et al., 2017] with limited window size. Standard deviations estimated from five runs, note that the type NLL conditioned on correct event duration. Time + Type NLL in bits/event, Full NLL in bits/dim.
NEECD
ROC
Time + Typ:
External
Damping slange Basc fasquancy
Postioon suise
Evarl
Moa Singloclas
(0.005)
3.010 (0,003)
(0.0)
00.00
(0.0)
(0.0)
(0.0)
(0.0)
Only Discrete Marks
0,474 (0.006)
wg
0,96 (0.01)
(0.003)
(0:01)
0:91
(0.01)
PPPC
(0.07))
(0.00))
(0.00.3)
0,90 (0.01)
0.92 (0.01)
Sliding Window Classiter
0.36 (0.06)
0.50
0,96 (0.04)
(0.06)
0,89 (0.06)
0,82 (0.02)
window size. We evaluate all methods using the area under the receiver-operator curve (AUC ROC) [Hanley and McNeil, 1982]. common metric to identify how well predicted events overlap with the ground truth [Schmidl et al., 2022]. FLEXTPP-C annotates most event types almost perfectly, and outperforms the random baseline significantly on the difficult "damping change" event type, which is hard to detect by construction. Naively, discrete mark MTPPPs cannot be evaluated with AUC ROC since they do not predict event durations, so we evaluate this metric using the average event duration.
5.4 Extracting Event Dependencies
How do events depend on one another under learned model? Some neural Hawkes process variants provide interpretability through structures their explicit triggering kernels q(14, m,, I, m), so that A(4,, m.ammmHHH,, (H,,)) Σ (t.m)EH, g(4,, m4, I, m) [lsik al., 2023, Zhu al., 2022]. Such kernels directly encode pairwise influence structures, providing global access to the modeled dependency structure.
Our framework offers complementary, local interpretability mechanism. To derive it analogously, we can solve eq. (2) for the intensity function A(t,) (H,) given a time density p(t: (4,,)
p(t, m. (H..)
A(ti, mi(He.) 1 f p(s, m. m,lHH,,ee )ds
(14)
Here, we have reintroduced marks my
We can extract the local triggering kernel via eq. (14) by evaluating A(12, m2 | (4,, m1) m))). To demonstrate this, fig. 7 in appendix A.4 replicates synthetic setup from Isik et al. [2023]. We show

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that our model can recover influence curve matching the ground truth with RMSE 0.01, indicating that our learned event dependencies are both accurate and recoverable.
These approaches exhibit broader tradeoff between global interpretability and modeling flexibility. Kernel-based models provide concise, fully inspectable description of event interactions, but their rigidity can misrepresent complex real-world dynamics. For instance, some domains exhibit state- dependent effects-such as advertising "fatigue." where repeated exposures first increase and later decrease response probability- that cannot be captured well by monotone additive influence kernels. In such cases, the model is not expressive enough for the true dependency structure, and the resulting explanations appear structured but do not reflect the true data-generating process.
Our model instead supports local interpretability: affects intensities or subsequent event sequences, yielding contextual, fine-grained explanations. This aligns with complex event sequences, where influences are often situational rather than universal.
can ask how specific event subset of events
6 Conclusion
In this work, propose simple yet powerful method to model more general Marked Time Point Processes - ones with mixed-type (discrete and continuous) marks and auxiliary contextual informa- tion. Our intensity-free modeling approach treats MTPP as one joint sequence consisting of auxiliary information (if available), event arrival times, and marks; we then model the sequence autoregressively using a single Transformer with appropriate output heads. We observe that incorporating additional information generally improves modeling performance; this is expected from an information-theowm perspective conditioning reduces entropy, which is the minimum achievable negative log-likelihood [Cover and Thomas, 2006]. From a modeling perspective, we observe that complex intensity func- tions may not be necessary intensity-fres modeling with good one-dimensional density estimators may be enough to model temporal processes well.
Our generalized MTPP framework also highlights how MTPPs can be used versatile prediction tool for annotating input time series. Crucially, MTPPs naturally model the joint probability of each prediction, that each sampled annotation from the model is consistent explanation of the input. The formulation also naturally allows for overlapping events. We envision future work to extend this paradigm for annotating spatio-tempont sequences to enhance uncertainty quantification in the annotation of time series, such as audio, video, as well as scientific measurements.
Broader Impact. Modeling critical data, such as in the context of medicine, can cause harm through wrong or wrongly interpreted predictions, such as those arising from biases in the training data and distribution shifts. On the positive side, modeling additional variables and incorporating context can increase prediction accuracy and enable novel applications.
7 Limitations
Limitations of autoregressive modeling. Our approach inherits the limitations autoregressive modeling. In particular, when scaling to high-dimensional marks such images, alternative gen- erative modeling approaches may be more suitable [Chang et al., 2025]. Another direction is to jointly learn representation of the marks that is better suited for downstream modeling [Tschaanenn et al., 2024]. Similarly, if the marks follow special structure such as special geometry or topology, autoregressive models cannot be applied faithfully and generic methods such as [Sorrenson al., 2024] can be used to model these dimensions.
Alternative data types. In work, we consider discrete and continuous data. Other mark modalities, such as sets or ordered discrete variables, could be studied the future.
Limitations of Transformer backbone. The compute of Transformers scale quadratically with the length L of the underlying sequence: O(L²). This complexity can make them unsuitable for modeling very long sequences. However by construction, our framework is compatible with other autoregressive models such as recurrent neural networks [Elman, 1990], linear-attention Transformers [Katharopoulos et al., 2020], state-space models [Gu et al., 2021] that have better length scaling.
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Acknowledgments and Disclosure of Funding
We thank Kushagra Pandey for additional discussions and feedback. This project was funded through support from the Chan Zuckerberg Initiative. Additionally, Stephan Mandt acknowledges funding from the National Science Foundation (NSF) through an NSF CAREER Award IIS 2047441, IIS- 2007719, the NSF LEAP Center, and the Hasso Plattner Research Center at UCI. Lukas Laskowski acknowledges financial support from SAP SE. Parts of this research were supported by the Intelligence Advanced Research Projects Activity (IARPA) via Department of Interior/ Interior Business Center (DOI/IBC) contract number 140D0423C0075. The U.S. Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright annotation thereon. Disclaimer: The views and conclusions contained herein are those of the authors and should not be interpreted necessarily representing the official policies endorsements, either expressed or implied, of IARPA, DOL/IB, or the U.S. Government.
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Appendix: Transformers for Mixed-typp Event Sequences
A
Experimental Details
We base our code on PyTorch [Paszke et al., 2019], PyTorch Lightning [Falcon and The PyTorch Lightning team, 2019], numpy [Harris et al., 2020], hydra [Yadan, 2019] and pandas [The pandas development team, 2020, McKinney. 2010]. Our rational-quadratic spline [Durkan et al., 2019] implementation adapted from FrEIA [Ardizzone et al., 2018].
Unless stated otherwise, we use the AdamW optimizer [Loshchilov and Hutter, 2019] and a one cycle learning rate scheduler [Smith and Topin, 2019] in the PyTorch implementation with factfaactrr of 10 and a pct_stare start of 0.
A.1 EasyTPP
The TPs [uue et al., 2024] benchmark contains the following datasets:
Amazon [Ni et al., 2019] features user reviews where each product category serves as a distinet mark. Retweet [Zhao al., 2015] forecasts the popularity of retweet cascades, with event types categorized by user influence levels based on follower counts. Taxi [Whong, 2014] captures pickup and dropoff events across New York City, where marks are constructed from the Cartesian product of five predefined locations and two action types. Taobao [Xue et al., 2022] models user browsing behavior on e-commerce platform. using item categories as marks. Lastly, StackOverflow collects user badges over time [Du et al., 2016].
Table 5 shows the hyperparameters
We identified them using grid search optimizing for validation negative log-likelihood, separately for each dataset. This mirrors the procedure from which obtain baselines [Chang et al., 2025]. We stop training early when the validation NLL has not improved over 300 epochs, and use the checkpoint of best validation for evaluating the model.
We ran all experiments in parallel on single NVIDIA H100 GPUs, taking about 3 hours for all experiments to finish.
Table 5: Hyperparameters used for the Easy TPP benchmark.
Amazon
Retweet
Taobao
Taxi
StackOverflow
nepoocss
1000
Thhead
4
256
Non-linearity
GELU
Transformer depth
5
5
5
dx
12
32
12
24
Páropout
0.4
0.2
0.38
0.44
0.46
Tibins
11
10
Batch size
159
246
207
176
204
Learning rate
0.001
0.00015
0.0008
0.0005
0.0004
21

