Learning Recursive Multi-Scale Representations for Irregular Multivariate Time Series Forecasting
Authors: Boyuan Li
Zhen Liu
Yicheng Luo
Qianli Ma
Venue: ICLR 2026 Poster (2026)
Keywords: Irregular Multivariate Time Series
Time Series Forecasting
Multi-Scale Learning
Primary area: learning on time series and dynamical systems
TL;DR: We propose a recursive multi-scale modeling approach that preserves sampling patterns for irregular multivariate time series forecasting task, which boosts performance of existing models while maintaining good efficiency.

Abstract: Irregular Multivariate Time Series (IMTS) are characterized by uneven intervals between consecutive timestamps, which carry sampling pattern information valuable and informative for learning temporal and variable dependencies.
In addition, IMTS often exhibit diverse dependencies across multiple time scales.
However, many existing multi-scale IMTS methods use resampling to obtain the coarse series, which can alter the original timestamps and disrupt the sampling pattern information.
To address the challenge, we propose ReIMTS, a **Re**cursive multi-scale modeling approach for **I**rregular **M**ultivariate **T**ime **S**eries forecasting.
Instead of resampling, ReIMTS keeps timestamps unchanged and recursively splits each sample into subsamples with progressively shorter time periods.
Based on the original sampling timestamps in these long-to-short subsamples, an irregularity-aware representation fusion mechanism is proposed to capture global-to-local dependencies for accurate forecasting.
Extensive experiments demonstrate an average performance improvement of 27.1\% in the forecasting task across different models and real-world datasets.
Our code is available at [https://github.com/Ladbaby/PyOmniTS](https://github.com/Ladbaby/PyOmniTS).

Published as a conference paper at ICLR 2026
LEARNING RECURSIVE MULTI-SCALE REPRESENTA- TIONS FOR IRREGULAR MULTIVARIATE TIME SERIES FORECASTING
Boyuan Li, Zhen Liu, Yicheng Luo, Qianli Ma'
School of Computer Science and Engineering, South China University of Technology {csboyuanli, cszhenliu, cs cslmoyychheng201] @mmail. scut. edu. cn qi gianl icuuscut. .uuttteddd.c... edu.cn
ABSTRACT
Irregular Multivariate Time Series (IMTS) are characterized by uneven intervals between consecutive timestamps, which carry sampling pattern information valu- able and informative for learning temporal and variable dependencies. In addition, IMTS often exhibit diverse dependencies across multiple time scales. However, many existing multi-scale IMTS methods resampling obtain the coarse series, which can alter the original timestamps and disrupt the sampling pattern infor- mation. To address the challenge, we propose ReIMTS, Recursive multi-scale modeling approach for Irregular Multivariate Time Series forecasting, Instead of resampling, ReIMTS keeps timestamps unchanged and recursively splits each sam- ple into subsamples with progressively shorter time periods. Based on the original sampling timestamps these long-to-short subsamples, an irregularity- -ware repre- sentation fusion mechanism is proposed to capture global-to-local dependencies for accurate forecasting. Extensive experiments demonstrate an average performance improvement of 27.1 % in the forecasting task across different models and real- world datasets. Our code is available at httips://gihubb.coo wwa.iboooommmiaaaae www.om//aaaaaaymmammiiaai
INTRODUCTION
Multivariate Time Series (MTS) are commonly seen in real-world applications such as healthcare, weather, and biomechanies Zhang al. 2023b Shukla & Marlin 2021b). While extensive research
efforts have been devoted to MTS forecasting task NNi et al. 2023; Zhang & Yan 2023; Yu
et al. 2024), these methods often assume the input to be regularly sampled and fully observed. In reality, varying sampling rates or schedules can be applied to different series, giving rise to Irregular Multivariate Time Series (IMTS). IMTS forecasting for informed decision-making challenging due to irregular time intervals within each variable and unaligned observations across variables, where
an increasing number of studies have paid attention to Yalavarrhi al. 2024 Zhang al. 2024
Mercatali et al. 2024).
Under different temporal resolutions, IMTS can exhibit different patterns reflected in temporal and variable dependencies, similar to hourly, monthly. and yearly patterns in regularly sampled time series. For example, the healthcare dataset PhysioNet" 12 (Silva et al., 2012). IMTS samples contain biomarker (variable) readings for ICU patients during their first 48 hours after admission. In these samples, a 6-hour window corresponds to the common clinical monitoring period (Seymour Christopher W. et al. 2017), while 24-hour window reflects daily cycles of patients, both of which are useful for assessing disease fluctuations (Klerman et al. 2022 Luo et al. 2025).
