Adaptive Time Encoding for Irregular Multivariate Time-Series Classification
Authors: Sangho Lee
Kyeongseo Min
Youngdoo Son
Hyungrok Do
Venue: NeurIPS 2025 poster ()
Keywords: Irregular sampling
Time encoding
Attention mechanism
Consistency regularization
Multivariate time-series classification
Primary area: deep_learning
TL;DR: We propose a novel time encoding approach that learns effective reference points and incorporates temporal and intervariable dependencies to enhance classification performance on irregular multivariate time series.

Abstract: Time series are often irregularly sampled with uneven time intervals. In multivariate cases, such irregularities may lead to misaligned observations across variables and varying observation counts, making it difficult to extract intrinsic patterns and degrading the classification performance of deep learning models. In this study, we propose an adaptive time encoding approach to address the challenge of irregular sampling in multivariate time-series classification. Our approach generates latent representations at learnable reference points that capture missingness patterns in irregular sequences, enhancing classification performance. We also introduce consistency regularization techniques to incorporate intricate temporal and intervariable information into the learned representations. Extensive experiments demonstrate that our method achieves state-of-the-art performance with high computational efficiency in irregular multivariate time-series classification tasks.

Adaptive Time Encoding for Irregular Multivariate Time-Series Classification
Sangho Lee', Kyeongseo Min', Youngdoo Son?; Hyungrok Do
School of Industrial and Systems Engincering, Gyeongsang National University Department of Industrial and Systems Engineering, Dongguk University-Sen Department of Population Health, NYU Grossman School of Medicine
Abstract
Time series are often irregularly sampled with uneven time intervals. In multivari- ate cases, such irregularities may lead misaligned observations across variables and varying observation counts, making it difficult to extract intrinsic patterns and degrading the classification performance of deep learning models. In this study, we propose an adaptive time encoding approach to address the challenge of irregular sampling in multivariate time-series classification. Our approach gener- ates latent representations at learnable reference points that capture missingness patterns in irregular sequences, enhancing classification performance. We also introduce consistency regularization techniques to incorporate intricate temporal and intervariable information into the learned representations. Extensive experi- ments demonstrate that our method achieves state-of-the art performance with high computational efficiency in irregular multivariate time-series classification tasks.
Introduction
Multivariate time series, which con- sist multiple variables over time, prevalent in diverse domains such as healthcare and finance [1O [1]]. In practice, time series often irregu- larly sampled with uneven time inter- vals between consecutive observations due to cost-saving measures, sensor failures, medical interventions [4) As shown in Figure in multivariate cases, observations across different variables may not be aligned, and the number of observations in each variable can differ recorded at each time point. These irregularities hinder
Varlable
(9 observations)
Variable
(6 observations)
Variable
(7 observations)
Time
Figure 1: Example of irregular multivariate time series
because different subsets of variables the capture of intrinsic patterns, causing standard deep learning models, which assume that input sequences are regularly sampled, to perform poorly classification tasks [16].
To address irregularities, previous work has developed deep learning models that directly learn from irregular time series to improve classification performance (2, 30). In particular, recent studies have exploited attention mechanisms to focus on partial observations irregular time series, successfully capturing complicated temporal patterns and achieving superior classification performance 3
Despite their superiority, these methods encounter two notable limitations. First, they struggle fully exploit missingness patterns inherent in uneven time intervals, which reflect the underlying processes that generate irregular time series [32]. For example, patients' examination schedules, which vary with changing health conditions or treatment needs, tend to reveal their health status. Second, they
*Coresponning author (younggdoo@ddonguuu...)
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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often overlook intervariable relationships, which are particularly beneficial for classifying multivariate Although some studies have considered these relationships as well as the challenge of irregular sampling 42 47 they have usually used graph neural networks that require a high computational burden to capture intervariable dependencies S 41
time series 88 45).
To address these issues, we design a novel interpolation-based encoder-classifier framework, Adaptive Time Encoding Network (ATENet), which learns reference time points and generates effective representations for irregular multivariate time-series classification. Specifically, we propose an Adaptive Time Encoding (ATE) that learns reference time points, which serve as queries in an attention mechanism in each training iteration, and creates fixed-length representations at the learned reference points. This approach reduces information loss by interpolating with unevenly spaced time points, effectively capturing missingness patterns from partially observed irregular time series, also avoids the need for manual tuning of reference points. Moreover, we introduce temporal and intervariable consistency regularization terms to enhance representation quality by efficiently capturing intricate temporal patterns between consecutive observations and structural relations between variables, thereby boosting classification performance. Consequently, ATENet successfully classifies irregular multivariate time series by transforming them into fixed-length representations at the reference points that are adaptively learned to reflect both temporal and intervariable dependencies.
To demonstrate the effectiveness and efficiency of our method, we performed a series of experi- ments on irregular multivariate time-series classification. ATENet achieved superior classification performance with high computational efficiency compared to ttate-of-the-art (SOTA) methods. This study has the following main contributions:
We design novel interpolation- based cncoder-classifer framework that learns effective representations for irregular multivariate time-series classification;
Our encoding approach directly learns reference points, rather than manually finding the optimal ones, to capture underlying patterns within irregular time series;
We introduce temporal and intervariable consistency regularization terms to explicitly consider intricate temporal dynamics and relationships across variables;
The proposed method achieved SOTA performance with high computational efficiency in irregular multivariate time-series classification.
2
Related Work
Irregular time series are characterized by uneven time intervals between adjacent observations. In multivariate cases, these irregularities mean that observations may not be aligned across variables, and the number of observations in each variable can also differ [12]. Such irregularities complicate the analysis for time series, often leading to poor classification performance of deep learning models.
traditional approach dealing with these irregularities is temporal discretization, which discretizes observations into consecutive and non-overlapping uniform bins [8 22). This approach is simple but requires additional handling for bins with more than one observation and leads to missing data
when bins are empty 30
As alternative to temporal discretization, some previous studies intuitively preprocessed missing observations using various imputation or interpolation schemes and then fed them as regular sequences to standard deep learning models 23 23 However, the absence of observations can be informative on its own, making the regular imputation not always beneficial [1 19]. Moreover, they can distort the inherent distribution of time series, leading unintended distribution shifts (47
Thus, several studies have developed deep learning models that directly learn from irregular time series to improve classification performance by preserving their intrinsic characteristics. For example, Che et al. ( took the observed values and missing indicators as inputs for gated recurrent units and handled irregular time intervals through decay mechanism. In addition, Wu et al. [40] focused on dynamically capturing temporal dependencies of irregular time series.
Some recent works have exploited attention mechanisms to successfully capture missingness patterns in irregular time series by considering all observations within the time series and finding informative
ones [36, 48). Horn et al. incorporated attention mechanism with differentiable set function

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learning to handle misaligned observations across different variables. Shukla and Marlin 30 introduced a multi-time attention mechanism to learn temporal similarity from partial observations and generate continuous-time embeddings. However, they struggle to fully exploit missingness patterns that underlie irregular time series. Moreover, they do not explicitly capture intervariable dependencies, which provide rich information in multivariate time-series classification [8 45).
While some studies have attempted reflect intervariable relationships along with irregularities 42 46 47 49 their computational complexities are extremely high due to the use of graph neural networks or additional complex attention mechanisms to capture intervariable dependencies
3 Proposed Method
We propose novel interpolation- based encoder-classifie framework, ATENel, for irregular multivariate time-series classification. The en- coder directly takes irregular se- quences as inputs and generates their representations at learnable reference points, and the classifier predicts their class labels. In particular, a novel time encoding approach, ATE, is in- troduced to learn effective reference time points for capturing missingness patterns of irregular multivariate time series and generate latent representations at these reference points. Additionally, introduce temporal and intervariable consistency regularization techniques to incorporate intricate temporal dynamics and relationships across variables into the representations, thereby enhancing classification performance. Figure Iillustrates an overview of ATENet.
Inter Narall Conslstency
Query
Key Hi.d
Representaton P,
Imegular
Figure 2: Overview of the proposed method
3.1 Problem Statement
Let Fn)) be of N labeled samples, where X,, is an irregular multivariate time series, andy, ,, E (0, 11. is its one-hot encoded label vector. The observations in each variable E (1...., of X, irregularly recorded at different time points; hence, the number of observations Tn can differ across variables. Thus, for each variable v, we denote Xnv E Xn as a tuple (nvv.xo)) where lnv (lavi.... ,InTT.. and Xnv (Xnvl, .,nVTT } are the sets of the observed time points and values, respectively.
Given set of learnable reference time points r (FI.... ,k], define encoder f X,, Zn and a classifier g Zn - In, where zn E R VxK is V-dimensional representations for each K reference points, and , RC denotes the softmax probabilities for each class c E {1.-... .C) with respect to Xn. Note that the dimension of to enforce intervariable consistency between X,, and zn. Our objective to optimize f. g. and r to learn effective representations for irregular multivariate time-series classification. In the remainder of this paper, we omit the sample index n for brevity when the context is clear.
zn is set equal to the number of variables V of X,
3.2 Adaptive Time Encoding
In the encoder f, we introduce ATE that transforms irregular multivariate time series X into representation on learnable reference points. To enhance representation quality. two consistency regularization techniques for reflecting temporal and intervariable dependencies are also suggested.
3.2.1 Learnable Reference Time Points
Previous studies with attention mechanisms generally transform an irregular sequence into fixed- length representation by interpolating with regular time intervals [5. 30 However, their repre- sentation may be insufficient to substitute the input sequence due to information loss caused by disregarding its irregularity time intervals, and their classification performance tends to highly depend on the choice of reference points [3 50). Thus, explicitly learn the reference points to
3

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allow uneven time intervals and adaptively represent the partial observations of the irregular sequence without manually exploring the optimal reference points.
Specifically, we first learn a globally shared set of reference time points, which are not fixed but jointly optimized with model parameters capture task-relevant temporal structures across the training data. These reference points serve as soft anchors that reflect representative temporal patterns, such common event timings, even when sequences data exhibit diverse alignment distributions, the learned reference points are flexibly positioned to reflect such variations. Importantly, although the reference points are shared, the attention-baue based interpolation is computed individually for each sample, conditioned on its actual observations. This design enables the model adaptively align each sequence with the learned temporal structure, effectively handling variability in observation frequencies or event timings. Moreover, this design choice is motivated by three key benefits compared to using fully individualized reference points:
irregular misaligned. When the training
Robustness and stability; It can mitigate sensitivity to per-sample noise and outliers.
Generalization: It captures dataset-level temporal structure while retaining per-sample adaptability through attention-base interpolation.
Efficiency: It reduces computational overhead compared to per-sample optimization without losing flexibility.
A detailed comparison between globally shared and fully individualized reference points is provided in Appendix G
Let = fr,,... be a query parameter that a globally shared set of learnable reference time points uniformly initialized from zero to one. Note that during model training, this query parameter is optimized in an end-to-end manner. Given a v-th variable X, = (f,, E X, our approach takes a query time point rı and of keys and values, L, and x,, input of the encoder f and then obtains V-dimensional representations Zy at rk-
Following Shukla and Marlin [30], first derive time embedding vector of size L for tyr fy using a set of H time embedding functions 4 = (Ø)....
.HH. "... Two popular time embedding functions are:
1. Sinusoidal embedding function
38
&n (tvrr [sin( (sin(ttt/72 2/L),
if is even [cos(tvr/?21i))) (211), if f is odd
(I)
where & (I...., L} is E-th embedding component for lyr, and T is the number of all possible observations when fully observed (maximum sequence length). This function is independent of h, deriving the same embedding vector for all // time embedding functions.
2. Learnable embedding function
Whe fyr + bbe ssnn lyr + bae),
i
&n [C] =
otherwise
where whe and bur are learnable parameters that represent the frequency and phase shift of the sine function, respectively. It captures non-periodic patterns over time when l = 1; otherwise, it captures periodic patterns.
Our approach is agnostic to this function; hence, its choice is treated hyperparameter.
Subsequently, define interpolation weights based interpolation weights кy (rk, tvr) are computed as a scaled inner product attention between the time embedding vectors (tvr) and (rk), which corresponds the actually observed time point fyr E ly and the reference point rk. respectively, as follows:
attention mechanism. Specifically, the
kn( fvz)
(3)
ΣT en
where T, denotes the number of observations in Xy, and is a scaling parameter, Note that the same tn is equally applied to all variables. Then, obtain an univariate time function for X th (T..X.).