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Table 6: Our method outperforms the previous intensity-free IFTPP [Shchur et al., 2020] on all Easy TPP datasets [Xue et al., 2024] in terms of negative log-likelihood (lower is better, lowest value in bold, second lowest value underlined). (Top) Extract of table 2 comparing our FLEXTPP to IFTPP. (Bottom) Ablation of our transformer backbone with IFTPP's prediction head for continuous data, mixture of K log-normal distributions.
Model
Amazon
Retweet
Taxi
Taobao
StackOverflow
FLEXTPP (Ours) IFTPP [Shehur al., 2020]
-0.633 (0.039)
5.646 (0.070)
-0.763 (0.005)
-1.402 (0.013)
2.133 (0.004)
-0.496 (0.002)
10.344 (0.016)
-0,453 (0.002)
-1.318 (0.017)
2.233 (0.009)
K 16 log- log-normal
2.211 (0.004)
6,450 (0.001)
-0.734 (0.002)
-1.354 (0.004)
2.253 (0.005)
K = 32 log-normal
2,210 (0.018)
6.449 (0.001)
-0.732 (0.004)
-1.354 (0.006)
2.251 (0.004)
K 64 log-normal
2,208 (0.007)
6.450 (0.001)
-0.727 (0.004)
-1.355 (0.004)
2.263 (0.006)
K 128 log-normal
2.215 (0.003)
6.451 (0.001)
-0.719 (0.006)
-1.336 (0.003)
2.266 (0.003)
Table 7: Hyperparameters used for EHRSHOT.
Pepoccs
7hhaad
Taa'
Non-linearity
Transformer depth dx
Abbiss
Batch size
Learning rate
2000
256
GELU
128
0.0005
A.2 Patient Record Data
EHRSHOT [Wornow et al., 2023] models irregular time series of clinical events from electronic health records, using lab tests and procedures as distinct marks.
The dataset has been split into Train- ValiiaaiiidiiTessssss with ratio of 70%-15%--15% We pick the top 20 most common diseases as subdatasets to train and test the models. For each disease, we capture the top 10 most frequent Current Procedural Terminology (CPT-4) codes that denote medical services and procedures as discrete events, and model the 5 most relevant disease-relatee lab results as events with their type and continuous value.
We perform early stopping during training when the validation NLL has stopped decreasing for over 200 epochs, and use the checkpoint of best of validation NLL for testing.
To make fair comparison, all the model share the same model structure. Sinusoidal positional encoding are applied across all models, within each event. The positions are encoded within each event. For each event, arrival time, event type (lab test or procedure), lab test/procedure type, and lab test result (if applicable) are placed at positions 1, 2, 3, and 4, respectively. The metadata (age, gender, ethnicity, and race) are fed as additional tokens into the beginning of the time series, serving as the condition part of the model. More details of the model structure can be found in table 7.
For hyperparameter tuning, the best hyperparameters batch size is 128 and the best learning rate is 0.0005, searched from the spaces [64, 128, 256] and [0.0001, 0.0005, 0.001] across all models and subdatasets. The best dropout rates are listed table searched from the space [0.0, 0.1, 0.2].
The best chosen based the validation
We ran all experiments in parallel on single NVIDIA Quadro RTX 8000 GPU and single NVIDIA Quadro RTX 5000 GPU, taking about 120 hours for all experiments to finish.
A.3
Conditional Event Detection
A.3.1
Dataset
We generate our dataset by integrating the SDE described in eq. (13). We give the default values for all parameters in table 11; some values are fixed for all time series and some are sampled anew for each time series.
These parameters are then modified during the SDE integration. Recovering these modifications will later be the prediction to be made by the model.
To this end, we first sample the number perturbation events to occur (compare table 11). Then, we sample the start time, duration and ramp time for each modification event according table 12.
22

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Table 8: Dropout Rates used for EHRSHOT.
Dataset
Procedures
+ Lab Tests
ESGPT
ESGPT-C
FLEXTPP
FLEXTPP-C
Type 2 diabetes mellitus
0.0
0.0
0.0
0.0
0.0
0.0
Transplanted kidney
0.0
0.0
0.1
0.1
0.1
0.1
Transplanted lung
0.1
0.0
0.1
0.1
0.1
0.1
Dyspnea
0.0
0.0
0.0
0.0
0.0
0.0
Atrial fibrillation
0,0
0.1
0.0
0.0
0.0
0.0
Cardiac transplant disorder
0.0
0.0
0.1
0.1
0.1
0.1
End-stage renal disease
0.1
0.1
Transplanted heart
0.1
0.0
0.0
0.0
Congestive heart failure
0.0
0.0
0.0
Chronic pain
0.0
0.0
0.0
Neoplasm of female breast
0.1
0.0
0.1
0.1
0.1
0.1
Obstructive sleep apnea
0.1
0.0
0.0
0.0
0.0
0.0
Diabetes with complication
0,0
0.0
0.1
0.1
0.1
0.1
Anemia
0,0
0.0
0.0
0.0
0.0
0.0
Coronary artery disease
0.0
0.0
0.0
0.0
0.0
0.0
Hypothyroidism
0.0
0.0
0.1
0.1
0.1
0.1
Acute myeloid leukemia
0.1
0.0
0.1
0.1
0.1
0.1
Depressive disorder
0.0
0.0
0.0
0.0
0.0
0.0
Transplanted liver
0.0
0.0
0.1
0.1
0.1
0.1
Acute kidney injury
0.0
0.0
0.0
Table 9: Table 3 Time + Discrete Procedure NLL (4) with standard deviations over five runs.
Procedures
Lab Tests
ESGPT
ESGPI-C
FLEXTPP
FLEXIPP-C
Type diabetes mellitus
0.691 (0.0020)
0.202 (0.0012)
0.186 (0.0010)
0.182 (0.0010)
0.147 (0.0006)
0.143 (0.0012)
Transplanted kidney
0.755 (0.0130)
0.170 (0.0021)
0.199 (0.0020)
0.192 (0.0028)
0.134 (0.0007)
0.130 (0.0014)
Transplanted lung
0.912 (0.0019)
0.089 (0.0003)
0.078 (0.0006)
0.075 (0.0002)
0.068 (0.0003)
0.063 (0.0000)
Dyspnea
0.681 (0.0019)
0.162 (0.0003)
0.162 (0.0011)
0.155 (0.001 1)
0.121 (0.0006)
0.117 (0.0005)
Atrial fibrillation
0.715 (0.0072)
0.081 (0.0001)
0.075 (0.0003)
0.071 (0.0003)
0.062 (0.0001)
0.059 (0.0005)
Cardiac transplant disorder
0.887 (0.0055)
0.034 (0.0001)
0.034 (0.0004)
0.033 (0.0005)
0.029 (0.0002)
0.027 (0.0004)
End-stage renal discase
0.697 (0:0035)
0.166 (0.0012)
0.169 (0.0020)
0.128 (0.0012)
(0.0008)
Transplanted heart
0.034 (0.0024)
0.887 (0.0001)
0.033 (0.0002)
0.032 (0.0004)
0.029 (0.0003)
0.028 (0.0001)
Congestive failure
(0.0040)
0.704 (0.0006)
(0.0026)
0.103 (0.0007)
(0.0005)
Chronic pain
0.735 (0.0042)
0.099 (0.0002)
0.095 (0.0004)
0.093 (0.00066
0.076 (0.0017)
0.073 (0.0009)
Nooplasm female breast
0.716 (0.0025)
(0.0007)
0.040 (0.0006)
(0.0003)
0.032 (0.0003)
0.030 (0.0006)
Obstructive sleep apnea
0.695 (0.0023)
0.093 (0.0006)
0.090 (0.0007)
0.089 (0.0013)
0.061 (0.0006)
0.059 (0.0002)
with complication
(0.0022)
(0.0004)
(0.0017)
(0.00L3)
(0.0007)
(0.0005)
Anemia
0.655 (0.0025)
0.164 (0.0013)
0.165 (0.0012)
0.158 (0.0007)
0.127 (0.0006)
0.126 (0.0008)
Curonary artery diseuse
(0.0021)
(0.0011)
0.138 (0.0008)
(0.0012)
0,108 (0.0006)
(0.0003)
Hypothyrodismm
0.735 (0.0013)
0.224 (0.0010)
0.212 (0.0011)
0,208 (0.0013)
0,166 (0.0007)
0.159 (0.0009)
myeloid leukemia
(0.0065)
(0.0021)
(0.0011)
(0.0012)
0.124 (0.0009)
(0.0005)
Depressive disorder
0.683 (0.0027)
0.136 (0.0008)
135 (0.0011)
0.1 (0.0007)
0,108 (0.0006)
0.105 (0.0013)
Transplanted liver
0.799 (0.0063)
0.183 (0.0008)
0.192 (0.0015)
(0.0024)
0,144 (0.0019)
0.142 (0.0026)
Acute kidney injury
0.201 (0.0026)
0.645 (0.0003)
0.191 (0.0006)
081 (0.0004)
0.144 (0.0010)
0.139 (0.0005)
Depending on the type, sample the event properties via table 13. The ramp time avoids sudden changes in parameters, so that the events are harder to detect.
The events replace the parameters in eq. (13) with the following dynamic coefficients:
Tx (1) Or,00 +
Σ
all; E)
(15)
E: DT
w(t) wo
II
(1+ (t: E)we),
(16)
E: m. VC= =C &
7(1) = 7
II
(1 + a(1; EYTE),
(17)
E: m DT== =B
f()) =
Σ
Elt:E)
(
1-T!
2TT
(18)
m
Byc The function a<I; F) Here, the sums/products run over all events F. of the corresponding type m turns off the event outside of its domain and interpolates over the ramp time at the beginning and end
23