Although IMTS have varying dependencies at different scales under scenarios like healthcare and weather (Menne et al. 2016), capturing them into multi-scale representations while maintaining the original sampling patterns remains challenging. On the hand, multi-scale methods for MTS typically assume inputs to be regularly sampled and fully observed (Shabani et al.] 20233 Wang al. 2024a CCen al. 2024), which are not well-suited for IMTS. On the other hand, multi-scale methods for IMTS are still underexplored (Zhang et al. 2023a Luo et al. 2025 Marisca et al. 2024).
"Corresponding author.

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Published as a conference paper at ICLR 2026
These multi-scale IMTS methods often involve resampling obtain moarse-grain series, which balances the number of observations across different variables but may disrupt the original sampling pattern. As depicted in Figure [ the upper sample is from the healthcare dataset PhysioNet" 12, while the lower one downsampled using the same way as (Zhang et al. 2023a). Variable Bilirubin in the original sample shows relatively dense observations in the first 12 hours and sparse observations in the subsequent 36 hours, indicating careful monitoring of disease progression at the beginning of ICU admission (Lakshman et al. 2025| Holford 2019 Morrill et al. 2020)). After downsampling to the coarse series, the dense-to- spasse sampling pattern of variable Bilirubin is disrupted, affecting subsequent dependency learning. Additionally, the disruption of urgent to mild clinical monitoring
information is disrupted, where information obtained through more frequent monitoring could be beneficial for early clinical decision-making (Miller et al. 2007).
To preserve essential sampling pattern informa- tion during multi-scale dependency learning in the above scenarios, we propose ReIMTS, recursive multi-scale approach for IMTS fore- casting. At each scale level, ReIMTS splits an IMTS sample into smaller subsamples with shorter time periods, while maintaining the orig- inal sampling timestamps for all observations and thus preserving the original sampling pat- tern. By recursively splitting the sample in top-down manner, input IMTS are viewed
urgent
mild
0h
12h
24h
36h
48h
density
fine
Bilirubin
HR
2
Ezt4
tg
t
Eg
[g t10
coarse
Bilirubin
from global to local perspective. Each back- bone captures dependencies within specific scale level, and learned latent representations are transferred from higher scale levels to lower ones. Leveraging global-t-loccl multi-scale rep- resentations learned from preserved sampling patterns, ReIMTS employs irreulaarity aawar fusion mechanism to capture semantics across different scales, thereby providing accurate fore- casting results. Moreover, ReIMTS is compat- ible with most existing IMTS models due to its flexible architectural design, boosting their forecasting performance in plug-and and-play way.
HR
ti
Figure 1: Existing multi-scale methods for IMTS resample the coarse series to balance differences sampling densities across different variables. In the original sample from the healthcare dataset PhysioNet" 12. liver function marker Bilirubin and heart rate (HR) exhibit dense- to-se-t sampling pattern reflecting urgent to mild clinical monitor- ing, which is disrupted in the coarse series.
Our main contributions are as follows:
We introduce recursive splitting based on time periods for IMTS samples to preserve the original sampling patterns across all scale levels, and leverage IMTS backbones to capture dependencies different time periods as multi-scale representations.
We propose ReIMTS, a recursive multi-scale method for IMTS forecasting. Using iregularity-awar representation fusion, it recursively captures global-to-local dependencies and provides accurate predictions.
Extensive experiments including twenty-six baseline methods and five IMTS datasets on IMTS forecasting are conducted. Tested on six IMTS backbones, ReIMTS consistently boosts their forecasting performance in all settings while maintaining good efficiency.
2 RELATED WORK
2.1
IRREGULAR MULTIVARIATE TIME SERIES FORECASTING
In recent years, an increasing number of studies have paid attention to IMTS forecasting (Yalavarthi
ct al.) 2024 Zhang et al. 2024; Mercatali et al. 2024). From model architecture perspective.
methods for MTS modeling can be broadly categorized into RNN-based (Che et al. 2018 Shukla &
Marlin 2019), ODE-based (Rubanova et al., 2019 Bilos et al. 202. Mercatali et al. 2024). GNN-
based (Yalavarthi et al. 2024; Zhang et al. 2022 Luo et al. 2025). Set-based (Homn et al. 2020).
Diffusion-basae (Tashiro al. 2021) }, and Transformer-based (Zhang al. 2023a). While variety
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of model architectures have been employed in IMTS modeling, most of them follow the encoder- decoder structure. Therefore, inputs for their decoders can include temporal representations (Che
et al., 2018: (Shukla & Marlin 2019 Rubanova al., 2019; Bilos et al., 2021; Mercatali al.