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Temporal Consistency
(x
Inter- Inter-Variable
Random
Masking
Consistency
Key 1
ml
(Car)
(2,
Learable Reference Time Points (r)
(a) Temporal consistency regularization
Intervariable consistency regularization
Figure 3: Procedures for (a) temporal and (h) intervariable consistency regularization techniques
using the interpolation weights as follows:
(rr = E (n(r,, 'Frr
(4)
T=1
where lur ty and Xyr xy denote observed time point and value in X,. This function serves as a kernel smoothing for X, [30]. Finally, for each reference point rı E r, the representation zı: e RV is generated by linear combination of the univariate time functions corresponding rą across V variables and H heads. Formally, the r'-th embedding component of Zk, where v' {I,..., V), is calculated follows:
11
V
[v']
Σ
Σ
hhr () W Whvv':
(5)
A= v=1
where Whvv' are learnable parameters. Following these procedures for all reference points parallel, we obtain the final representation z (Z), ,tx] for X.
3.2.2 Temporal Consistency Regularization
In general, time series contain information redundancy, easily enabling the recovery of missing observations through local temporal patterns obtained from adjacent observations. By hiding several observations of the time series with a high masking ratio, this information redundancy can be removed, thereby forcing the model capture complex temporal relations (13). Thus, we introduce novel temporal consistency regularization term that exploits a masking technique to capture intricate temporal patterns in Figure 3h illustrates the temporal consistency regularization technique.
Given æ-th sample X,, = x,,) E D, we define binary mask m E RxT, where T is the maximum sequence length. Then, the masked keys and values, f, and x are derived by element-wise multiplication of m with In and xn, respectively, as follows:
I, =n o m, x,, Xn m.
(6)
We randomly pick the masking ratio 0.91 in every epoch to avoid the effort of finding the optimal masking ratio. Such random masking can encompass a variety masking ratios, thereby enhancing the capability to capture sophisticated temporal patterns of X Consequently. we generate a masked context view z,, 'z ,z,x) of X, by Eqs.
with t and x',,
To encourage temporal consistency, we employ both instance-wise and point-wise contrastive loss functions suggested by Yue al. 44 which are complementary they capture coarse-grained and fine fine-graieed temporal dependencies, respectively. For Xn, the instance- contrastive loss LrCı, designed maximize the similarity between the representation Znk 2n and its corresponding masked context view z', E zzz while minimizing the similarities to representations at the same reference point T from other samples in the same batch. This loss calculated follows:
LTCL, =
1
Σ
log R=1
K
Jnnk Z'
K
ΣB=1
[nveb) gaank Zbb
where the batch size, the number of reference points, and is the indicator function. In contrast, the wisn contrastive loss LICP,, which uses the representations of X,, at different
5

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reference points as negatives, is calculated by
K
e Fic
LICP,
log
(8)
K
Ek'=1 eznn En En
1 leee ernt Enke
k=1
Finally, the temporal consistency regularization term is defined follows:
LTC, = (Lrcı, + LTCP,)
(9)
3.2.3 Intervariable Consistency Regularization
Prior works that deal with intervariable relationships, which are known be informative for multi- variate time-series classification, have high computational burden because they employed graph neural networks or incorporated further complicated attention mechanisms. Thus, to efficiently reflect the intervariable relationships, exploit an intervariable consistency regularization term that is simply calculated based on the outer product. Figure briefly displays the intervariable consistency regularization technique.
Given Xn xn) and its representation Zns we first define two outer product matrices for x, and denoted as Pn and Qn, as follows:
Pn = [x Qn = (z
(10)
where the sigmoid function, and [-] is the rounding operator. The dimensions of Pn and Qn are both [[V|| x [IVI|. Following the outer product's 's properties, which capture the structural relations between two vectors (33. Pn and Q,, can reflect intervariable dependencies x, and Zn. respectively,
Then, we encourage intervariable consistency by employing the binary cross-entropy loss as follows:
Lvc,
E
Pij log qij (1 - Pij) log(1 (1- qij),
(11)
where Pij and qı are the (i, j) elements of Pr and Qn. respectively. Note that Pn is regarded as the ground truth of intervariable relations that should be maintained in the latent representation. Through this loss, we can efficiently capture intervariable dependencies, enriching the representation Σn.
3.3 Adaptive Time Encoding Network
ATENet is an end-to-end framework that sequentially combines encoder configured by ATE with a classifier for irregular multivariate time-series classification. The encoder f directly takes a labeled irregular sequence (Xn. Fn) D input and generates representation z, for the set of learnable reference time points r. The classifier then uses in to predict the softmax probabilities y,-
3.3.1 Simple Classifier
If the encoder f learns the representations that successfully substitute irregular multivariate time series through ATE, we can achieve high classification performance even with a simple classifier. Thus, simply design the classifier g as gated recurrent unit followed by two fully connected layers, where the first layer includes batch normalization and GeLU activation function.
Let [yn1. }nc} }o and f, (fm1.... .... }nc} be the one-hot encoded label vector and predicted softmax probabilities for an irregular multivariate time series X,, where C is the number of classes. We define classification loss as the cross-ent cross-entropy combined with label smoothing, parameterized by n,, to prevent overfitting of the model and improve its generalization performance (4 as follows:
LcLn = Σ (11 (1- yne + ") log Inc-
(12)
3.3.2 Optimization
Given D = [(Xn. , p we train f. g, and with the following loss function:
N
f= Σ
(Le + aLCT, + +Lvc,,).
(13)

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Metric
Datast
DGM
MIGNN
Reindrop
Warpfommer
MTSForme
ATEN
P12M
71,0542.0
61.59a5.7
83.39unse
68
81.19
79.35
86.11am7)
55.54.12
AUROC
F19
49.60u503
80.00u1.2:
69 80u141
49.82.3.
57.16.t.
68.36um
85.07a30
59.05.141
77.56us
61.64.154
78.57
64.70.2m
17,89.142
70.40.1.0
74.5741.
85.4
88 8896.2
17.17.
82.02.11
7944.114
PAM
92.21a03
46.87a00
91.72a0m
96.95au
96.6
74.666770
98, 23.32
9) 97.90aue
98. 98.59
99.18.0.1
P.2-M
52 77
25 00
14.83+1.5
24 34.25v5.0
46 91
14.4--..0
42. 14
41 11.84+1
48 55
53.31-300
AUPRC:
P12-L
P19
31.24
92.42a1.30
51. 12
96 48
93.41.0.0
47,57a2.77
96444172
41.13
20.00a4
94. 94.16aa
94.65
28.05.6.
30.34.150
95 26.2846.31
96.57an.5
$0.6342.22
96 36.99
41. 41.12
57.96.
97. 33.43
97.30
41 41.16.300
BAM
74.95
88.25a1
75.78
88.85a2000
M6.734421
91, 91,50unst
36.4361233
95, 85.48
92.73a1.0
94.21um31
97.61.325
Arenage Ronk
7,50
6.58
8.25
6.75
8.13
6,63
9.13
3.78
4.63
2.38
2,00
Table I: Classification performance of ATENet and baselines. The best score in each dataset shown in bold.
where a and B weight the temporal and intervariable consistency regularization terms, respectively.
In summary, Lcr,, allows the representations be directly affected by class labels and capture discriminative features relevant to classification, while LTC, and Lvc, capture inherent temporal patterns and intervariable relationships in irregular multivariate time series, thereby enhancing classification performance. Pseudo-code and complexity analysis are given in Appendices A and
Experiments
4.1
Experimental Settings
Here, we briefly describe the experimental settings. The implementation details and sensitivity analyses for hyperparameters are provided in Appendices D Dand]
Baselines. We compared ATENet with 10 SOTA methods: mTAND
DGM
40
GRU-D
2) MTGNN 42 Transformer [38, Trans-mean, SeFT (9), Raindrop 47
Warpformer 46). and
MTSFormer 49
All baselines, except Trans-mean, are mentioned in Section 2 Trans-mean is
method that combines Transformer with average interpolation, which imputes missing observations by the average observed value of each variable.
Datasets. To validate our method, ATENet, we used three irregular multivariate time-series datasets:
P12 [ which includes 11,988 patients recorded by 36 sensors in the first 48-hour stay in the intensive care unit, has two predictive binary class labels: in-hospital mortality (P/2-M) and hospitalization length (P12-L).
P19 [27] contains 38,803 patients monitored by 34 sensors. Each sample is annotated with a binary class label for the occurrence of sepsis.
PAM 25 has 5,333 samples for eight activities of daily life measured by 17 sensors.
Further details for each dataset are provided in Appendix C
Evaluation metries. We employed the area under the receiver operating characteristic curve (AUROC) and area under the precision-recall curve (AUPRC) to evaluate classification performance while considering the imbalance in each dataset. We repeated each experiment five times and reported the averages and standard deviations.
4.2 Experimental Results
4.2.1 Classification Performance
Table I shows the averages and standard deviations of AUROC and AUPRC scores of the baselines and ATENet for each dataset. The results of statistical tests, which confirm the significance of the differences in classification performance, are given in Appendix B
ATENet remarkably outperformed the baselines by achieving the best average rank of 2.00 across all datasets and metrics, demonstrating the effectiveness of ATENet for irregular multivariate time-series classification. Especially for the P12-M and P12-L datasets, which have the most variables, and the PAM dataset, which has the longest sequences, our method showed the highest classification performance both AUROC and AUPRC scores. Moreover, ATENet performed significantly better than the baselines in most cases (see Table A2). In Appendix F we further discuss these results.
7