---

Table 10: Table 3 Full NLL ()) with standard deviations over five runs.
Dataset
ESGPT
ESGPT-C
FLEXTPP
FLEXTPP-C
Type 2 diabetes mellitus
0.754 (0.0038)
0.758 (0.0056)
0.641 (0.0050)
0.638 (0.0027)
Transplanted kidney
0.859 (0.0070)
0.863 (0.0225)
0.670 (0.0083)
0.668 (0.0111)
Transplanted lung
0.851 (0.0013)
0.857 (0.0200)
0.581 (0.0060)
0.546 (0.0122)
Dyspnea
0.560 (0.0111)
0.549 (0.0185)
0.463 (0.0038)
0.438 (0.0021)
Atrial fibrillation
0.388 (0.0119)
0.376 (0.0091)
0.204 (0.0048)
0.192 (0.0090)
Cardiac transplant disorder
0,552 (0.0524)
0.594 (0.0553)
0.408 (0.0116)
0.393 (0.0203)
End-stage renal disease
0.757 (0.0145)
0.753 (0.0112)
0.580 (0.0037)
0.578 (0.0032)
Transplanted heart
0.736 (0.0233)
0.701 (0.0163)
0.546 (0.0041)
0.521 (0.0036)
Congestive heart failure Chronic pain
0.846 (0.0102)
0.861 (0.0116)
0.525 (0.0066)
0.509 (0.0096)
0.765 (0.0046)
0.743 (0.0075)
0.162 (0.5)
0.165 (0.0078)
Neoplasm of female breast
0.608 (0.0068)
0.608 (0.0141)
0.516 (0.0309)
0.461 (0.0270)
Obstructive sleep apnea
0.710 (0.0075)
0.676 (0.0097)
0.5 (0.0354)
0.187 (0.0285)
Diabetes with complication
0.694 (0.0113)
0.703 (0.0114)
0.579 (0.0023)
0.582 (0.0047)
Anemia
0.322 (0.0014)
0.296 (0.0190)
0.238 (0.0121)
0.245 (0.0097)
Coronary artery discase
0.966 (0.0246)
0.986 (0.0247)
0.636 (0.0138)
0.625 (0.0134)
Hypothyroidism
0.666 (0.0068)
0.664 (0.0063)
0.524 (0.0037)
0.528 (0.0080)
Acute myeloid leukemia
0.727 (0.0131)
0.735 (0.0139)
0.567 (0.0161)
0.561 (0.0050)
Depressive disorder
0.813 (0.0038)
0.826 (0.0101)
0.608 (0.0129)
0.545 (0.0133)
Transplanted liver
0.907 (0.0211)
0.902 (0.0150)
0.727 (0.0104)
0.725 (0.0159)
Acute kidney injury
0.706 (0.0037)
0.711 (0.0037)
0.621 (0.0042)
0.605 (0.0028)
Table 11: Base parameters of the harmonic oscillator specified in eq. (13). The observation noise is randomly sampled for each time series. The notation indicates that the corresponding value is sampled.
Property
Value
Damping To
0.1
Base frequency wi
30 2n (30 Hz oscillator)
Time range
0.11 in 10s steps
Noise strength on position dx,0
0.01
Noise strength velocity o,
1.0
Observation noise
LogNorm(p== log(O.01), =log(.1))
Number of perturbation events
u(f1....,5) 55)
Table 12: Shared properties for all events are randomly sampled for each event, independent of other events. The last column indicates whether that property is to be predicted by our models.
Property
Distribution
To be predicted?
Event duration öt.
U( (|025, 0.5))
Event start &
24( 0, duration)
Event type mpe
~ [[(([tppe defined in table 13))
Ramp time f,
~(( duration/4)
Table 13: Custom event properties per event type and how we draw them. They are all predicted by our model.
Event Type
Property
Distribution
A: External force
Magnitude 3
U([,, 1.5))
Force shape s
U4 (sin, square, sawtooth))
Periodicity T ~ [4(00.1.0011)
B: Damping change
Factor Kw
~ U(([055115)
C: Base frequency change
Factor Kr,
+ sa, where ~ U(1-1,1) and [(((0.1,02)
D: Position noise
Additional noise o.,
5((1.0,5.0))
24

---

of the event:
0
ift iftsta tg iftg < tg + åtg
t-tg fr
att: E)
1
iftg f,E S tg + òtg 4,E
(19)
(1g +0tg fr.6)
ift < < tg + +ôg
iftg ötg $
We use sdeint's itoint [Jaekel, 2015] to solve the SDE, initializing to x = 1.0, c = 0.0. After integrating, we add independent observation noise to each time point. We avoid extreme values by softly clamping the time series in [-10, 10), where C' = L/2 and L 10:
poft_clip(z)) sign(z)) clipped
(20)
|
r S L if r
where clipped =
(21)
L + (C -
L
1
k C-L
(22)
We generate 100,000 input time series with annotations, using 80% for training, and 10% for validation and testing each. We provide the code for generating the data in the supplementary files.
A.3.2 MTPP-based event detection
It is straightforward to turn the prediction of the above events into generative prediction task via an MTPP.
To this end, we utilize event E's start time I as its arrival time, the type of change per table 13 as the discrete mark type m type and the duration as well as the other properties as the additional marks. Coneretely:
(A) 4, N(B) N(C) N(D) 2,
d(A) (cont, cont, disc, cont), d(B) d(C) d d(D) (cont, cont).
(23)
(24)
As conditioning network, we preprocess the imput time series using a Transformer with full attention (non-causal). It shares the embedding dimension dg = Raeadx with the autoregressive backbone of the MTPP model. To tokenize the data, we split the incoming time series into windows size l, and map them through linear layer to the embedding size dg. The conditioning Transformer has depth 2, dr 256 and dropout 0.
All other hyperparameters are specified in Table 14, each determined from a hyperparameter optimiza- tion. Interestingly, the discrete-only variant has significantly more monotonic bins the continuous distribution than our FLEXTPP-C. We think that this is due to the requirement to model a more complicated distribution for the next-time prediction. We stop training the last 300 epochs did reduce the validation loss and evaluate each run using the checkpoint with minimal validation loss. Training takes about three hours per run, with five parallel runs on a single NVIDIA H100.
We make use of two complementary positional encodings: A learned embedding encoding the position in the event, and positional encoding of the event in the sequence.
A.3.3 Ablation on Event Property Order
In an autoregressive model, we can change the order of variables to obtain the same joint distribution via the chain rule of probability:
1. II
( X²) II (x. 1=1
(x((xx [=1
(.. Xza-)))
(25)
We find that for the event annotation dataset, it is beneficial deviate from the order in eq. (3):
(ti, mi, m (ts, m, duration, other event properties,).
(26)
25

---

Table 14: Hyperparameters of the MTPP-based model.
Discrete mark MTPP FLEXTPP-C
Nepochs
1000
Thead
Yiff
256
Non-linearity
GELU
Transformer depth dx
7
28
Pdropout
0.25
0.2
10bins
20
Batch size
160
Learning rate
0.001
Conditioning window size
200
240
Table 15: Ablation comparing different orderings of each event's data for FLEXTPP-CC in the event annotation task. Event parts: Start of event, Type of event, Duration, and remaining Properties. Values in brackets are standard deviations over eight runs. Time Type NLL bits/event, Full NLL in bits/dim.
Order
Time Type NLL ())
Full NLL (L)
SDTP
-0.867 (0.005)
-0,930 (0.007)
STDP
-0.596 (0.004)
-0.778 (0,006)
STPD
-0.595 (0.005)
-0.775 (0.006)
and instead model in the order:
(f:, duration,, m,; other event properties,).
(27)
Table 15 compares the validation negative log- ligllikels different orders. Note that hyperparam- eters optimized for eq. (27), and thus cannot exclude that there are hyperparameters for which the other orders perform just as well (for example, increase the number of bins of the spline to model more complex distributions in alternative orderings). In the end, eq. (25) suggests that the full likelihoods should be identical across reordering the data.
A.3.4 Baseline: CNN-based Time Series Classifier
We compare FLEXTPP-C to CNN-based classifier for conditional event detection. We follow the structure from the time series anomaly detection survey by Schmid! al. [2022] and make use of convolutional neural networks as classifiers [Zhao et al., 2017]. The approach uses classifier that predicts the class at time point t E [0, 1] of what events it observes given slice of the time series of size I around t. At inference time, this classifier is applied in sliding-window approach. The finite window size of the classifier limits its capability to detect events. We assume that every timestamp has been annotated by counting the number of events per event type that could occur and write that into a normalized vector y(t) E [0. 1|m+1 to be predicted with m being the number of different event types (plus one type for "no event"). This allows the classifier to model multiple concurrent events through weighted class activations. However, it does not allow it to differentiate this from uncertainty in the prediction,
analyze in appendix A.3.5.
Following [Schmidl et al., 2022], for training, we cut the input time series into slices of length with strides lg. We found / 500 and 4 = 100 to perform best. Each resulting window is then assigned the label vector its central timestamp.
Then, we train convolutional neural network to map the observations to the target vector y(t) using cross-entropy loss. We used Adam optimizer with learning rate of 0.001 trained for epochs.
Multiple runs were trained concurrently on single NVIDIA A100 Tensor Core GPU, and each single run completed within 2 hours of starting.
The classifier consists of two convolutional blocks, each followed by batch normalization, a non-linear activation function, temporal downsampling through pooling, and dropout for regularization (sec
26