2024), variable representations (Luo et al., 2024; Zhang et al. 2024, Luo et al. 2025 Marisca et al.
2024h, observation representations Yalavarthi al. 2024 Zhang al. 2002
Horn et al. 2020),
combinations thereof.
2.2
MULTI-SCALE MODELING FOR TIME SERIES
Existing methods for regularly sampled time series have widely adopted multi-scale information during modeling for accurate predictions. From sampling pattern perspective, Pyraformer (Liu et al.
2022), NHITS (Challu et al. 2023). Scaleformer (Shabani et al.) 2023). and TimeMixer (Wang et al.
a embedding merging resampling that disrupts original observed timestamps to obtain different scales, potentially missing out on sampling pattern information. Pathformer (Chen et al.
2024) and MOIRAI (Woo et al., 2024) segment time series based on the number of observations rather than time periods, which cannot preserve the sampling rate information. LAMS-RNNs (Chen al., 2021) was designed based on RNNs for regularly sampled time series, thus not well adapted for IMTS. Multi-scale modeling in IMTS methods is relatively underexplored. Warpformer (Zhang al. 2023a), Hi-Patch (Luo al. 2025), and HD-TTS (Marisca al., (024) address irregularities within IMTS, but they also employ resampling to get different scales and still cannot preserve the
original sampling patterns.
PROBLEM DEFINITION
With a total of T timestamps and V variables, an IMTS sample can be denoted as a set containing Y observation tuples S {tt,, 2,, uz)l = ...., Y), where t, E fo....,T) T), 2; R, and {1...., } represents the timestamp, observed value, and variable indicator respectively. For the IMTS forecasting task, the set of forecast queries Q = {q 1, ,..; Yх} containing Yo observations is derived by combining (4z. uy) of the j-th observation tuple within the forecast window. We aim to learn forecasting model F()). such that given an input IMTS sample S and forecast query as input, it accurately predicts the corresponding observed values Z:
F(S, Q) Z.
(1)
4 METHODOLOGY
The overview of our proposed method, ReIMTS, is illustrated in Figure We first explain how to learn representations recursively at different scale levels in Section 4.1 Subsequently. detail the irregularit-awware representation fusion in Section 4.2 Training loss design is described in Section Finally, we discuss the differences between our method and existing approaches in Section Details on the operations are available at Algorithm T Further discussion of how backbones address irregularities and forecast-related queries can be found the Appendix
4.1 RECURSIVE LEARNING ACROSS SCALES IN IMTS
In this section, explain the methods for obtaining representations at each scale level, and how we ensure that the shape of global representations at the current scale matches the shape of local representations in the subsequent scale. should be noted that in the following discussion, 'global' and 'local' are used to describe relative scales between upper and lower levels, rather than considering all N levels. During data preprocessing, we align the raw multivariate time series within each sample based on timestamps to obtain the zero-padded sample S E R X at scale level 1, where L is the maximum number of observations in univariate time series. Also, corresponding mask M {0, 13 1 is created, indicating actual observations with is and zero-pate zero-padded values with Os. As shown in the left panel of Figure 2 for each scale level n E {I...., NN among the total N levels, an IMTS sample S is recursively partitioned by time periods to generate a series of subsamples. At scale level n, we denote the length of time period as 7 the number of subsamples as pm T= and the maximum number of observations in univariate time series after splitting and zero padding
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Input IMTS
Backbone Models
Original Sample
48h
Scale 48hx1
encoder
V23
decoder
Ey ta
V2
V/3
encoder
Subt canse
V1
cample
V
decoder
split
Scale
24hx2
V2
V22
V23
Scale
encoder
12h
12h
12h
15
12h
decoder
12hx4
absent
[1 C2
C3
05
C6
t
Cg
tg
E10
variable
0h
12h
24h
36h
48h
representation
fuse
concatenate
Figure 2: The architecture of ReIMTS with three scale levels. For the original IMTS sample on the top left, ReIMTS recursively splits into subsamples with shorter time periods each scale level. ReIMTS is compatible with most IMTS models. and we use graph neural networks as backbones here illustrate multi-scale variable representation learning. Local representations from lower scale levels are fused with global ones from upper scale levels. The decoder in the lowest scale concatenates representations and decodes them into forecast predictions.