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FILM
FII
PL23
F11L
F12
SOP
00
02
04
25
02
24
00
3.2
04
0.
02
04
02
04
00
32
03
62
04
02
24
(a) Leave-fixed-seesss--ot
(b) Leave-randommssnsorss
Figure 4: AUROC scores of ATENet, MTSFormer, and Raindrop when dropping variables with various ratios [0.1.055] in (a) leave-fieed-sessee sensors-uu and (b) feave-randone wandon-sensoos---ne sensors-out scenarios
4.2.2 Robustness to Missing Variables
ATENet can mitigate a drastic performance drop even when some variables are missing by introducing intervariable consistency to capture the structural relations of inputs. We examined the robustness of ATENet by selecting subset variables and hiding their observations in the test set. Following Zhang al. [47, set up two scenarios:
Leave-fixed-sensore -on The most informative variables determined by information gain analysis are dropped [47]. The dropped variables are fixed across every sample.
Missing variables are not fixed but are selected randomly from
each sample.
In Figure we compared the AUROC ATENet and those of MTSFormer and Raindrop, which are the SOTA methods that showed the second-bes and third-bess, performance in Table I under these scenarios where variables are removed at various ratios ranging from 0.1 to 0.5.
As shown in Figure 4h, ATENet showed more robust performance with low standard deviations than MTSFormer and Raindrop the leave-fixed-senssrss-oe scenario. MTSFormer and Raindrop also take into account intervariable dependencies, but their performance remarkably declined on most datasets. Especially in the P19 dataset, Raindrop's ' performance notably dropped when 40% of variables were removed. In addition, in the PAM dataset, MTSFormer showed performance drop of approximately 50% when 50% variables were removed.
In the moneerrndom--eenoon showed significantly better robustness to missing variables than MTSFormer and Raindrop. For example, Raindrop's 's performance dropped by approximately 30% when more than 20% of variables were randomly dropped in each sample of the PAM dataset.
scenario, as exhibited in Figure 4b, the proposed method also
Therefore, this shows the robustness of ATENet to the absence of variables by successfully capturing intervariable relationships in irregular multivariate time series. The complete results, including comparison of ATENet with all baselines, are provided in Appendix G.I
Furthermore, our method can perform robustly when some observations are missing along the time axis by effectively capturing intricate temporal dependencies owing to learnable reference points and temporal consistency regularization. The results of these experiments provided in Appendix H
4.2.3 Computational Efficiency
The proposed method efficiently reflects intervariable relationships irregular multivariate time series by solely computing the outer product of variables and that of representations. Figure 5 shows the number of parameters and processing time of ATENet with those of MTGNN, Raindrop. Warpformer, and MTSFormer, which achieved high classification performance among the baselines by considering structural relationships between variables (see Table D..
We observed that ATENet is remarkably efficient compared to MTGNN and Raindrop, which require high computation complexities due to their use of graph neural networks, terms of both the number of parameters and processing time. In particular, for all datasets, the proposed method requires at least 10 times fewer parameters and achieves speeds at least times faster than Raindrop. Moreover, although the efficiency gains over Warpformer and MTSFormer are not as large as those over Raindrop and MTGNN, our method remains more efficient, as both rely on additional complicated attention mechanisms to capture intervariable dependencies.
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Regular
Sparze
Number of betrrdter
P12.M
85.43
83.61
$5.65
$5.54
31.
AUROC
P12L
77.35
73.35
77.35
79.64
99.00
51:36
51.00
AUPRC
P12L
97.55
97.54
97.55
97.70
P-2-1
PIB
PR2
0.
P12.
PT9
(a) Number of Parameters
(b) Processing Time per Epoch (s)
Figure 5: (a) Number of parameters and (h) processing time per epoch Table Classification performance of for MTGNN, Raindrop, Warpformer, MTSFormer, and AT'Eett
ATENet and ablation models
4.3 Ablation Studies
We investigated the effects of three key components of ATENet: learnable reference time points, temporal consistency, and intervariable consistency.
4.3.1 Learnable Reference Time Points
To examine the impact of learnable reference time points, we compared the classification performance of the proposed method against ATENet with fixed reference time points. We designed three ablation models where the reference time points are at regular time intervals (Regular), increasingly sparse time intervals (Sparse), and increasingly dense time intervals (Dense), respectively. In precise, their reference time points r {ri. .rkk) were characterized as follows:
Regular: F4 m (k 1). (1,... .K)
Sparse: Fa = (k-1) 1) yk E (1, (1, .K)
Dense: rą = =ree (k-1), e (1, (1. .K
As presented in Table 2 our method outperformed three ablation models, showing the effectiveness of learnable reference points in classification performance.
Distribution of Observed Time Points
Furthermore, in Figure 6 we visualized the distribution of observed time points across all training samples in the PAM dataset and illustrated the attention weights corre- sponding to the learnable and fixed (Regular) reference points using an example sequence from the same dataset. As shown in Figure 64, the blue bars indicate the overall distribution of observed time points, while the learnable reference points (green circles) predominantly located in regions with high observation density. In Figure (bp the blue dots denote the observed values, and the learnable reference time points (green circles) adaptively align with clusters of these observations (brown circles), effectively capturing irregular sampling patterns and emphasizing in- formative observations through highly deviated attention weights. In contrast, Figure 6] shows that the Regular ar reference points fail to capture temporal irregularities and find informative time points for classification, as their at- tention weights are rather uniformly distributed. These results reaffirm the benefit of our approach in reflecting missingness patterns in irregular sequences and reducing information loss that may occur with uniformly spaced interpolation, leading more effective representations for classification.
Oiserict Time Aee
(b) Learnable Reference Time Points
Mehhoogg Parts
Obsenved T Poirs
(c) Fixed Reference Time Points (ReguLar)
Figure 6: Visualization of (a) distribution of the observed time points and attention weights for (b) learnable reference points from ATENet (c) fixed ones (Regular)

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4.3.2 Temporal Consistency Regularization
To capture intricate temporal patterns, our method encourages temporal consistency by us- ing instance-wise and point-wise contrastive loss functions, LrCι and LTCP. As listed in Table ATENet w/o Lrc, ATENet w/o LrCP, and ATENet w/o LICι dropped the average per- formance compared ATENet. Thus, we vali- dated that temporal consistency regularization is useful for capturing temporal dependencies spanning various time intervals, thereby enhancing classification performance. The complete results are provided in Appendix G.2
Metric
w/o Lrc
wdo Lrcr
w/o Erci
w/o Lvc
AUROC AUPRC 1.28
0.20
0.13
0.91
3.22
0.57
1.63
3.33
Table Average performance drop rate (%) of ablation models without consistency regularization compared ATENet
4.3.3 Intervariable Consistency Regularization
The proposed method efficiently captures in- tervariable relationships by ensuring intervari- able consistency between inputs and their rep- resentations. As shown in Table 3 ATENet w/o Lvc highly dropped the average performance of 3.33% the AUPRC compared to ATENet, demonstrating that this regularization term can provide rich information for accurate classifi- cation. The complete results for each dataset are provided in Appendix G.2 Furthermore, as shown in Figure [ the learned representation progressively aligns with the input structure during training. highlighting the efficacy of intervariable consistency regularization in reflecting intervariable information.
Figure 7: Visualization of intervariable relations from the imput and from the learned representations epochs I and 20
Conclusion
We propose ATENet, novel end-to-end framework designed to enhance classification performance on irregular multivariate time series by learning their effective representations. In particular, we introduce ATE, which learns reference time points and generates representations at these reference points. This approach can successfully capture missingness patterns without information loss caused by disregarding uneven time intervals and without the need for expensive tuning process find optimal reference points. ATE also introduces temporal and intervariable consistency regularization terms, ensuring the enrichment of temporal information and efficient reflection of intervariable relationships. series experiments on irregular multivariate time-series classification demonstrated that ATENet outperformed the SOTA methods with high computational efficiency.
Acknowledgments
This research was partially supported by the National Research Foundation of Korea (NRF) grant funded by the Ministry of Science and ICT (MSIT) RRS-2023-002084122 by the Korea Mete- orological Administration Research and Development Program (KMI; RS-2025-02222 1093 and RS- RS-2025-022 12889)) and by the U.S. National Institutes of Health (NIH) under Grant RO1 AG065330 (HD).
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A Overview of ATENet
In this study, we propose ATENet that sequentially combines encoder configured by our encoding approach, ATE, with a classifier to enhance classification performance on irregular multivariate time series.
While ATENet might appear to incorporate familiar components such as attention- interpolation and contrastive regularization, its key contribution lies in the effective integration and optimization of these components to address the unique challenges of irregular multivariate time-series classification.
Adaptive encoding process: We propose novel encoding framework that learns reference time points in end-to-end supervised manner, eliminating the need for predefined an- chors or handcrafted temporal discretization. Unlike prior approaches, our method directly optimizes the reference points with respect to both the task objective and the empirical distri- bution of observed time points. This design enables the model to align irregular sequences in task-aware and data-adaptive temporal space, thereby improving both the expressiveness and generalization of the learned representations across varying sampling patterns.
Consistency regularization: To further improve the quality and robustness of representa- tions, ATENet incorporates two lightweight yet effective regularization techniques:
Temporal consistency regularization: This component enforces stability in the learned representations under random temporal masking, perturbation strategy spe- cialized for sparse or irregular time series. By promoting invariance to partially missing observations, it enhances generalization under temporal noise missingness.
Intervariable consistency regularization: We design a novel contrastive objective that encourages structural consistency across variables by exploiting the outer product be- tween imput and representation spaces. This approach efficiently captures intervariable dependencies and serves as a lightweight alternative to complex graph-based or recur- rent models, enhancing cross-variable coherence without incurring high computational overhead.
In Algorithm A
we present pssuud-coode of our method to describe its overall learning procedure.
Algorithm A1 Learning procedure of ATENet
Input: Set of N labeled irregular multivariate time-series samples = {(X,,, F,) J n= set of time embedding functions o (61.... &h), and the number of learnable reference time points Output: Trained encoder f, classifier g. and reference time points r = (r Initialize encoder f. classifier g. and reference points r.
2: for each epoch do
3: for yn) do
4: # Learnable Reference Time Points
5: Obtain time embedding vectors for X, and using the time embedding functions in Generate 2n = [Inl.". Enk } at learnable reference time points by Eqs. 3 5).
6:
7:
# Temporal Consistency Regularization
8:
Randomly pick masking ratio 0.9].
9:
Generate masked view z -'.. xxxx by Eqs.
10:
Compute temporal consistency regularization term LrC, by Eqs.
7-
# Intervariable Consistency Regularization
12:
Obtain two outer product matrices Pn and Q₂ for Xn and respectively, by Eq. (L0). Compute intervariable consistency regularization term Lvc, by Eq. (TT).
14:
# Classification Loss Function
S - g(z,)
16:
Compute classification loss LCL. by Eq.
end for
18:
# Optimization
Update f.g and by Eq. 13
20: end for
21

---

Dataset
Number of sumples
Number of variables
Number of observed points
Number of classes
Sparsity ratio (56)
P12-M
11,988
36
215
2
88.4
P12-L
11,988
36
215
88.4
P19
38,803
34
60
2
94.9
PAM
5,333
17
600
8
60.0
Table A1: Dataset statistics three datasets. Sparsity ratio ratio between the number of missing observations and that of all possible observations when fully observed.
B Complexity Analysis
Here, let N, V, C, and be the number of instances, variables, classes, and the maximum sequence length in an irregular multivariate time-series dataset D, respectively. In addition, let // be the number of embedding functions (attention heads) in the encoder f and J be the maximum hidden dimension in the classifier g, respectively.
ATE consists of the procedures for interpolation on learnable reference points based on the multi-time attention mechanism (MTA) [30] and computing two consistency regularization terms.
Interpolation on learnable reference points leverages the MTA that has time complexities for computing query, key, and value matrices for H attention heads (O(NV² + NV2T)), calculating the scaled dot product attention for H heads (O(NVKT)), and concatenating the results from H heads with linear transform (O (O)NV²K)). Thus, the time complexity of this procedure is summarized (NV((V +T + KT)).
Temporal consistency regularization proceeds the random masking to inputs (O(NVT) and additional MTA for the masked inputs (VV +T++K))) hence, its time complexity is also dominated by O(NV(VK VT KT)).
Intervariable consistency regularization has time complexities for computing the outer product of variables and that of representations (O + VK))).
Therefore, the time complexity per epoch of ATE is dominated by ((NV(VV+VT+KK) In general, K s T; hence, the time complexity can be reduced to O (NVV(V++)), While the attention mechanism incur relatively large computational cost, our approach introduces minimal computational burden for reflecting intervariable relations, compared to existing methods that account for intervariable dependencies in multivariate irregular time series by leveraging graph neural networks.
ATENet consists of the encoder with the time complexity of O(NVT(V + K)). The classifier in ATENet is constructed by a gated recurrent unit (GRU) followed by two fully connected layers with batch normalization and a GeLU activation function; hence, it requires the additional time complexity of ((N KJ + C)). Thus, ATENet has the time complexity per epoch of O(NVT(V K) NJ(VK + KJ + C)). When C is smaller than J, the time complexity per epoch can be reduced to O(NVT(V + K) + NJ(V + KJ)). In Figure of the main body, we compare our method existing methods in terms of the number of parameters and processing time per epoch.
C Detailed Description on Datasets
To evaluate the proposed method, ATENet, we employed three irregular multivariate time-series datasets as follows:
P12 (PhysioNet Mortality Prediction Challenge 2012) 7 is one of the popular healthcare datasets recorded by 36 sensors for 11,988 patients, after dropping 12 inappropriate samples [9]. during their first 48-hour stay in the intensive care unit. This dataset has two predictive labels: in-hospital mortality (P/2-M) and hospitalization length (P/2-L). A positive class of the P12-M dataset indicates in-hospital death, and this dataset has 13.8% positive samples. For the P12-L dataset, each patient is assigned binary class label indicating the length of hospitalization. While a positive class indicates stay longer than three days, a negative class indicates stay of three days or less. This dataset has 93% positive samples, thereby being highly imbalanced.
P19 (PhysioNet Sepsis Early Prediction Challenge 2019) 27 another popular healthcare dataset containing 40,336 patients monitored by 34 irregularly sampled sensors, including
22