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table 16). The first block increases the number of feature channels, and the second further refines the representation while reducing the temporal resolution. The resulting feature maps are flattened and passed through fully connected layer with intermediate activation and additional dropout. final linear layer maps the representation to the desired number of output classes. To recover per-timestamp predictions from the window-har basee CNN outputs, we aggregate the predicted label vectors of all windows that include a given timestamp:
j(t)
Σ i(ws),
(28)
[W()]]
(EW
where
W = (w; E EEW;
(29)
the set of all windows that include timestamp This averaging doubles the field of view for each timestamp's ' prediction and improves robustness and smoothness over time.
Table 16:
Architecture of the 1D CNN used for window-ban based event classification. The input has shape (batch_size) 1, + 1), where + the window length.
Layer
Operation
Conv1
Convid(1, 32, kernel=3, padding-1)
(atchloormid ReLU()
(arPPPoolddkeeeee_ssiiiiii Dropout(p=O.2)
Conv2 Convid(32, 64, kernel=3, padding-1) (atchNoorm1d644)
ReLU
(aaPPolld(<eerre__ssieee Propout(p=0.2)
Flatten
view view(bath__size -1)
FC1
Linear (64 [+]]
128)
ReLU ()
Dropout (p=0.3)
FC2
Linear (128, m.)
A.3.5 Method Comparison
In this section, we expand on the evaluation in section 5.3. We compare the conditional MTPP with only discrete marks + fixed average event length, our FLEXTPP- C also modeling duration and event properties, and a sliding window classifier. We compare via samples, likelihoods, and terettimstamp class probabilities.
Samples from MTPP approaches Figures 4 to 6 shows a total of six randomly selected test time series. First, we show the predictions of the MTPP approaches: Both the classical MTPP (only discrete marks) and our method detect events accurately, except for the damping change, which is hard detect in the data given its subtle effect. However, the flexible mark structure is more useful since it models event durations and the event properties.
For the MTPP with only discrete marks, visualize the events with constant event duration of (.5 + 0.025)/2 = 0.2625, which is the average length.
The sliding window classifier does not directly yield such samples since it has no understanding of event starts.
Likelihoods Table 4 compares likelihoods of the MTPP approaches. The resulting classification likelihood from the sliding window classifier is not directly compatible with the likelihoods of our model in eq. (5), since they operate in different spaces.
27

---

0.5
ree the soteetttaaaoooo ktd
-15
bempig Charge
Damping
-1.
EEREee Tatteri 3:37
Host Time Sertes
-2.5
Only
Fuent
Extrrni Force
Damsing
Sass Trequency Change
Pesil Nobe
Bvent
Truth
M
Disomte
Irput tine setto 41
Eust Notaene
-20
Dhree
1re0e heare 1.22
Postor 10
Only Discrete Marks
Pusiiian
Figure Uncurated model and baseline predictions on the event prediction task (1/3). (In boxes) random annotation from the
Input time series, ground truth event annotations (blue), well discrete-only MTPP model (orange) and our flexible-mar modalltyy model (green). The ground truth and models also list event properties, which not available for the discrete-only model. (Below plot) Predicted p(y(t) time series) from the three models (ours, discrete-only MTTP, baseline CNN).
28

---

6-
FIA sme vetor X00
jolne, aededt
shat
postter rdile +4.00
hostoon bocte
Cameling
DucpinyClugg
Input Series
ken patd dit
Trufh
dansdg
Discmin
Fo War
1e0 Tar 2.perodetty
Une
Only Discrete Marks
Ours
Inpot Ume sutica A00
Darsanng Change
bateraal camoo
Diterdll Fore
Only
Event 7ype
Eaterall forre
Damping Chanpe
Sase Trequency Change
Figure 5: Uncurated model and baseline predictions on the event prediction task (2/3). Same as fig. 4.
29

---

insuttree
dunding Pucer
Irput Time Sertes
Dumplin Ctange
Ground Tuth
Only Dacrete Marts
Outs
pestioo pestucc 3.72
Meite
time
Only Discrete Marks
Ours
Event Bys
Extamal force
CNN
Camping Change
Base Prequeccy Change
Posiion heise
No Evant
IygE Simie
Ground Tuth
Only Biorete Marks
Dues
www
0.0
-25
Tan
10.0
Eesesl frce
bushreaarc Charme
Enqarnyy Charge
Cosms
Daes Coange:
Diemall havee
Daapinng Chance
teo wxted wittt
time
Only Discrete Maris
Ours
Figure 6: Uncurated model and baseline predictions on the event prediction task (3/3). Same as fig.
30

---

Class probabilities per timestamp To compare the different modeling approaches, we evaluate [tmee series) at each time stamp given the time series. To get these predictions about the class distribution at time /. from the MTPP models, we approximate the trained models p(v(t) ttime series) by averaging event occurrence over 100 sampled event annotations. For the MTPP with only discrete marks, we again use the average event duration for all predicted events.
the class probabilities (timee
Figures visualize the resulting probabilities for the three approaches. One can see that all three methods mostly agree at which time some event starts, However, the discrete-marks MTPP is biased when multiple events occur since it does not predict the duration of the events. Also, it learns heavier distributions for the events.
The classifier is less well calibrated in terms of regards of which class it expects. We think that this is due to a fundamental limitation of the formulation of annotation as classification: By construction, classifier- based approach cannot differentiate between being unsure about which event class to predict and there being several events present. For example, let's assume there are two event types A
and B and the classifier predicts the following values:
p(event A at wwwiddw) 1/2 plevent B (|window) 1/2, p(no event (/window) 0.
(30)
This result could be caused by (a) the model certain that both events A and B being present, or (b) there is some event, but it is unclear what type of event (A or B3) there is. We think that this ambiguity in the task representation leads to an overall high uncertainty in the predictions of the classifier.
Table quantify the performance of the models the macro- aacro-averaged Receiver Operating Characteristic Area Under the Curve (ROC AUC) [Hanley and McNeil, 1982] the per-timestamp y(t) vectors. This metric is computed by adopting a one-vs-rest strategy: for each class, a binary ROC AUC score calculated by treating the current class as the positive class and all others negative. The final score is then obtained by averaging the individual AUCs across all classes:
1 m m
Macro AUC =
AUC
(31)
Here, each AU Ck represents the ROC AUC score for class k = 1,...,m, + 1 (compare ap- pendix A.3.4).
Each ROC curve is insensitive to a badly calibrated model because it is based on the ranking of predicted scores, not their absolute values. Therefore, the CNN Classifier still yields useful ROC AUCs despite the notably worse performance in predicting p(v(t) time series) in figs. 4 to 6.
A.4 Extracting triggering kernel
For this experiment, we sample N 100, 000 event sequences from the following intensity function:
T(( tx)
x((H)) = μ + Σ a sin
(32)
B
1-488
We choose μ 0.1, a 0.2,3 and sample T 4 events per sequence.
We then train a FLEXTPP with hyperparameters given in table 17.
Figure 7 shows the above kernel and the kernel extracted from our model. To get it from our model, we average over & 0.1, 0.2, .... 10.0 and evaluate the intensity function from the learned probabilities via eq. (14) as a function of to f + 0.033.... f + 10.0.
B Details on Architecture
Figure in the main text visualizes our architecture. Figure 8 visualizes the architecture with more details and shows the sampling according to algorithm The multi-head attention block is causal, meaning that token can only attend to tokens 1, .,..., - 1. The transformer works with token dimension of dæ = Theadd and the forwarr networks each transformer block have a hidden dimension of da.
31

---

0.40
Extracted Intensity
0.30
Intensity
0.20
0.10
0.05
0.00
4
time difference
Figure 7: FLEXTPP (orange) can accurately learn the triggering kernel in eq. (32) (blue) from data.
Table 17: Hyperparameters of the kemel extraction model.
FLEXTPP
Repochs
200
Thead
4
Thf
256
Non-linearity
GELU
Transformer depth
2
dx
16
Pdropout
0.1
Tibins
10
Batch size
1024
Learning rate
0.0008
Conditioning
Network
0.0
Multhheaded Attention
Add and Norm
Feed Forward
Add and Norm
Peent
DropoLt
Plu
Pluue
Prant
Figure 8: Details on our transformer architecture and visualization of sampling. The multi-head attention layer includes both causal attention and dropout. Sampling occurs rego-segress.vely. where each token is fed into the model after being sampled, until the terminal token is generated.
32

---

The output embeddings of the transformers are ignored for the condition tokens, and the others are passed into small neural network predicting the parameters the continuous respectively discrete distributions each. These networks Pcont respectively Pdise have one hidden layer with hidden width max deone) (2 max (dg, ddise)) ReL.U activation. Even though different positions in the sequence may allow separate numbers of discrete values, we find that we never sample a disallowed class at inference (indicating that the network has learned the sequence accurately) and so we do not need to track the actual number of allowed classes depending on position. Instead, we set the number of classes to the maximum number of classes any token has to support. For values that are by construction positive (that is all arrival times relative to the previous event, well durations for the time series annotation experiments), we first take the logarithm these values. We also reflect this in the likelihood computation, which is based on linear time.
This is how we feed data into the transformer:
First, we preprocess the condition with some network to transform from its corresponding modality one or several tokens (for example the large vector for the time is not directly compatible with the transformer token-based embedding). We provide the details in each experimental section in appendix A.
Then, we embed each value in X as a token in eq. (3) depending on its type: For discrete entries D, disc, learn an affine layer wx + b. where w, E Rd and x E is the scalar to be embedded. We shift these tokens to the position, since the ith output of the transformer is mapped to the distribution p(X; x)),, which must only have access to the history. The first entry is replaced with 0 as a beginning of sequence identification (there is no history for the first entry).
a learned embedding vector for each possible class. For continuous entries,
We also embed the data type D (E {disc, contj) to be expected for each token using a learned embedding. These embeddings added to the shifted value tokens. They are not shifted, the type of entry can be determined at inference time using algorithm 1.
Finally, we add positional encoding to inform the model about where it is in the sequence. We give the details on the positional encoding and the conditioning networks for each case separately.
the number of events per sequence is not constant over the dataset, we mark the end of the sequence with special "EOS" mark type (m = EOS). Note that since the end of sequence is never fed into the model as it is the last entry in sequence and all values are shifted by one. Instead the "EOS" event only enters when evaluating the last sequence entry's 's distribution after the transformer.
33