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eight vital signs and 26 laboratory values. We remove the samples with extremely short or long time series, thereby remaining 38,803 patients with more than one and less than 60 observations. Each patient has binary class label that indicates the occurrence of sepsis within the next six hours. This dataset highly imbalanced due to about 96% negative
samples.
PAM (PAMAP2 Physical Activity Monitoring) [25] PAM has 5,333 samples with 600 continuous observations measured by 17 sensors after modification following Zhang et al. |47. This dataset has eight human activities of daily life. To make the samples irregular, we randomly removed 60% of the observations. Each sample is annotated with one of eight activities of daily living. The number of samples is balanced across all eight activities.
The characteristics of each dataset are given in Table A1 To handle missing values in irregular time series, first set the missing values to zero. The input then configured by concatenating the observations with a binary mask indicator, which was set to 1 when an observation existed and otherwise. Following Zhang al. 477) for the P12-M, P12-L., and P19 datasets, we applied batch minority class upsampling. We also excluded static information (e.g.. age, gender, height, and weight) from model training focus on each method's ability capture temporal patterns within irregular time series. All datasets were split into training (80%), validation (10%), and test (10%) sets.
D Implementation Details
In ATENet, the encoder f maps an irregular multivariate time series X = (t.x) with variables to V-dimensional time embeddings at K reference time points. The encoder f consists of multi-head attention with H embedding functions (attention heads), each deriving time embedding vector of size L for each observed time point. In this study, both K and L were set to 128. For the P12-M, P12-L. P19, and PAM datasets, we set H to 2. 4, 2, and 1, respectively, while using learnable, learnable, sinusoidal, and learnable embedding functions in that order. The subsequent classifier g is constructed by a GRU followed by two fully connected layers, where the first layer includes batch normalization and GeL.U activation function, and the second one uses softmax an activation function. The GRU dimension was set to 32, and the two fully connected layers had dimensions of 32 and C, respectively, where C is the number of classes. Additionally, the scaling parameter e Eq. (3) and the smoothing parameter 17 in Eq. (12) of the main text were set to 128 and 0.1, respectively.
For model training, we set the batch size B to 128 and ran the model for 20 epochs. For the P12-M dataset, we used the Adam optimizer with an initial learning rate of 0.0001 and assigned weights of 0.01 and 0.1 to the temporal and intervariable consistency regularization terms, and B, respectively. In the P12-L. dataset, we used the Adam optimizer with an initial learning rate of 0.001 and set both ar and B to 0.01. In the P19 dataset, rate of 0.01, and adjusted a and / to 0.01 and 1, respectively. For the PAM dataset, we maintained a learning rate of 0.01, while setting a 0.1 and f to 0.01. Note that all hyperparameters were selected based on performance on the validation set, and the final results were obtained from the model that achieved the best validation performance. The impact of each hyperparameter further explored in Appendix[[ [
also employed the Adam optimizer, but with initial learning
We repeated each experiment five times and reported the averages and standard deviations. All experiments were executed on a PyTorch platform using an Intel Core 10-00X at 3.70 GHz CPU, 256 GB RAM, and an NVIDIA GeForce RTX 4090 24 GB GPU.
E Statistical Tests
To confirm the significance of the differences in classification performance in Table the main text, we conducted statistical tests. Specifically, we adopted paired t-test to compare the proposed method to each baseline on each dataset. The following markers indicate the results of the significance tests:
indicates that ATENet performed significantly better than the baseline with a smaller v-luuue than 0.05.
indicates no significant difference between the methods being compared.
x indicates the baseline performed significantly better than our approach.
23

---

Metric
Dataset
ITAND DGM
GRU-D
MIGNN Transformer
Trans-uncan
SeFT
Raindrop
Warpformer
MTSFormr
P12-M
<<<r
PIZ-L
AUROC
P19
PAM
P12-M
P12-L
AUPRC
P19
PAM
Table A2: Statistical significance results comparing ATENet with each baseline each dataset
As shown in Table A2 the proposed method, ATENet, performed significantly better than the baselines in most cases.
F
Limitations
Here, we discuss some limitations of our work and suggest potential directions for future research.
F.1 Marginal Performance Gains and Trade-offs
As shown in Tables and A2 our method did not outperform some baseline methods, particularly GRU-D, Raindrop, and MTSFormer, on the P19 dataset. While the learnable reference time points designed adapt irregular patterns, the P19 dataset may exhibit extreme variability and noise in sampling times and values, making it challenging for any method based on reference time points capture nuanced patterns effectively and generalize the reference time points for all data [6]27]] For example, as shown in Table of the main text, our method and mTAND, which leverage reference time points, showed relatively low classification performance on the P19 dataset compared to the other datasets. Therefore, in future work, we expect to enhance classification performance on such challenging datasets by incorporating additional techniques, such as Kalman filter or wavelet denoising, to mitigate the effects of extreme variability and noise in sampling.
Furthermore, our key contribution lies in the encoder, which transforms irregular multivariate time series into fixed-length representations at learnable reference points. To demonstrate its effectiveness without relying on complex backbones, we deliberately used simple classifier. However, more com- plex classifiers may improve performance by capturing richer class-speciff patterns. In preliminary experiments on the P12-M dataset, replacing the simple decoder with a transformer and temporal convolutional network yielded slight AUROC improvements of 0.13% and 0.50%, respectively, but with 1.08x and 2.29x increases in processing time per epoch, respectively. These marginal gains suggest that classifier complexity may trade off with the overall efficiency of our method. Designing classifiers that balance accuracy and efficiency is a promising direction for future work.
F.2 Robustness to Start-Time Mismatch
First, start-time mismatch (or misalignment) is not inherently problematic in modern sequence modeling approaches such as Transformers or recurrent models 24 do not rely absolute timestamps but instead learn representations based the relative positions or temporal dynamics within each sequence. Consequently, the fact that sequences start at different times does not invalidate the model's ability to learn meaningful patterns, nor does it by itself constitute distribution shift.
29 20
35 2]. These models
Second, in many real-world time-series domains, start times are often not entirely random. Instead, they tend to follow domain-specific routines or event triggers. For example, patient monitoring typically begins at symptom onset or ICU admission in clinical data, and measurements in industrial settings may align with batch starts or fault occurrences. Thus, even without explicit synchronization, there is often implicit regularity that the model can exploit. ATENet is designed to capture such latent patterns by learning reference points and generating representations aligned them. Moreover, even in scenarios where start times are highly variable or nearly random, ATENet is still likely to work well by learning uniformly distributed reference points that provide broad temporal coverage without depending strict alignment.
24

---

F.3 Generalization under Temporal Distribution Shifts
Regarding generalization to datasets with different temporal distributions (i.e., distribution shift), our experiments conducted under within-dataset settings. However, shifts in temporal dynamics, such as variations event density or measurement frequency between training and deployment environments, may affect the effectiveness of the learned reference points. In such cases, the learned reference points may fail to align with informative regions in the target data, potentially degrading interpolation quality and downstream performance. We identify this limitation as an important direction for future work.
F.4 Robustness under Extremely Sparse Observation Scenarios
Similar other attention-basee based methods, ATENet may underperform in extremely sparse observation scenarios due to the fundamental lack of information. However, ATENet is designed to be more robust such sparsity than conventional approaches by:
Learning reference points that adapt to data-driven observation patterns, especially around informative regions;
Using attention- -baeed interpolation that effectively aggregates information from both nearby and even distant observations;
Introducing temporal consistency regularization based on random masking, which enhances representation quality even when data is partially missing.
As shown in Appendix H. ATENet demonstrates strong robustness under high levels of missingness. Specifically, the model maintained competitive performance when up to 50% of the observations were randomly dropped, indicating that method remains effective long minimal level of temporal coverage is preserved.
Nonetheless, in extremely sparse settings where few or no observations exist near any reference point, performance can degrade. We will address this limitation future work that robust extremely sparse scenarios.
G Complete Results
Here, we present the complete results of the experiments, which demonstrate robustness to missing variables and the effectiveness of temporal and intervariable consistency regularization terms.
G.1 Robustness Missing Variables
ATENet can mitigate a drastic performance drop, when some variables are removed, by introducing intervariable consistency regularization to capture structural relations between variables in irregular multivariate time series. In Section 4.2 of the main text, investigated the robustness of ATENet by selecting a subset of variables and hiding their observations in the test set. Following Zhang et al. [47, considered two scenarios: leave-fixed-senson setedd-snsoos-out and Gaave-radom-sennsee sensors-out.
In Tables A3 and A4 we provide the complete results for the classification performance of ATENet and that of the baseline methods when eliminating variables by various ratios e [.5] for both scenarios, respectively. In most cases, the proposed method performed more robustly than the baseline methods by achieving a higher classification performance. In contrast, although MTGNN, Raindrop. Warpformer, and MTSFormer consider intervariable relationships, their classification performance significantly declined in most datasets. For example, in the PAM dataset under the leave-fixed- sensors-out scenario, MTGNN exhibited a maximum performance drop of 30% in AUROC and 60% in AUPRC. Raindrop showed maximum performance drop of 40% in AUROC and 70% in AUPRC. Both Warpformer and MTSFormer showed about 50% and 80% performance drop in AUROC and AUPRC, respectively.
These results demonstrate the robustness of ATENet against missing variables by successfully capturing intervariable relationships in irregular multivariate time series.
25