Reviews:
[{"review_id": "TjgFuC6L9I", "reviewer": "Reviewer_hdCQ", "summary": "This paper extends Marked Temporal Point Processes (MTPPs) by introducing a framework that supports mixed-type (discrete/continuous) and variable-length marks through normalizing flows, particularly effective in healthcare scenarios like EHR analysis. It establishes conditional modeling as a core principle using an autoregressive Transformer architecture, which eliminates numerical integration bottlenecks and enhances dependency capture compared to RNN-based model. The proposed intensity-free approach employs direct joint probability modeling, significantly improving computational efficiency in complex event generation. Empirical validation across medical and financial domains demonstrates superior prediction accuracy, especially in long-term forecasting through advanced historical encoding, revealing synergistic interactions between temporal dynamics and mark information.", "questions": "Please clarify whether complexity calculations exclude attention weight matrix generation and provide quantitative GPU memory usage data, as the self-attention mechanism inherently requires O(N²).", "limitations": "yes", "rating": 5, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 4, "significance": 2, "originality": 3, "strengths_and_weaknesses": "Strengths：\nThis study demonstrates significant advancements in marked temporal point process modeling through two core innovations：1）it pioneers hybrid-type (discrete+continuous) and variable-length mark processing using normalizing flows, overcoming the fixed-type mark limitations of traditional MTPPs like the RMTPP framework；2) the conditional modeling framework via autoregressive Transformer，achieving higher conditional information utilization compared to the attention-based improvements, particularly enhancing structured output tasks in cross-modal scenarios.\nWeaknesses：\nThe research exhibits certain limitations: The combined computational load from Transformer and normalizing flow architectures increases parameter count by 5× compared to RNN-based models, potentially hindering edge device deployment. While effective for medium-dimensional marks like medical codes, the approach lacks validation on high-dimensional sparse marks (e.g., genomic data).", "was_revised": false, "final_justification": "", "rebuttal": "We thank the reviewer for their helpful feedback!\n\n> This study demonstrates significant advancements in marked temporal point process modeling through two core innovations [hybrid-type processes and conditional information utilization]\n\nThanks for acknowledging these contributions. We would also like to point out these additional contributions of our work:\n\n1. **Intensity-free outperforms intensity-based**. Previous work argued that intensity-based methods dominate due to \"fewer modeling restrictions\" [https://arxiv.org/pdf/2412.19634, Section 4]. Our approach brings intensity-free modeling back on the table, outperforming all intensity-based methods (except for DLHP in one dataset, see Table 1), all while avoiding numeric integration at training and rejection sampling at inference time.\n2. **Successful extraction of triggering kernels** (new thanks to reviewer M7Vi). We are adding a successful evaluation on the interpretability of our model to the camera ready version. See our answer to M7Vi for details.\n\n\n> The combined computational load from Transformer and normalizing flow architectures increases parameter count by 5× compared to RNN-based models, potentially hindering edge device deployment.\n\nOur model is several orders of magnitude smaller than transformers that have been deployed to edge devices. For example, recent work quantizes the weights of Llama 3-8B (8 billion parameters, which is four orders of magnitude larger than our largest model) to run it on a Raspberry Pi 5 at ~500ms/token [1].\n\nThe normalizing flow itself has at most 88(!) parameters predicted by the transformer, and likelihood computation/sampling takes around one millionth of a second on a consumer GPU for each entry. This is comparable to the compute required for a Hawkes process intensity evaluation.\n\n\n[1] Ardakani et al. LLMPi: Optimizing LLMs for High-Throughput on Raspberry Pi. CVPR Workshop Paper 2025\n\n\n> Please clarify whether complexity calculations exclude attention weight matrix generation and provide quantitative GPU memory usage data, as the self-attention mechanism inherently requires $O(N^2)$.\n\nTransformers are not memory-bound: This remarkable effect can be achieved by computing the attention matrix in chunks and never storing it in full in memory. Then, the **memory consumption of a transformer is linear in sequence length** $O(n)$. Computing the attention matrix as needed without ever realizing it in full is one of the tricks in modern attention implementations such as PyTorch’s `scaled_dot_product_attention`, e.g. based on FlashAttention [2].\n\nConcretely, on a GPU with 12GB VRAM and our largest EasyTPP model, **we can fit a maximum sequence length of two million tokens** for a batch size of 1.\n\n[2] Dao. FlashAttention-2: Faster Attention with Better Parallelism and Work Partitioning. ICLR 2024\n\n\nWe hope that this elucidates the properties and contributions of our approach, and we are happy to address further questions in the upcoming discussion."}, {"review_id": "e6zQDdE9EM", "reviewer": "Reviewer_M7Vi", "summary": "The paper proposes a marked temporal point process framework for predicting event type, event time, and variable-length discrete/continuous longitudinal covariates, given event history and static covariates, by leveraging an autoregressive likelihood. It employs an autoregressive transformer for encoding event history and conditioning on static covariates. Additionally, the paper leverages normalizing flows for event time and continuous longitudinal covariates prediction. Experimental results demonstrate that the proposed  approach achieves competitive event time and event type likelihood predictions compared to baselines on two real-world and one synthetic dataset.", "questions": "- Could you provide a complexity analysis in terms of the number of parameters, training/inference time, and scalability relative to baselines?\n- Eqn 9: Could you clarify how the normalizing flow function is specified, *e.g.*, what is different or shared across marker types and event times? Also what is $f^\\prime$?\n- Could you clarify the empirical benefits of conditioning on longitudinal covariates, *i.e*., Equation 10 *vs.* Equation 12?\n- Tables 3 and 4: (i) Could you clarify the models used for \"only discrete events\" and \"Lab tests w/o values\"? (ii) Could you provide complete results, including baselines from Table 2?\n- Figure 3: The qualitative results in Figure 3 are difficult to follow; could you clarify?\n- How does the model capture the influence of event interactions on event time?", "limitations": "- The main limitations of the proposed approach are its complexity relative to baselines and its lack of interpretability. The paper should expand the discussion on these aspects.", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 4, "originality": 3, "strengths_and_weaknesses": "**Strengths**\n\n- The paper is relatively well-written and easy to follow.\n- The use of autoregressive transformers for conditional generation given variable length discrete/continuous longitudinal covariates is interesting.\n- Experimental results demonstrate that the proposed approach achieves competetive ikelihood predictions compared to baselines.\n\n**Weaknesses**\n- The proposed approach seems more complex and might not be scalable relative to baselines, which is worsened by the use of normalizing flows for both continuous marker metadata and event time.\n- The paper seems to focus on the likelihood metric, overlooking model interpretability, which is important in practice. For example, by not modeling the intensity function, it is unclear how the model captures the influence of event interactions on event time. The paper should also benchmark the interpretability aspect and compare it with classical Hawkes and interpretable neural Hawkes approaches, *e.g.*, [1, 2].\n- The proposed approach seems to yield small gains relative to baselines (including FlexTPP vs. FlexTPP-C). The paper should also report error bars of the reported negative likelihood.\n- While the paper clearly describes the ablation study of the proposed model (Equations 10-12), the experimental results do not seem to highlight the benefits of conditioning on the variable length discrete/continous longitudinal covariates, which is the key contribution of this work compared to baselines. The paper should also consistently provide benchmarks for the proposed FlexTPP (with/without the longitudinal covariates), *i.e.*, Eqn 10 *vs.* Eqn 12. \n- Table 4: The paper should report the metrics on event type and event time predictions separately and provide non-likelihood-based metrics, such as RMSE, for event time predictions.\n- *Minor*: Line 91 - The intensity probabilities should be conditioned on the event history.\n\n**References**\n\n- [1] Isik et al., \"Hawkes Process with Flexible Triggering Kernels\",  MLHC 2023.\n- [2] Shixiang et al. , \"Neural spectral marked point processes\",  ICLR 2022.", "was_revised": true, "final_justification": "Thanks to such a comprehensive rebuttal that addresses most of my concerns, I have increased my score to acceptance.", "rebuttal": "We thank the reviewer for the detailed, diverse, and helpful comments.\n\nWe begin with main limitations, followed by specific responses.\n\n> The main limitations [...] are its complexity relative to baselines and its lack of interpretability.\n\nLet’s start with interpretability:\n\n> The paper should also benchmark the interpretability aspect and compare it with classical Hawkes and interpretable neural Hawkes approaches, e.g., [1, 2].\n\nThat is an excellent suggestion! Building on the reviewer’s references [1, 2], we find that our model offers a comparable level of interpretability—albeit in a local, query-based form—by targeted inspection of how past events influence future intensities.\n\n**Interpretability through targeted intensity inspection**\n\nIn Hawkes Process with Flexible Triggering Kernels [1], the method learns a kernel $q_{m_1 m_2}(|t_1 - t_2|)$. It measures how an event $(m_1, t_1)$ influences the intensity of a future event $(m_2, t_2)$.\n\nSimilarly, Neural Spectral Marked Point Processes [2] learns kernels $q(m_1, t_1, m_2, t_2)$ that compose the intensity for the next event.\n\nWe can extract these kernels using our Eq. (2, left), which computes intensities from the event pdf and cdf.\n\nWe experimentally confirm that our model accurately predicts intensities such as  $\\\\lambda(t_2|t_1)$ via Eq. (2, left) for a synthetic example from [1, Figure 2]. We find that the RMSE distance between the true kernel and the one extracted from our method is $0.01$. You can imagine Figure 2 in reference [1] with our line closely following the true kernel.\n\nWe will add the above result as an interpretability section to our paper, and are happy to provide any additional details to the reviewer upon request.\n\n**Global vs. Local Interpretability**\n\nTaking a step back, there is an inherent tradeoff between globally interpretable models and highly flexible ones.\n\nStructured approaches that learn kernel-based pairwise event influences allow for a simple complete understanding of the model’s behavior. However, they are limited in flexibility and can misrepresent data with nonlinear dynamics. For example, in marketing, an effect such as ad fatigue can’t be modeled, where seeing an ad once or twice increases the chance of conversion, but repeated exposures eventually stop having any effect or may even cause disengagement. The ground truth structure of real data is usually not clear and so interpreting a kernel-based model can yield spurious explanations.\n\nWhile our model is not globally interpretable, it supports local interpretability through queries about how specific past events affect future intensities, allowing fine-grained analysis and uncertainty estimation.\n\n\n> [Regarding Complexity] The proposed approach seems more complex and might not be scalable relative to baselines, which is worsened by the use of normalizing flows [...].