---

Moric
Datset
Dopp Bostn
mitaNi
DGMP
GRI-D
MIGNN
Trandooner
Yomnmoo
Rairshpp
Worpformer
ATENN
24
4
61.566.
53.38ams
68 1.05
$1 19ai
29:35a18
54. uun
35. 15
0.1
63.80u33
58.13sm
14.581122
54.23
77.56u123
P12-M
0.3
64,44234
67.20.15
29
51.134035
69:32
0.4
60.35238
62.70
47.144255
54,74839
50.65.235
60,6722.9
67.53
50 60.26133
50.35
58.766300
69 69:04225
0.4
61.00
61:25
47.37vo 1
5487
57 91
57 17:9--
66 06-
50 Stace
48:05v in
55 15.640199
63. Mexte
34
0.1
72.04112
PIZ
0.3
0.2
55.3244
15.00.1
00.16
st. 34 w
08
58 18
50 19.5
17 17
64.00.26
66 1h
56 50
55 55.564444
66 50
72.54
74 Mh
75, 35.5
04
17
17.45-1
AUROC
0.5
24.56a2.0
$2,59
67.09.46
53.35
53.354206
63.37
49.35a4:30
10000
17.56
18.57.50
45
54
0.1
78.79
96, W033or
51 77.7
75 a
17
12 1
72.54
54.77177
12
P1P
033
0.2
39
78.34x1
K5.10am
52.0
61.7
75 20.00
68.01.10
14
50 52
450084 i
48000s
14.8803
77
0.5
96.00
74
14.7-199
17.5
00005
40.04c
75 15
01.72 96.8
06 06.0
97. 97.8-a03
14,0
96 18.3
97.04cc 4
96. Maua
99. Ba
0.1
55 T4.154
Motion
71.8
M6.60o in
PAM
0.3
52.35
52.85.1
60.45.13
47.56a
0.4
69.66
61.552230
8253
$1.5
$2 52.9
63.47223
50 10.79008
53.09
74.66
0.4
60.4 94
68 08.33amm in
50 10.1im
50 m0
15 3588-133
59 Bi
4000 w
50 Win
1483
34.2
4L05
0.1
20.20
P12-M
63
0.2
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Matha
15.17
214312
1M85-20
24 1
1399
24 16
11 Moccos
23 Ma
17
24 15
79
04
2401.2.0
13.9uM 4
18.2
2065.300
20,00.355
24.57220
20 79a2s
15.4422
23.21x100
22.53,331
13:25
18.052200
1857
18.57
92.42.100
96
M6
0.1
92.45a:::
06.34.2.
03.4
46.23.1.0
94.3 44.5
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96.34c
90 Lous
PIZAL
0.3
0.2
94.146123
06.33am
77-1
03.46.::11 31
06.27.1.
94 2428
94 24.26.1.0
54 16-0
03.30a
97.05
AUPRC
0.5
94.0241
06.23.5.4
95,
25.00
31.34 is
51.12,53
47.37
41.13:5m
29 00.0s
28 .5.05
30.54
50.6553
41.12at 30
57 1
41 He
0.1
389135
36 30
18.55a
P19
0.3
29.09a
10.08.13:3
23,09ua s
40.5.
30.40.24
18.7u
47.5
0.4
10:36010
70.56
40.7-15
14 40-00-m
4:37
20 No
4.5
4820
0.
34.4611 u
21
4077-mm
40.76-mm
7.70
4580sc 14
4.Mars
41 W.
30.4
75:76a2
91. 10.50
35.4311
95
91.75a:4
94.3 a42
978
0.1
37.51uss
PAM
0.3
0.2
42.360
40.72a4
6:00iam
57.25.45
41.54ac.2
50
6301::5
52.1
50556030
43 13.2842
11,47,334
45. 45.06.244
27.1141.4
24.7
27.0
15
15
12.5.um
30.02.0
54 34.7841
55 14
0.4
29
54.30am
24.54533
47.25233
40.75113
45.58aa
24.071000
18:20a:
36 14.88
63. 63.5as55
0.5
90.9.1
24
7
12
17
13.55
12.0o11
Table A3: Classification performance of ATENet and baselines when dropping variables with various ratios
E 0.5] in the leave-fixed oexed-sensors-ou scenario. Drop Ratio denotes the ratio of missing variables.
G.2 Effects of Temporal and Intervariable Consistency Regularization
To validate the influence of the temporal and intervariable consistency regularization terms, compared the classification performance of ATENet to that of ablation models, ATENet w/o LrC. ATENet w/o LTCP, ATENet w/o LTCı and ATENet w/o Lve in Section 4.3 of the main text. Table A5 presents the complete results of these ablation studies.
As result, ATENet outperformed the ablation models in most cases, demonstrating the effectiveness of both temporal and intervariable consistency regularization terms in enhancing classification performance. Specifically, removing temporal consistency (ATENet w/o Lrc) exhibited an average drop in AUPRC of 1.28%, whereas removing intervariable consistency (ATENet w/o Lvvc caused larger average drop of 3.33%. These findings indicate that both components are beneficial, with intervariable consistency showing a more substantial effect in our experimental settings.
G.3 Futher Analysis
G.3.1 Empirical Trade-offss Between Flexibility and Stability
We evaluated a variant that computes reference points individually for each sample. Although this approach offers better flexibility, it can be more sensitive to noise and irregular sampling, often resulting in unstable training and degraded generalization performance.
As shown in the Table A6] the globally shared design (ours) showed comparable or slightly better performance across most datasets. Notably, the fully individualized variant showed a substantial drop in performance on the P19 dataset, which may contain highly variable and noisy sequences (see Appendix(F) (F). This highlights that globally shared reference points, combined with sample-specific crention-basct interpolation, offer better robustness under challenging conditions.
26

---

Maric
Patser
Dong Raiio
ITAND
DGMF
GRIID
MIGNN
Teadomeer
Tranomon
S:F7
Rensipp
Warplomeer
MYSSonnur
ATENe
64. 18...
11.06.2i
61,50u..
82.92am32
$3.38aus
68.05...m
81.19eui x
20.35
84.11
85. 35
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76 m
61.25
6404-110
30
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84 25.55.
P12-M
0.3
57.774559
77.23
77.17
57.33
78,20uc00
04
4
57
37.00
50 08
90 90,06
76 26.50mm0
0.5
65 25:0
64 3400-177
49 S4-00
97.42
74.36ees
14.8700s
67
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73.76r1
75, 75.4607
5900
61.66134
P12-L
0.3
0.2
56.16
67:mm
6864
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90:30
65.47463
37.5422.
58. 18,00
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66.572.
54.56115
54, 15.15
70.57..15
75, 75.74
044
54.99500
06.001144
15.6
63.59uss
57.524248
58,3622d
27:25:220
48 18.75
75 15.10
AUROC
65.00-.x
58
66 66.11 mn
45.4
55.07
76.5
65:4
0.1
77 77.48
37.19.2.
64 40.0
$1.35
77.3
72.05.2
81.514271
53 33.6..m
87.184155
54.44155
P19
0.2
0.3
76
1000
45.7845300
77.35
77.00
76.55225
1
76.62426
25.0
75 17
77 17.85 x
79,652.00
43 43.00
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24.73a139
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72.09
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74.36.155
73.50-22
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98.73 28.7348:2
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0.1
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42 42.14
41.96...8
48.53a35
38.7
44
21:8-24
20:18
4364:22
P12-M
17.30.2
26.00.20
14.90.1
21,99.57
39 19.063364
19.50u33
10
D4
34.0941.8
14.0.100
13. 1330
21,02
37.714325
39 20.20.20
10.33.20
22.34.311
17.5
37,48341
42.56
0.5
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14
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35.8540
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06.3
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94 2111
56.37
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08.18.311
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0,3
0.2
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26.33
93 48
95
94.44110
94.13a1s
95 22.
96
06.0424
32
96.75
97 40
04
56.00.0
95.796115
93.8
05395
91.96277
AUPRC
04.00.
91-am
95.03.m
14
31,12
D.1
25. 15.99...
9.05..36
41 1.....
33.40412
25, 26.90350
25. 12.12
28.57 23357
45.75
34
54,15413
40
P10
0.S.
38 64-1 s
6:30
17 M0
15.00-1::
1971
10 15
70-3
41.70um
780 e
7:
11
59544M
14.872009
31,99u530
27.18.534
18.30
4401.41
5466279
48.05as
25
T6 9512/a
18.26:13
75 78:m
H6 75
91, Mhni
95.4533:1
73
94.31mm
0.1
5088
83.24/215
54 10..0
$1.96214
42.34
76.40.00
26.40u..
40.21.25.1
90.7346111
94.5204
BAM
12:40-10
m
31:41- e
34
28.06-1 71
51.50 m
0.4
27.96.21
$4.20,21
54.09.055
59.056000
60.00000
20.25.1.0
23.12,300
15914377
67.63.300
27.51225
0.5
49.16-24
27.34
4676
32.8641
$4.42.cu
19.474.
22.55am
17.0
60.79cm
72.5
Table A4: Classification performance of ATENet and baselines when dropping variables with various ratios random--ennsorsoou sensors-out scenario. Drop Ratio denotes the ratio of missing variables.
E [0.1.0.5] in the leave- ganueeraddo--aoe
Metric
Dataset
w/o LTe
w/ Lrer
w/o LrCı
w/o Lvc
ATENet
P12-M
85.53
85.61
85.62+1.20
85.4921.17
15.5421.26
P12-L
19.86=1.95
79.81
79.56x1.9
79.08=2.92
79.64.2.41
AUROC
P19
83.19
83,43=2.23
81.39+3.16
81.75=2.21
84.02+1.38
PAM
99.02+0.23
99,01=0.22
99.08=0.30
98.84=0.52
19.18=0.15
Average Performance Drop Rate (%)
0.20
0.13
0.91
3.22
P12-M
53.2822.05
L3.3421.87
53.39
53.31 12.93
P12-L
97.72x9.47
97.72.0.38
97.6620.49
97.56e0.47
97.70s0.38
AUPRC
P19
36.75x3.75
38.87=5.24
35.08=5.48
29.32=4.18
41.16x3.02
PAM
96.93=1.08
97.57=0.40
97.14=0.68
96.65=1.16
97.61
Average Performance Drop Rate (%)
1.28
0.57
1.63
3.33
Table A5: Classification performance of ablations related to temporal and intervariable consistency regulriittionn
P-12M
P-12L
P19
PAM
Method
AUROC
AUPRC
AUROC
AUPRC
AUROC
AUPRC
AUROC
AUPRC
Fully Individualized Variant
85.07
52.28
79.39 79.64
97.71
81.53
30.09
99.02
96.96
ATENet (ours)
85.54
53.31
97.70
84.02
41.16
99.18
97.61
Table A6: Classification performance of ATENet and fully individualized variant
G.3.2 Comparison with Prefrain-then--inetum Frameworks
Pretrain-then-finene frameworks, such as Modern 21 aim to learn penrpal-purpose represen- tations through task-age pretraining followed by finetuning on downstream tasks. In contrast, ATENet adopts task-specific learning strategy that directly optimizes representations for the classi-
27

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P-12M
P-12L
P19
PAM
Method
AUROC
AUPRC
AUROC
AUPRC
AUROC
AUPRC
AUROC
AUPRC
ModernTCN ATENct
81.16
42.92
71.20
96.47
75.31
17.73
98.35
93.30
85.54
53.31
79.64
97.70
84.02
41.16
99.18
97.61
Table A7: Classification performance of ATENet and ModernTCN
P-12M
P-12L
P19
PAM
Method
AUROC
AUPRC
AUROC
AUPRC
AUROC
AUPRC
AUROC
AUPRC
FreRA
73.63
33.39
68.28
96.14
78.36
31.60
93.94
76.31
FGTI
82.87
46.12
72.75
96.91
81.54
43.21
99.31
97.05
ATENet
85.54
53.31
79.64
97.70
84.02
41.16
99.18
97.61
Table A8: Classification performance of ATENet and frequeney-doman approaches
fication objective. This approach can provide several advantages, including better task alignment, lower computational cost, and architectural simplicity.
To empirically evaluate the effectiveness of this design, we compared ATENet with Modem a recent pretrain-thes te--ttthnennnneeeeeee method. As shown in the A77 ATENet consistently outperformed ModernTCN across all datasets in both AUROC and AUPRC, demonstrating that taec-specific learning can be highly effective even without explicit pretraining.
G.3.3 Comparison with Trequency-Domalle Approaches
Frequency-domane approaches offer a complementary perspective on time-series analysis. However, their applicability irregular multivariate time series is limited by the assumption of uniform sampling inherent in most Fourier-based methods 266 39 When this assumption violated, as is become unstable unreliable.
often the case in irregular settings, frequency-base based representations This limitation likely contributes to the scarcity related studies in this domain.
Nevertheless, we compared ATENet with two recent frequency based methods: FreRA [37 and FGTI [43] Although these methods were originally developed for regularly sampled data or different tasks, we adapted them to the irregular multivariate time-series classification setting enable fair comparison. As shown in the Table A8 ATENet outperformed both methods most cases. While FGTI achieved comparable performance ATENet in a few cases (e.g.. AUPRC P19), it relies on a diffusion- architecture with significantly more parameters and longer processing time. In contrast, ATENet showed competitive results with simpler and more efficient design.
H Robustness to Missing Observations
Learnable reference points and temporal consistency regularization can enhance the capability of capturing inherent temporal patterns by focusing partial observations with inconsistent time intervals in irregular time series. That is, ATENet can robustly perform when some observations missing along the time axis. To validate this effect, in Figure Al compared the AUROC of ATENet with that of MTSFormer and Raindrop, which showed the second-best and third-best performance in Table of the main body, across various missing ratios (0.1,0.5) Here, randomly hid observations in each sample of the test set along the time axis instead of using all observations for certain variables. As a result, ATENet consistently performed, unlike Raindrop. despite the presence of missingness along the time axis, demonstrating that our method effectively captures intricate temporal dependencies.
I Sensitivity Analysis
We analyzed hyperparameters affecting ATENet, including the time embedding function, the number of heads in MTA, the learning rate, and the loss weights. Here, we report classification performance using the AUPRC, which was used select the best models for each dataset.
28

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P12.M
F12L
F19
RAM
90.0
80
87.5
90
AUROC
70
75
85.0
80
82.5
70
80.0
ATEhet
ATEN
ATENet
77.5
NTStomer
60
Mrstormar
50
65
0.0
0.2
0.0
0.4
0.2
0.4
0.2
0.4
Missing Ratio
Missing Ratio
Missing Ratio
Missing Ratio
Figure Al: AUROC scores of ATENet and Raindrop missing ratios [0.1, 0.5] along the time axis
100
100
100
80
80
AUPRC
AUPRC
Leurnable Function
PM2-M
P124
P19
PAN
P12-M
F124
P19
RAX
0.0001
0.001
0.0:
0.
Datsser
Datnoet
Learning Rate
(a) Time embedding function (b) Number of heads
(c) Learning rate
Figure A2: AUPRC scores according to (a) time embedding function, (b) number of heads, and (c) learning rate
Time embedding function. We analyzed the influence of the time embedding function & by comparing the AUPRC for sinusoidal and learnable functions. As shown in FigureAAp, although the classification performance for the P12-L and PAM datasets was not sensitive to d, the classification performance on the P12-M and P19 datasets differed by about 5% depending on Φ. These performance gaps stem from how these embedding functions capture temporal dependencies and unique patterns in each dataset. The sinusoidal embedding function is fixed and periodic, thereby successfully capturing predictable and cyclic temporal patterns. Thus, it performs well in datasets with smooth cyclic temporal structures. However, this function may struggle with non por-pprio data, as it cannot adapt to complex time dependencies. In contrast, the learnable embedding function is more flexible in capturing non-penne non-periodic patterns and is able to learn temporal representations specialized to the data, making them advantageous for datasets with more complex non-cyclic patterns. To sum up, the choice of time embedding function impacts classification performance based on the complexity of the temporal patterns in each dataset. Thus, exploring the optimal embedding function is necessary to enhance classification performance. this study, we set & to sinusoidal embedding function for the P19 dataset, whereas learnable for the remaining datasets.
Number of heads. To examine the effect of the number of time embedding functions (attention heads), we compared the AUPRC on each dataset using various Hs. As shown Figure A2p. the classification performance slightly differed depending on H in the P19 dataset. However, the performance differences for the other datasets were small, indicating that ATENet not highly sensitive to the number of heads. We set the number of heads H in the P12-M, P12-I., P19, and PAM datasets to 2, 4, 2, and I, respectively.
Learning rate. In Figure A2p. compared the AUPRC of ATENet by varying the learning rates. Consequently, the classification performance on the four datasets differed according to the learning rate. In this study, the learning rates for the P12-M, P12-L., P19, and PAM datasets 0,001, 0.01, and 0.01, respectively.
0.0001,
Loss weights We use two loss weights a and B associated with temporal and intervariable consis- tency regularization terms to reflect intricate temporal and intervariable dependencies, respectively. Figure A3 exhibits the AUPRC of ATENet for various pairs of a and B. The performance differences for the PI2-M, P12-L, and PAM datasets were relatively small, indicating ATENet's robustness
29

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0.01
8
0.10
a= 1,00 & 8
0.01 & 0.10
0.10
0.10
1.00 & 0.10
0.01 & 1.00
0.10
1.00
1.00
8.00
100
80
AUPRC
40
20
P12-M P12-L
P19
PAM
Dataset
Figure A3: AUPRC according weights for temporal and intervariable consistency regularization terms
against a and B. However, for the P19 dataset, the performance gap is significantly high. Therefore, in this study, we pair of (a, B3 for the P12-M, P12-L, P19, and PAM datasets (0.01, 0.1), (0.01, 0.01), (0.01, 1), and (0.1, 0.01) through grid search for E (0.01, 0.1, I} and B (0.01, 13.
J
Code Availability
The code for reproducing our experimental results is available on GitHub https://gtthub.co/ shlee-labs/ATENell
30