\n\nThe flow adds negligible cost (one millionth of a second on consumer GPU); most computation comes from the autoregressive transformer, similar to SAHP and NHP\n\n\n> Eqn 9: Could you clarify how the normalizing flow function is specified, e.g., what is different or shared across marker types and event times? Also what is f’?\n\nThe normalizing flow models 1D conditional distributions over continuous values, with shared structure over types. Just like categorical logits, it is parameterized based on the history through the transformer.\n\nEqn (9) is the standard change of variables equation underlying normalizing flows and autoregressive models in particular. Such a model learns an invertible function mapping $x$ to a standard normal in the latent space. The density $p(x)$ implied by the flow is proportional to the likelihood of $z=f(x)$ under the standard normal, and proportional to the volume change $f’(x)$, which in 1D is just the derivative of $df(x)/dx$ with respect to its input.\n\n\n> How does the model capture the influence of event interactions on event time?\n\nThe autoregressive transformer takes in all previous events (times, mixed-type marks) as a vector $H_i$ to predict the parameters of the next event time $p(t_{i}|H_i)$. \n\nThis is similar to Self-Attentive Hawkes Processes and Transformer Hawkes Processes, although they follow an intensity-based approach, which requires numeric integration at training and rejection sampling at inference time. Additionally, we outperform them on EasyTPP in Table 1. We model the next event time as a one-dimensional probability distribution in an intensity-free fashion, which avoids these issues.\n\n\n> Could you provide a complexity analysis in terms of the number of parameters, training/inference time, and scalability relative to baselines?\n\n**Our model is somewhat larger, but trains and runs at comparable speed** to competitors.\n\nIn detail, let us report the geometric mean for the requested metrics:\n\n- Parameter count: We use a mean of 325k parameters, which is about 3-10x larger competitors.\n- Training speed: We achieve a training speed of around 2400 sequences of length 200 per second, over 2x faster than AttNHP and NHP. RMTPP, SAHP, THP and IFTPP are 2-5x faster than us.\n- Generation speed: ~70 sequences of length 200 per second, with similar relation to competitors as training. We did not implement a KV-Cache, which speeds up sampling by a factor in sequence length.\n- Scalability: Self-attention inherently has access to the entire event history in each prediction. This makes memory scale linearly $O(n)$ with sequence length (one would naively assume that memory use is quadratic, but the attention matrix never has to be realized in memory, e.g., using FlashAttention [3]). Notably, we can fit a sequence of over a million entries on a GPU with 12GB of VRAM for our largest model. Also, transformers with four orders of magnitude more parameters than our biggest model have been deployed on edge devices (e.g., Llama 3-8B on a Raspberry Pi at 500ms/token using quantization [4]).\n\nReferences:\n\n- [3] Dao. FlashAttention-2: Faster Attention with Better Parallelism and Work Partitioning. ICLR 2024\n- [4] Ardakani et al. LLMPi: Optimizing LLMs for High-Throughput on Raspberry Pi. CVPR Workshop Paper 2025\n\n\n> Could you clarify the empirical benefits of conditioning on longitudinal covariates, i.e., Equation 10 vs. Equation 12?\n\nEq. 10 and 12 are not directly comparable since they do not concern the same variables. To assess whether including additional longitudinal variables is useful, we need to look at Eq. (13). It tells us the likelihood of events (e.g. medical interventions for health data) depending on the knowledge of the covariates: $p(t_\\text{procedure}, t_\\text{procedure}| \\text{past procedures}, \\text{covariates})$.\n\nTable 3 shows the NLL as in Eq. (13), e.g. the first row (lower is better, std < 0.002 in all cases):\n\n| Covariates | Procedure NLL |\n|--|--|\n| No covariates | 0.691 |\n| + time, lab test type | 0.202 |\n| + lab test results | 0.147 |\n| + demographics | **0.143** |\n\nThe more longitudinal covariates we include, the better we can predict the next medical procedure.\n\n\n> The proposed approach seems to yield small gains relative to baselines (including FlexTPP vs. FlexTPP-C). The paper should also report error bars of the reported negative likelihood.\n\nWe report standard deviations in Appendix A, Tables 6, 9, 15, confirming significance.\n\nFor FlexTPP (our model, unconditional; Eq. 11) vs FlexTPP-C (our model, conditional; Eq. 12), the reviewer is correct that only 60% of the winning NLL is at least one standard deviation away from the other model.\n\n\n> Figure 3: The qualitative results in Figure 3 are difficult to follow; could you clarify?\n\nFigure 3 shows a sequence from the time series annotation dataset, where the goal is to infer events affecting the input signal. The ground truth events (blue) consist of a frequency change by a factor of 1.14, and additional noise of 1.63.\n\nThe discrete-only model (orange) predicts event start times and types but cannot predict durations or continuous parameters. The depicted duration is chosen to fit the text. In contrast, our model (green) predicts start, end, and parameter values, accurately modeling the full event structure. To our knowledge, this is the first point process model applied to such a task.\n\n\n> Table 4: The paper should report the metrics on event type and event time predictions separately and provide non-likelihood-based metrics, such as RMSE, for event time predictions.\n\nWe agree that non-likelihood-based metrics can be helpful for interpreting the model performance. Thus, we reported AUC ROC in Table 4.\n\nHere are the RMSE values for Table 4 (standard deviations in brackets):\n| Model | RMSE |\n|---|--|\n| no condition | 0.198 (0.001) |\n| only discrete marks | 0.192 (0.009) |\n| FlexTPP-C | **0.152** (0.002) |\n\nWhile this clearly favors our method, we think that RMSE is not a good metric for this task. A model that samples events autoregressively can have a good RMSE but if one of the generations fails (e.g. because the model is tuned for RMSE via a regression loss), the rest of the sequence cannot be meaningful.\n\nWe therefore report AUC ROC in the paper since (a) they are based on a full generated sequence of events from each model and (b) are an accepted quantity in the time series annotation literature [5].\n\n[5] Schmidl et al.: Anomaly detection in time series: a comprehensive evaluation. VLDB 2022."}, {"review_id": "OhcqtMLzP9", "reviewer": "Reviewer_ZDCH", "summary": "This paper extends Marked Temporal Point Processes (MTPPs) to support variable-length marks with mixed discrete and continuous data types, proposing FLEXTPP—a Transformer-based architecture that flattens heterogeneous event data into sequences and models them autoregressively. The approach uses categorical distributions for discrete marks and normalizing flows for continuous values, for distribution modeling.", "questions": "To the best of my understanding, the proposed approach proceeds as follows:\n(1) Start with events consisting of timestamps and mixed-type marks.\n(2) Flatten each event into a sequence of the form $[t_1,  type_1,  mark_{1,1}, \\dots, mark_{1,n}, t_2, type_2, \\dots]$.\n(3) Feed this sequence into a Transformer.\n(4) Train or sample the model in an autoregressive manner.\n\nCan you specially list what has been done more than above, and what's the contribution/innovation from a point process view.\n\nI may be misunderstanding some aspects and would welcome clarification to reassess my evaluation of this work.", "limitations": "Yes, the paper discussed their limitations", "rating": 5, "confidence": 2, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 2, "strengths_and_weaknesses": "**Strengths:**\n\nThe paper addresses a practical limitation in existing MTPP methods by supporting variable-length, mixed-type marks, which is important for real-world applications such as electronic health records. The proposed framework is clean and general, and the empirical evaluation is relatively comprehensive, showing good performance across multiple benchmarks.\n\n**Weaknesses:**\n(1) The model conditions each mark component on all previous times and marks in a fully autoregressive manner, which can be unnecessarily restrictive, or misrepresent the data. For example, blood pressure and heart rate are recorded at the same time for a patient, but there is no natural dependence on each other.  \n\n(2) While the approach is well-executed, it largely applies standard sequence modeling to flattened temporal data. I feel the main novelty is in the data representation (mixed-type, variable-length marks) rather than methodological innovation.\n\n(3) The likelihood values are reported in the experiments, but not sure how significance the improvement is without statistical test.\n\n**Suggestion.**\nThe paper complicates its presentation by deriving the approach through intensity functions in Section 3.1, despite ultimately proposing an intensity-free model that directly parameterizes $p(t_i, m_i | H_{t_i})$. The detour through intensity functions $\\lambda(t, m |H_t)$ and the conversion in Equation (2) is unnecessary. Equation (3) merely states the standard likelihood for time series data, not a derived result. The exposition would be clearer and more focused if it began with the goal of modeling $p(t_i, m_i | H_{t_i})$ directly, with only a brief mention of intensity-based methods as a contrasting approach.", "was_revised": true, "final_justification": "The author clearly listed their contributions in the rebuttal. I have also read through other reviews and the authors' responses. I am convinced it is a solid paper.", "rebuttal": "We thank the reviewer for the helpful comments. We particularly appreciate the call to list contributions from a point process point of view.\n\n> The model conditions each mark component on all previous times and marks in a fully autoregressive manner, which can be unnecessarily restrictive or misrepresent the data. For example, blood pressure and heart rate are recorded at the same time for a patient, but there is no natural dependence on each other.\n\nThe described knowledge about the true dependent structure can be integrated into our model: If there is prior knowledge about the (in)dependence between certain predictions, this can be guaranteed to be fulfilled by the model by masking out the corresponding attention weights in the transformer.\n\nFor example, assuming we want to predict $p(\\text{blood pressure}, \\text{heart rate}|\\text{past events})$ as independent variables, we can zero out entries of the fully autoregressive attention mask:\n\n$\\\\begin{pmatrix} 1 & 0 \\\\\\\\ 1 & 1 \\\\end{pmatrix} \\\\mapsto \\\\begin{pmatrix} 1 & 0 \\\\\\\\ 0 & 1 \\\\end{pmatrix} $\n\nThis results in an exactly independent prediction $p(\\text{blood pressure}, \\text{heart rate}|\\text{past events}) = p(\\text{blood pressure}|\\text{past events}) p(\\text{heart rate}|\\text{past events})$.\n\n> While the approach is well-executed, it largely applies standard sequence modeling to flattened temporal data. [...] Can you specially list what has been done more than above, and what's the contribution/innovation from a point process view.\n\nFrom a point-process view, we contribute:\n\n**A new state-of-the-art for intensity-free modeling**. \n\nContrary to the original IFTPP paper, we find that normalizing flows are a highly effective basis for intensity-free modeling (see their comment on normalizing flows in section 3.1 in https://arxiv.org/pdf/1909.12127). We combine a transformer backbone with neural spline flows, achieving closed-form likelihoods and fast sampling. This outperforms their approach (Table 1).\n\n\n**Intensity-free outperforms intensity-based**. \n\nPrevious work argued that intensity-based methods dominate due to \"fewer modeling restrictions\" [https://arxiv.org/pdf/2412.19634, Section 4]. Our approach brings intensity-free modeling back on the table, outperforming all intensity-based methods (except for DLHP in one dataset, see Table 1), all while avoiding numeric integration at training and rejection sampling at inference time.\n\nFrom a high level, this strengthens the connection between the point process and generative modeling literatures.\n\n\n**Point processes go beyond homogeneous marks**.\n\nWe show that point processes are a natural model for generative models of series of complex events such as patient records and time series annotations.