Reviews:
[{"review_id": "bCIpI5oumP", "reviewer": "Reviewer_8fHo", "summary": "This paper investigates the challenging temporal classification task with irregularly measured time-series as inputs. The authors propose a novel interpolation-based encoder-classifier structure, ATENet, with learnable reference points for the time-series embedding. In addition to the gradient from classification loss, two additional regularization terms are introduced in ATENet to enhance the representation quality of embeddings from the encoder. Specifically, with randomly masked data points, the instance-level and point-level contrastive losses are utilized to encourage the encoder to effectively capture unique temporal characteristics of the input time-series. In the meantime, the consistency loss enables ATENet to preserve temporal dependency structure of the input in its latent embeddings in the sense of outer products. The high-quality time-series representation learned by the encoder of ATENet enables a straight-forward design of the classifier network which greatly contributes to the improved computation efficiency compared to transformer- or graph-based approaches. Experimental results on three real-world datasets show that ATENet achieve better time-series classification accuracy over multiple state-of-the-art approaches. The authors also provide detailed ablation study to demonstrate the effectiveness of their different design choices in ATENet.", "questions": "1. What is the implicit assumption on time-series sparsity in AETNet? Is AETNet applicable to any time-series data?\n2. Are the missing patterns always important to time-series classification? What is the performance of AETNet on datasets with missingness at random?\n3. Does the time-series interpolation in Eq. 4 introduce inductive biases to AETNet? Would it be affected by noisy signals?\n4. Is the set of key reference points $\\mathbf{r}$ globally shared by all samples in a dataset? What is the impact of this design?\n5. Is the outer product in Eq. 10 sufficient to model complex temporal patterns and dependencies across time steps, especially when the time-series are irregularly measured?\n6. There should be additional baselines with time-series embeddings in the frequency domain.\n7. ATENet consistently has lower performance than MTSFormer on P19 datasets according to Table 1 and Figure 4. There should be analysis on the underlying reasons and potential limitations of ATENet.", "limitations": "yes", "rating": 3, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 3, "strengths_and_weaknesses": "Strengths\n- ATENet enables efficient processing of irregularly measured time-series through interpolation at key reference points and fixed length representation of predictive temporal patterns. Further, the reference points could be flexibly learned based on the training data instead of being manually designed which usually requires domain knowledge and expertise.\n- The usage of positional encoding of observation time $t$ and reference point $r$ as key and query in attention mechanism is interesting and might be potentially equivalent to the concept of dynamic time warping (DTW) which is well-known to be effective for comparison of time-series of variable lengths.\n- The notion of temporal consistency between the latent embedding $z$ and input time-series $x$ is sort of novel, and the design of corresponding regularization terms indeed have huge contribution to the classification performance according to the ablation study results in Table 3. The high-quality latent representation also enables a simplified classifier model, which contributes to the improvement in computational efficiency of ATENet compared to other models.\n\nWeaknesses\n- The fundamental assumption on the sparsity of the time-series data is not explicitly discussed. For instance, for meaningful interpolation of the irregularly measured time-series in Eq. 4, the sampling frequency of the input signals should satisfy certain criteria. If the measurement is overly sparse, ATENet may fail to distinguish different input time-series due to the lack of effective data points.\n- The authors should also discuss any potential inductive biases introduced by the attention-based interpolation described in Section 3.2.\n- It is unclear if the set of reference points $\\mathbf{r}$ is globally shared by all samples or dynamically computed for individual input time-series. The authors need to justify for a global set of reference point $\\mathbf{r}$ if applicable.\n- Relevant study applying Fourier transform and spectral analysis should be discussed in literature review, and there should be additional baselines (utilizing frequency domain representations) from these researches.\n- The performance gain of AETNet seems to be marginal except for AUPRC on P12-M and PAM dataset.", "was_revised": true, "final_justification": "My major concerns with the global reference points of ATENet and the associated challenges from time-series alignment remain unresolved after the rebuttal. In contrary to many modern sequential models like RNNs, Transformers and Mamba, ATENet's time-series interpolation mechanism is strongly coupled with the learned global reference points and may fail to generalize on novel data points due to distributional shifts. Therefore, I tend to maintain my rating for this work.", "rebuttal": "Thank you for your thoughtful comments. We tried our best to address all of your comments, including five weaknesses, **W1-W5**, and six questions, **Q1-Q6**. We hope our responses help to clarify our work and answer all the concerns.\n\n---\n\n### **W1 & Q1. Assumptions on Time-Series Sparsity**\n\nATENet implicitly assumes that the input time-series data are not excessively sparse. When observations are too infrequent or occur far from any reference points, the interpolation process becomes unreliable. This can lead to latent representations that fail to capture meaningful temporal patterns, thereby reducing their discriminative ability for downstream tasks.\n\nImportantly, ATENet does not assume uniform sampling of multivariate time series. In many real-world scenarios, such as clinical or industrial time series, observations are recorded irregularly, often reflecting meaningful event dynamics (e.g., dense measurements near symptoms or anomalies). ATENet is explicitly designed to leverage such irregularities as informative signals by:\n\n- **Learning reference points** that adapt to data-driven observation patterns, especially around informative regions;\n\n- Using **attention-based interpolation** that effectively aggregates information from both nearby and even distant observations;\n\n- Introducing **temporal consistency regularization** based on random masking, which enhances representation quality even when data is partially missing.\n\nThis design enables ATENet to handle irregular and sparse inputs without relying on strict assumptions (e.g., Nyquist sampling).\n\nTo empirically assess this robustness, we conducted experiments in Appendix H by randomly dropping observations along the time axis. The results show that ATENet maintains competitive performance even under relatively high missing ratios (up to 50%), demonstrating its effectiveness under considerable levels of sparsity.\n\n---\n\n### **Q2. Are Missing Patterns Always Important?**\n\nWhile missingness patterns are not always informative, they often reflect underlying processes in real-world applications, particularly in healthcare settings, where critical conditions often trigger more frequent measurements. The proposed method is designed to leverage such patterns when they are informative, but does not rely on them exclusively.\n\nWe will revise the manuscript to clarify this point more explicitly.\n\n---\n\n### **W2 & Q3. Inductive Biases and Robustness to Noise**\n\nOur attention-based interpolation is built upon a set of learnable reference time points and a scaled dot-product attention mechanism over time embeddings. This design inherently induces a form of temporal locality bias: observations that are temporally closer to a reference point receive higher attention weights, similar to kernel smoothing [1-3]. \n\nHowever, unlike fixed kernels or handcrafted interpolation schemes, our method learns both the reference points and time embeddings in an end-to-end manner. This adaptive design allows the model to flexibly capture irregular temporal patterns in the data, reducing reliance on rigid inductive assumptions while still promoting attention to informative temporal regions—such as those surrounding clinical events or machine anomalies—where observations tend to be dense.\n\nThis inductive bias can have nuanced effects in the presence of noise. On one hand, it may help suppress temporally isolated noise by assigning it low attention weights. On the other hand, noise that occurs near densely sampled regions may still receive relatively high attention, potentially degrading interpolation quality.\n\nAlthough ATENet incorporates temporal and intervariable consistency regularization to mitigate such issues, we acknowledge that extreme noise remains a challenge (as discussed in *Appendix F*). We therefore consider integrating noise-aware extensions, such as Kalman filtering or denoising transforms, as a promising direction for future work.\n\n##### [1] Li, S., Jin, X., Xuan, Y., Zhou, X., Chen, W., Wang, Y. X., & Yan, X. (2019). Enhancing the locality and breaking the memory bottleneck of transformer on time series forecasting. Advances in neural information processing systems, 32.\n\n##### [2] Niu, P., Zhou, T., Wang, X., Sun, L., & Jin, R. (2024). Attention as robust representation for time series forecasting. arXiv preprint arXiv:2402.05370.\n\n##### [3] Choromanski, K., Likhosherstov, V., Dohan, D., Song, X., Gane, A., Sarlos, T., ... & Weller, A. (2020). Rethinking attention with performers. arXiv preprint arXiv:2009.14794.\n\n---\n\n### **W3 & Q4. Globally Shared Reference Points**\n\nThe set of reference time points is shared globally across all samples within a dataset and is learned as task-adaptive parameters during training. Rather than being fixed or predefined, these reference points are optimized to align with common yet task-relevant temporal patterns across the dataset. This enables the model to perform meaningful interpolation even in the presence of irregular or sparse observations.\n\nAlthough the reference points are shared, the attention-based interpolation weights are computed individually for each sample, based on the unique observation timestamps of that sequence. This design allows ATENet to retain sample-specific adaptability while leveraging a global temporal structure that facilitates efficient computation and stable optimization, particularly beneficial under sparse or noisy conditions.\n\nWe will clarify this point explicitly in Section 3.2.1 of the revised manuscript.\n\n---\n\n### **W4 & Q5. Comparison with Frequency-Domain Approaches**\n\nFrequency-domain approaches offer a complementary perspective on time-series analysis. However, their applicability to irregular multivariate time series is limited by the assumption of uniform sampling inherent in most Fourier-based methods [1, 2]. When this assumption is violated—as is often the case in irregular settings—frequency-based representations can become unstable or unreliable. This limitation likely contributes to the scarcity of related studies in this domain.\n\nNevertheless, to address your concern, we compared ATENet with two recent frequency-based methods: *FreRA* [3] and *FGTI* [4]. Although these methods were originally developed for regularly sampled data or different tasks, we adapted them to the irregular multivariate time-series classification setting to enable a fair comparison. \n\nAs shown in the table below, ATENet outperforms both methods in most cases. While *FGTI* achieves comparable performance to ATENet in a few cases (e.g., AUPRC on P19), it relies on a diffusion-based architecture with significantly more parameters and longer processing time. In contrast, ATENet achieves competitive results with a simpler and more efficient design.\n\n| Dataset | P-12M |           | P-12L |           |  P19  |           |  PAM  |           |\n|-----------|---------|---------|---------|---------|---------|---------|---------|---------|\n|  | *AUROC* | *AUPRC* | *AUROC* | *AUPRC* | *AUROC* | *AUPRC* | *AUROC* | *AUPRC* |\n|  **FreRA**  |   73.63   |   33.39   |   68.28   |   96.14   |   78.36   |   31.60   |   93.94   |   76.31   |\n|   **FGTI**  |   82.87   |   46.12   |   72.75   |   96.91   |   81.54   | **43.21** | **99.31** |   97.05   |\n|  **ATENet** | **85.54** | **53.31** | **79.64** | **97.70** | **84.02** |   41.16   |   99.18   | **97.61** |\n\nWe will expand the literature review to include these frequency-based approaches and explicitly discuss their limitations under irregular sampling.\n\n##### [1] Reschke, M., Kunz, T., & Laepple, T. (2019). Comparing methods for analysing time scale dependent correlations in irregularly sampled time series data. Computers & Geosciences, 123, 65-72.\n\n##### [2] Wang, H., Pan, L., Shen, Y., Chen, Z., Yang, D., Yang, Y., ... & Tao, D. FreDF: Learning to Forecast in the Frequency Domain. In The Thirteenth International Conference on Learning Representations.\n\n##### [3] Tian, T., Miao, C., & Qian, H. (2025). FreRA: A Frequency-Refined Augmentation for Contrastive Learning on Time Series Classification. arXiv preprint arXiv:2505.23181.\n\n##### [4] Yang, X., Sun, Y., & Chen, X. (2024). Frequency-aware generative models for multivariate time series imputation. Advances in Neural Information Processing Systems, 37, 52595-52623.\n\n\n\n---\n\n### **W5 & Q6. Marginal Performance Gain**\n\nWe acknowledge that the performance gains of ATENet are relatively marginal on some datasets, especially the P19 dataset. Nonetheless, ATENet achieves superior classification performance on other datasets while offering substantial improvements in computational efficiency, requiring significantly fewer parameters and achieving faster training times (see *Figure 5*). This trade-off between performance and efficiency can be particularly valuable in resource-constrained settings.\n\nAs discussed in *Appendix F*, the P19 dataset may exhibit extreme variability and noise in sampling times and values, making it difficult for interpolation-based methods, such as mTAND and ATENet, to capture subtle temporal patterns effectively and generalize the reference time points for all data.\n\nWe will revise Section 4.2 and Appendix F to better highlight this trade-off and explicitly acknowledge such limitations in challenging settings. \n\n---\n\n### **Q4. Role of Outer Product**\n\nThe outer product in Eq. (10) is not designed to capture temporal dependencies, but rather to model intervariable relationships within multivariate time series. Specifically, it encourages consistency between the structural relationships observed in the input variables and those encoded in the learned representations. This mechanism helps the model preserve meaningful cross-variable dependencies, which are particularly important in multivariate and high-dimensional settings."}, {"review_id": "feIb0bGv9O", "reviewer": "Reviewer_7wnM", "summary": "This paper proposes ATENet, an end-to-end encoder-classifier framework for irregular multivariate time-series classification. The key contribution is a novel Adaptive Time Encoding (ATE) module that learns reference time points to generate latent representations while capturing irregular sampling patterns and missingness. To further enhance the learned representations, the framework introduces two regularization terms: temporal consistency (capturing fine-grained temporal dynamics) and intervariable consistency (modeling dependencies across variables efficiently without graph neural networks). The proposed method is evaluated across multiple real-world benchmarks and demonstrates strong performance and computational efficiency compared to state-of-the-art methods.", "questions": "Pretraining vs. End-to-End: Have you considered comparing ATENet with pretrain-then-finetune frameworks (e.g., PrimeNet)? Your method does representation learning implicitly; how does it perform against explicit representation learning approaches?", "limitations": "The storyline, challenges and corresponding technical component, is complete, but to somehow incremental and not exciting.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 2, "originality": 3, "strengths_and_weaknesses": "Strengths:\n1.The paper identifies two concrete challenges in modeling irregular multivariate time series—(1) failure to utilize missingness patterns, and (2) neglect of inter-variable correlations—and addresses each with dedicated technical components.\n2.The method is tested on diverse datasets (healthcare and activity monitoring), and the experiments span multiple evaluation setups including robustness to missing variables and computational efficiency.\n3.The paper is easy to follow, with clear visualizations and ablation studies that support the claims.\n\nWeakness:\n1.  While the paper includes ablation studies, it remains unclear which component (adaptive reference points, temporal consistency, or intervariable consistency) contributes the most in specific cases. \n2. The paper combines known ideas (learnable queries, contrastive consistency, and interpolation attention) in a cohesive way, but may feel more incremental rather than fundamentally new to readers familiar with this area.", "was_revised": false, "final_justification": "", "rebuttal": "We appreciate your helpful comments. We tried our best to address all of your comments, including two weaknesses, **W1** and **W2**, and one question, **Q1**. We hope our responses help to clarify our work and answer all the concerns.\n\n---\n\n### **W1. Ablation Studies**\n\nAs shown in *Table 2* of the manuscript, the use of adaptive reference time points consistently improves classification performance across all datasets compared to fixed reference points (i.e., regular, sparse, or dense), highlighting their effectiveness in capturing irregular sampling patterns.\n\nAdditionally, *Table 3* and *Appendix G.2* demonstrate that both temporal and intervariable consistency contribute meaningfully to overall performance, with their relative impact varying depending on dataset characteristics. Specifically, removing temporal consistency results in an average AUPRC drop of 1.28%, whereas removing intervariable consistency leads to a larger average drop of 3.33%. These findings indicate that both components are beneficial, with intervariable consistency showing a more substantial effect in our experimental settings. \n\nWe will revise Section 4.3 to more clearly highlight the component-wise contributions.\n\n---\n\n### **W2. Novelty of Our Work**\n\nWhile ATENet builds upon familiar components such as attention-based interpolation and contrastive regularization, its key novelty lies in how these components are effectively integrated and optimized to address the unique challenges of irregular multivariate time-series classification.\n\n- **Adaptive encoding process**: We propose a novel encoding framework that learns reference time points in an end-to-end supervised manner, eliminating the need for predefined anchors or handcrafted temporal discretization. Unlike previous approaches, our method directly optimizes the reference points with respect to both the task objective and the distribution of observed timestamps. This design enables the model to align irregular sequences in a task-aware and data-adaptive temporal space, thereby improving both the expressiveness and generalization ability of the learned representations across varying sampling patterns.\n\n- **Consistency regularization**: To further improve the quality and robustness of representations, ATENet incorporates two lightweight yet effective regularization techniques:\n\n  - *Temporal consistency regularization*: This component enforces stability in the learned representations under random temporal masking—a perturbation strategy tailored for sparse or irregular time series. By promoting invariance to partially missing observations, it enhances generalization under temporal noise or missingness.\n\n  - *Intervariable consistency regularization*: We propose a novel contrastive objective that encourages structural consistency across variables by exploiting the outer product between input and representation spaces. This approach efficiently captures intervariable dependencies and serves as a lightweight alternative to more complex graph-based or recurrent models, enhancing cross-variable coherence without incurring high computational overhead.\n\nWe will revise the introduction to more clearly emphasize the key novelties of our approach.\n\n---\n\n### **Q1. Comparison with Pretrain-then-Finetune Frameworks**\n\nPretrain-then-finetune frameworks, such as PrimeNet [1] and ModernTCN [2], aim to learn general-purpose representations through task-agnostic pretraining followed by finetuning on downstream tasks. In contrast, ATENet adopts a task-specific learning strategy that directly optimizes representations for the classification objective. This approach can provide several advantages, including better task alignment, lower computational cost, and architectural simplicity.\n\nTo empirically evaluate the effectiveness of this design, we compared ATENet with *ModernTCN*, a recent pretrain-then-finetune method. As shown in the table below, ATENet consistently outperformed ModernTCN across all datasets in both AUROC and AUPRC, demonstrating that task-specific learning can be highly effective even without explicit pretraining.\n\n|  Dataset  | P-12M |           | P-12L |           |  P19  |           |  PAM  |           |\n|-------------|---------|---------|---------|---------|---------|---------|---------|---------|\n|             | *AUROC* | *AUPRC* | *AUROC* | *AUPRC* | *AUROC* | *AUPRC* | *AUROC* | *AUPRC* |\n| **ModernTCN** |   81.16   |   42.92   |   71.20   |   96.47   |   75.31   |   17.73   |   98.35   |   93.30   |\n|   **ATENet**  | **85.54** | **53.31** | **79.64** | **97.70** | **84.02** | **41.16** | **99.18** | **97.61** |\n\nIn the original manuscript, we did not include pretrain-then-finetune frameworks because our study focuses on fully supervised learning using only task-specific data, and most baseline methods also follow this setting, ensuring fair and consistent comparisons.\n\nWe acknowledge the importance of general-purpose representation learning and consider bridging task-specific and task-agnostic strategies a promising direction for future work. We will also include the additional results and discussion in the revised manuscript.\n\n##### [1] Chowdhury, R. R., Li, J., Zhang, X., Hong, D., Gupta, R. K., & Shang, J. (2023, June). Primenet: Pre-training for irregular multivariate time series. In Proceedings of the AAAI Conference on Artificial Intelligence (Vol. 37, No. 6, pp. 7184-7192).\n\n##### [2] Luo, D., & Wang, X. (2024, May). Moderntcn: A modern pure convolution structure for general time series analysis. In The twelfth international conference on learning representations (pp. 1-43)."}, {"review_id": "tAr7h4h1Cp", "reviewer": "Reviewer_x3TD", "summary": "The authors address the problem of classifying irregular time \nseries with missing values (IMTS). They propose a model \nthat for each channel interpolates the observations to a\nreference time points, that are initialized in regular intervals,\nbut then can be updated. Cross attention is used for\nthe interpolation. Finally latent representations are\nadded across attention heads and channels and the class\nprobabilities regressed on this. The loss is combined with\n- i) a contrastive loss for the reference point representations\n  of original instances and masked instances vs. other\n  instances,\n- ii) a contrastive loss for the reference point representations\n  of original instances and masked instances vs. other\n  reference time points (of the same instance), and\n- iii) a cross entropy loss between channels.\n\nIn experiments on four datasets against many baselines\nthey show that their model outperforms existing \nmethods.", "questions": "- q1. how did you optimize your hyperparameters? (w1)", "limitations": "yes", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 2, "strengths_and_weaknesses": "strong points:\n- s1. plausible and simple model: interpolate channels to an adaptive\n  list of reference points.\n- s2. good, mostly consistent lifts over the baselines.\n\nweak points:\n- w1. hyperparameters maybe trained on test?\n\nad w1. hyperparameters maybe trained on test?\n- how did you optimize your hyperparameters? \n  in appendix I you say \" Here, we report classification \n  performance using the AUPRC, which was used to \n  select the best models for each dataset.\" (line 635).\n  Does this mean you optimized your hyperparameters\n  on test? If so, would your results still stand if you had\n  to pick them on a validation sample within train?\n  Are the hyperparameters of the baseline models \n  also optimized on test?", "was_revised": true, "final_justification": "--- added after rebuttal\n- the authors' reply that their hyperparameters are optimited\n  on the validation sample resolves my main concern. \n- as overall lifts are small, I will update my score just by 1.", "rebuttal": "Thank you for your comments. We have carefully addressed your concern, including the weakness (**W1**) and its corresponding question (**Q1**). We hope our response helps clarify our work and answer your concerns.\n\n---\n\n### **W1 & Q1. Optimization on Hyperparameters**\n\nWe clarify that no hyperparameters were tuned on the test set. As described in *Appendix C*, each dataset was split into training (80%), validation (10%), and test (10%) sets. All hyperparameters were selected based on performance on the validation set, and the final test results were obtained using the model that achieved the best validation performance.\n\n We acknowledge that the explanation in *Appendix I* may have caused confusion, and we will revise the wording to avoid any potential misunderstanding. Note that this procedure was applied consistently to all baseline models as well."}, {"review_id": "oz5CpMudw1", "reviewer": "Reviewer_ASQ7", "summary": "This paper proposes an adaptive time encoding method that generates latent representations at learnable reference points to improve irregular multivariate time-series classification. The approach enhances performance by capturing missingness patterns and incorporating temporal-intervariable relationships through consistency regularization.", "questions": "1. The Adaptive Time Encoding (ATE) proposed in the paper uses a set of learnable reference time points, but it does not provide details on how the hyperparameter K is determined. Does the choice of K significantly affect classification performance? If the target dataset has a different time distribution from the training set, do the learned reference time points still generalize well?\n2. ATE uses a multi-head temporal attention mechanism for interpolation. However, in extremely sparse scenarios, this process may suffer from insufficient observation points, leading to uneven or even ineffective attention weight distributions. When the number of observations for an input variable is very limited, is the interpolation mechanism still effective?\n3. Among the comparison methods, only one is from 2024. Are there any other more recent methods that could be included for comparison?\n4. For Figure 6, could the raw data be provided as a reference? This would make the results more convincing.\n5. The meanings of the horizontal and vertical axes in Figure 7 do not appear to be explained.", "limitations": "yes", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 2, "originality": 3, "strengths_and_weaknesses": "Strengths: The paper is well-structured overall, with clear descriptions and rigorous analysis.\nWeaknesses: Some parts lack sufficient detail or justification, which will be listed in the \" Questions\" section.", "was_revised": true, "final_justification": "The author provided detailed answers to several of my questions, and I have no further questions. I don't think there are any other obvious issues with this paper and it can be accepted.", "rebuttal": "We appreciate your helpful comments. We tried our best to address all of your comments, including five questions, **Q1-Q5**. We hope our responses help to clarify our work and answer all the concerns.\n\n---\n\n### **Q1. Choice of Number of Reference Points & Discussion on Effect of Distribution Shifts**\n\n- ***Choice of number of reference points***: To evaluate the impact of the number of reference points $K$, we conducted additional experiments with five different values of $K$: 16, 32, 64, 128, and 256. As shown in the table below, performance generally improves up to $K=128$, after which it plateaus or slightly drops. This suggests that a moderate number of reference points (e.g., 64-128) offers a good trade-off between representation capacity (expressiveness) and regularization. Notably, $K=128$ yields the best results on most datasets.\n\n| # Reference Points ($K$) |   P-12M   ||   P-12L   ||    P19     ||    PAM     ||\n|--------------------|---------|---------|---------|---------|----------|---------|----------|---------|\n|                    | *AUROC*   | *AUPRC*   | *AUROC*   | *AUPRC*   | *AUROC*    | *AUPRC*   | *AUROC*    | *AUPRC*   |\n| **16**             |  84.67    |  50.41    |  77.99    |  97.56    |   81.20    |  30.92    |   99.08    |  96.99    |\n| **32**             |  85.19    |  51.15    |  79.29    |  97.75    |   83.37    |  33.52    |   98.78    |  96.58    |\n| **64**             |  85.17    |  51.27    |  **79.65**    |  **97.81**    |   83.93    |  38.00    |   98.99    |  97.09    |\n| **128**            |  **85.54**    |  **53.31**    |  79.64    |  97.70    |   **84.02**    |  **41.16**    |  **99.18**    |  **97.61**    |\n| **256**            |  83.87    |  47.58    |  78.62    |  97.77    |   81.25    |  31.99    |   98.93    |  96.91    |\n\n- ***Discussion on effect of distribution shifts***: Regarding generalization to datasets with different temporal distributions (i.e., distribution shift), our experiments focused on within-dataset settings. However, we acknowledge that such shifts in temporal dynamics —such as differences in event density or measurement frequency between training and deployment environments—may affect the effectiveness of the learned reference points. In such cases, the learned reference points may no longer align with informative regions in the target data, potentially degrading interpolation quality and downstream performance. We consider this an important advanced direction and leave it for future work.\n\n---\n\n### **Q2. Extremely Sparse Scenarios**\n\nWe agree that in extremely sparse scenarios, attention-based interpolation may become less effective due to insufficient observation points. However, this limitation is not unique to our approach; when observations are too sparse, no method is likely to perform well due to a fundamental lack of information.\n\nHowever, ATENet is designed to be more robust to such sparsity than conventional approaches by:\n\n- **Learning reference points** that adapt to regions with dense observations;\n\n- Using **attention-based interpolation** that flexibly aggregates information from even distant observations;\n\n- Introducing **temporal consistency regularization** based on random masking, which enhances representation quality even when data is partially missing.\n\nAs shown in *Appendix H*, ATENet demonstrates strong robustness under high levels of missingness. Specifically, the model maintains competitive performance when up to 50% of the observations are randomly dropped, indicating that our method remains effective as long as a minimal level of temporal coverage is preserved.\n\nNonetheless, we acknowledge that in extremely sparse settings, where few or no observations exist near any reference point, performance can degrade. We will include this limitation in Appendix F.\n\n---\n\n### **Q3. Additional Recent Baselines**\n\nTo address your concern, we included ModernTCN [1], a recent and relevant baseline for irregular multivariate time-series classification, in our main experiments. As shown in the table below, ATENet consistently outperforms ModernTCN across all datasets in both AUROC and AUPRC, demonstrating the effectiveness of our approach.\n\n|  Dataset  | P-12M |           | P-12L |           |  P19  |           |  PAM  |           |\n|-------------|---------|---------|---------|---------|---------|---------|---------|---------|\n|             | *AUROC* | *AUPRC* | *AUROC* | *AUPRC* | *AUROC* | *AUPRC* | *AUROC* | *AUPRC* |\n| **ModernTCN** |   81.16   |   42.92   |   71.20   |   96.47   |   75.31   |   17.73   |   98.35   |   93.30   |\n|   **ATENet**  | **85.54** | **53.31** | **79.64** | **97.70** | **84.02** | **41.16** | **99.18** | **97.61** |\n\n##### [1] Luo, D., & Wang, X. (2024, May). Moderntcn: A modern pure convolution structure for general time series analysis. In The twelfth international conference on learning representations (pp. 1-43).\n\n---\n\n### **Q4. Figure 6 – Raw Data Visualization**\n\nThank you for the suggestion. We will revise *Figure 6* to include an overlay or side-by-side presentation of the corresponding raw time-series data alongside the attention weight visualizations. This update will allow for a more direct comparison between the observed values and the model’s learned attention focus.\n\n---\n\n### **Q5. Figure 7 – Axis Explanation**\n\nThank you for pointing this out. In *Figure 7*, both the horizontal and vertical axes represent the variables in the multivariate time series. The matrices illustrate pairwise intervariable relationships captured from the input and learned representations. We will revise the figure caption to clearly indicate the meaning of the axes and improve clarity for the reader."}]

Author rebuttal:

Meta-review: This paper introduces a novel framework for irregular multivariate time-series classification. The method learns adaptive reference time points and incorporates two consistency regularizations to handle missingness and irregular sampling. Experiments show consistent improvements and better efficiency compared to a range of baselines.

Overall, this paper proposes a technically sound and well-presented framework for irregular multivariate time-series classification. The key contributions are the adaptive encoding of reference time points and the use of temporal/intervariable consistency regularizations, which systematically address missingness patterns and cross-variable dependencies. While the conceptual novelty and broader impact may not reach the highest bar for NeurIPS, the paper is technically solid, demonstrates consistent empirical improvements, and clearly articulates its methodological design. On balance, I recommend acceptance at the poster level.

The reviewers recognized the novelty of framing interpolation-based encoding for irregular time series, though some felt that the approach combines existing components in a way that may be perceived as incremental. One reviewer maintained concerns regarding generalization under distributional shifts, which the authors argued was outside the intended scope. Other reviewers were satisfied with the authors’ clarifications on hyperparameter tuning, baseline selection, and interpolation robustness.
Decision: Accept (poster)