\n\n[Note that reviewer ByqH pointed us to related work [1], which encodes data in a similar way to our model. However, their model regresses continuous marks instead of modeling them with a universal distribution. This is not expressive enough and empirically deteriorates under autoregressive sampling.]\n\n\n**Blackbox methods allow for interpretation**. [Thanks to suggestion by reviewer hdCQ]\n\nDespite being a blackbox method, our model allows extracting information about the underlying point process. In detail, we replicated an experiment from [2] by successfully extracting a triggering kernel from our model. Our extraction closely follows the ground truth compared to extracting the relation between events from the attention weights, which is the baseline in that paper.\n\n\nAgain thanks for pushing us to think more about the point process perspective. We propose overhauling the list of contributions in our introduction section.\n\n\n- [1] Matthew B et al. \"Event Stream GPT: A Data Pre-processing and Modeling Library for Generative, Pre-trained Transformers over Continuous-time Sequences of Complex Events\", NeurIPS 2023.\n- [2] Isik et al., \"Hawkes Process with Flexible Triggering Kernels\", MLHC 2023.\n\n\n> The likelihood values are reported in the experiments, but not sure how significance the improvement is without statistical test.\n\nWe report standard deviations in Appendix A, Tables 6, 9, 15, confirming significance. We will make the wording more precise on the significance of the difference between FlexTPP and FlexTPP-C in Table 3.\n\n\nWe hope that this clarifies the concerns of the reviewers. We are happy to provide further details in the subsequent discussion."}, {"review_id": "2wAEJklvfw", "reviewer": "Reviewer_ByqH", "summary": "This paper proposes a method for learning mixed-type Marked Temporal Point Processes using normalizing flows and finds that it improves predictive performance on a number of tasks.", "questions": "How is this different from https://arxiv.org/abs/2306.11547 and https://arxiv.org/abs/1909.12127? What does this paper add that is not in either of those two papers?\n\nCan you please address the questions about 4.2 listed in weaknesses?", "limitations": "yes", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 2, "significance": 3, "originality": 1, "strengths_and_weaknesses": "Strengths:\n- Marked temporal processes with mixed outcome types are very important\n\nWeaknesses:\n- The conditional handling seems overly engineered. Why not just add it as an event at the start of the sequence?\n- The lack of public source code makes it very challenging to understand and verify many of the results\n- The novelty here is very questionable. Marked Temporal Point Processes with mixed types have been explored before. https://arxiv.org/abs/2306.11547 is a recent example that has a nice open source codebase for handling Marked Temporal Point Process with mixed types.\n- Likewise, using normalizing flows for temporal point processes has also been explored. See https://arxiv.org/abs/1909.12127.\n- Related to the missing code, many of the experiments require more detailed information. Secton 4.2 is particularly lacking. How many patients are there per condition? How are you addressing the issue of multiple labels per patient inherent in EHR data? In Table 3 when you say \"Lab tests w/o values\" are you excluding the values only as prediction targets or as both prediction targets and features?\n- No notion of uncertainty or statistic soundness of many of the comparisons. This is especially important for small datasets like EHRSHOT.\n- Missing ablation experiments to test whether particular components (like the normalizing flows part) are helpful. This is something to remark upon because the current literature (like https://arxiv.org/abs/1909.12127) found that normalizing flows were not helpful.", "was_revised": true, "final_justification": "The authors have addressed all of my concerns, in particular the comparisons to prior work.\n\nIt's still a bit unclear why this paper got the opposite results of IFTPP (in that this paper found that normalizing flows were helpful while IFTPP found that they were not), and I wish there was more investigation into that, but I'm satisfied with the experimental results as they stand.", "rebuttal": "We thank the reviewer for their detailed comments and suggestions, as well as the helpful pointer to the literature:\n\n> What does this paper add that is not in [https://arxiv.org/abs/2306.11547 and https://arxiv.org/abs/1909.12127]\n\nIn short: **Our model generalizes and significantly outperforms both approaches.** These are our contributions over the literature:\n\n1. **Intensity-free outperforms intensity-based**. Previous work argued that intensity-based methods dominate due to \"fewer modeling restrictions\" [https://arxiv.org/pdf/2412.19634, Section 4]. Our approach brings intensity-free modeling back on the table, outperforming all intensity-based methods (except for DLHP in one dataset, see Table 1), all while avoiding numeric integration at training and rejection sampling at inference time.\n2. **Point processes beyond homogeneous marks**. To the best of our knowledge, FlexTPP is the first universal point process method for heterogeneous mark spaces. Event Stream GPT (https://arxiv.org/abs/2306.11547) does not use a normalizing flow for continuous marks, so we can model distributions more accurately.\n3. **Generalizing point processes to new tasks**. The generalized framework allows modeling structured prediction tasks as point processes, which we show with the successful annotation of events in a dense time series. Event Stream GPT is built to predict continuous marks with a Gaussian, which deteriorates sample quality over time and prevents sampling sequences.\n4. **Successful extraction of triggering kernels**. Based on the suggestion by reviewer M7Vi, we are adding an evaluation on the interpretability of our model to the camera ready version. See our answer to M7Vi for details.\n\n\nLet us now give more details on the two papers.\n\n> Difference to https://arxiv.org/abs/2306.11547\n\nWe thank the reviewer for pointing us to Event Stream GPT (ESGPT). The key difference is that **ESGPT models model continuous marks using unimodal Gaussians**, whereas our FlexTPP uses normalizing flows, which can approximate arbitrary distributions.\n\nThis flexibility leads to better generative performance: **FlexTPP(-C) achieves lower NLL than ESGPT(-C)** on all twenty but one electronic health dataset. For example, on the first three datasets in Table 3:\n\n| Dataset              | ESGPT | ESGPT-C | FlexTPP | FlexTPP-C | Improvement |\n|----------------------|-------|---------|---------|-----------|-------------|\n| Type 2 diabetes mellitus | 0.648 | 0.649   | 0.641   | **0.638** | **0.010**   |\n| Transplanted kidney      | 0.690 | 0.697   | 0.670   | **0.668** | **0.022**   |\n| Transplanted lung        | 0.816 | 0.800   | 0.581   | **0.546** | **0.254**   |\n\nMedian improvement: 0.10 nats, vs. std dev of 0.009 nats. The only case ESGPT outperforms is on Anemia (0.220 vs. 0.238).\n\nThe mismatch between a Gaussian and arbitrary distributions becomes especially pronounced when generating longer sequences. Because the model is autoregressive—using its own outputs as inputs for future steps—errors from the incorrect Gaussian assumption compound over time. We confirm this on the event annotation task (Table 4):\n\n|                          | Full NLL (lower is better) | Mean AUC ROC (higher is better) |\n|--------------------------|----------------------------|----------------------------------|\n| FlexTPP (no access to input sequence) | -0.01 (0.003)               | 0.5 (0.0)                     |\n| Discrete Marks + avg duration | n/a                        | 0.90 (0.01)                     |\n| FlexTPP-C (ours)         | **-0.79** (0.006)          | **0.92** (0.01)                 |\n| ESGPT-C                  | -0.14 (0.13)               | 0.87 (0.01)                     |\n\nThese results illustrate the critical benefit of modeling continuous marks expressively. While the data encoding is identical, our approach is both more general and performs better in practice. We will include ESGPT as a baseline in Tables 3 and 4 and cite the paper in the final version.\n\n\n> Difference to https://arxiv.org/abs/1909.12127\n\nIntensity-free Temporal Point Processes (IFTPP), like our FlexTPP, model the arrival time of the next event using a flexible one-dimensional distribution. We adopt their point process framework in Section 3.4, lines 96-98.\n\nHowever, the authors do not model more complex mark spaces such as variable-length and mixed-type.\n\nIn addition, on the EasyTPP benchmark, **our approach outperforms IFTPP in all cases**.\n\n\n> https://arxiv.org/abs/1909.12127 [...] found that normalizing flows are not helpful\n\nThe authors of that paper refer to particular expressive one-dimensional bijections that are expensive for sampling since they require numerically solving for an inverse (see their section 3.1). Neural spline flows [https://arxiv.org/abs/1906.04032] overcome this bottleneck since they are based on RQ splines, which have an analytic inverse function.\n\n> Regarding 4.2: How many patients are there per condition? How are you addressing the issue of multiple labels per patient inherent in EHR data? In Table 3 when you say \"Lab tests w/o values\" are you excluding the values only as prediction targets or as both prediction targets and features?\n\n1. Between 64 and 1515 patients (average: ~700 patients), of which we use 70% for training, and 15% each for validation and testing.\n2. We train one model for each condition, and filter the data for the relevant events: top 10 CPT-4 treatments for patients with that disease, top 5 lab tests for patients with that disease (see Appendix A.2)\n3. We are also excluding the values as features. The left part of Table 3 evaluates Eq (13), which measures the quality of predicting treatments given an increasing number of longitudinal covariates (first column: only previous treatments, second column: first column + time and type of lab results, third column: second column + lab results, fourth column: third column + demographic information).\n\n\n> No notion of uncertainty or statistic soundness of many of the comparisons. This is especially important for small datasets like EHRSHOT.\n\nWe report standard deviations in Appendix A, Tables 6, 9, 15, confirming significance. We will make the wording more precise on the significance of the difference between FlexTPP and FlexTPP-C in Table 3.\n\n\n> Ablation whether particular components (like the normalizing flows part) are helpful\n\nFor now, please refer to the data presented in the EasyTPP benchmark in Table 1 of our paper (comparing the setup of IFTPP in https://arxiv.org/abs/1909.12127 which uses a log-normal mixture instead of our spline flow), as well as the new data on https://arxiv.org/abs/2306.11547 for the EHRSHOT data, which uses a regression head for continuous marks instead of the spline. We propose adding a dedicated ablation on the EasyTPP benchmark comparing autoregressive backbones (attention vs RNN) as well as one dimensional distributions (intensity vs regression vs mixture vs normalizing flow) to disentangle the contributions.\n\n\n> The conditional handling seems overly engineered. Why not just add it as an event at the start of the sequence?\n\nIndeed, we do that for the EHRSHOT data. But for feeding time series data, it is inefficient to have 10000 input timestamps each have its own token. The conditional network therefore preprocesses the data.\n\n\nWe hope that this addresses the concerns of the reviewers and we are happy to address any further questions in the subsequent discussion."}]

Author rebuttal:

Meta-review: Following the final round of reviews, the paper received four "Accept" recommendations. The reviewers recognized the technical novelty of the proposed approach for modeling marked temporal point processes, as well as its strong empirical performance. They particularly emphasized the method’s ability to handle variable-length and mixed-type marks, which they considered a notable strength. Additionally, the rebuttal was well-received and had a positive influence on the reviewers’ assessments, as it effectively addressed most of their initial concerns.
Decision: Accept (spotlight)