as L" For the k-th subsample s(t)) with & E {l...., ""...,, its time period consists of the timestamps th [t]TT) (A 1) < t T k). Therefore, the set of all subsamples at scale level can be written as:
S" = (s(tt)
(2)
where S XV The mask is splitted in the same way obtain M It should be noted that L and 7 are distinct: whereas 7 incorporates real-world time units such as minutes, hours, or years, L merely denotes the number of observations without any time units. should also be noted that the split position is based on time periods rather than an equal number of observations, where the term 'observation' includes both actual observed values and zero-pate prro-padded values used for aligmment. As noted in previous studies (Chowdhury et al.) 2023 Zhang et al. (2224), splitting IMTS samples based on the number observations can result in subsamples that correspond different time lengths in reality. This can affect the learning of varying sampling density information in the original data. Therefore, we use a time period splitting approach to preserve the sampling information across all scale levels. The specific time periods chosen for each dataset are described in Appendix B.2
At scale level n, the IMTS backbone F² (-) uses its encoder F (-) to obtain latent representations E" of input subsamples S":
F
(S").
enc
The definition of the encoder vary across different IMTS backbones, with our implementation
details provided in Appendix
C For most existing IMTS models, latent representations fall into
three categories E [E E E ): temporal representations Ejjee PR"""x"" xD variable representations En e R xVx' and observation representations E P" xtxxXXXXX Here, D
denotes the hidden dimension.
During subsequent processing, E" is first transformed into G through irregularity-awar representa- tion fusion, and then reshaped into H to match the shape of E at the next scale. To compute G from E. we incorporate global representations from the upper scale when n > 1, as detailed in Section 4.2 For n 1, we simply set G E". Accordingly. G also consists of the three types obs ), each retaining the same shape as its corresponding counterpart in E". To further obtain H" from G we follow the implementation described in Appendix A Specifically, we split along the temporal dimension for temporal or observation representations, yielding H H obs and apply duplication for variable representations to obtain H The resulting output
GD E G
time G G
var
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H var- H at scale is then provided to scale its global representation. In the following section, we discuss how global-to-local representations are recursively fused across scales.
H E Hime
4.2 IRREGULARITY- REPRESENTATION FUSION
In this section, we introduce the irregularity aware recursive fusion of global-to-loce representations. At the lower scale level n 1, we want evaluate the importance of the global representation H from upper scale level n, while accounting for the inherent irregularity in the original IMTS.
Therefore, a lightweight scoring layer utilized to assign weights a to the global representation H Moreover, the binary mask M is also used to indicate irregularity.
H IMTS
H M
when H H H
time
obs
(4)
H
when H
H
ReLU (NTS),
(5)
where ReLU is the non-linear activation function and FF is feed-forward layer. It should be noted that the irregularity information for variable representations H has been encoded by the encoders of IMTS backbones, while padding values are still present in observation representations Hi and H Therefore, we use the mask M to distinguish between observations and padding values specifically in temporal and observation representations. The score then used to fuse the local representation En+1 and global one:
-+tt=Ent+ H
4.3 TRAINING OF REIMTS
In this section, we introduce the process for obtaining forecast values and training ReIMTS, At the lowest scale level N, the decoder of IMTS backbone Fae: takes the concatenated representation as input and predicts the forecast values Z:
Ż Face (Benncattt ())))
(7)
where the definition of decoder is the subsequent network modules after the encoder of IMTS backbone, and Concat denotes the concatenation of representations from the same sample. For a detailed explanation of the backbone decoder's 's structure, please refer to Appendix C The model is trained by minimizing the Mean Squared Error (MSH) loss between the predicted values Z for forecast queries and their corresponding ground truth Z:
Yo
1
L
Σ
3 2,)
should be noted that only forecast queries are used in loss calculations, which implemented by multiplying prediction Ž and binary masks Mę E (0,1)x LexV corresponding to the forecast horizon LQ-
4.4 DELINEATING FROM EXISTING METHODS
We discuss the differences and similarities between ReIMTS and existing approaches in this section, and depicted in Figure 3 Patch-based methods, such as tPatchGNN (Zhang et al. 2024) and PrimeNet (Chowdhury et al. 2023), can be viewed as variants of ReIMTS with only one scale level. Although they split samples based on time periods, tPatchGNN and PrimeNet are limited time period length during training. In contrast, ReIMTS can choose varying lengths at different scale levels, allowing for the exploration of richer multi-scale dependencies. Moreover, ReIMTS is plug-and-play method that seamlessly works with most encoder-decoder IMTS backbones. should be noted that tPatchGNN and PrimeNet learn global dependencies through mate- learning, while ReIMTS learns from its upper scale levels. Compared to multi-scale methods for regularly sampled time series such as Pathformer (Chen et al.],0024) MOIRAI (Woo al. 22024), and Scaleformer (Shabani al. 2023). the assumption of regular sampling and division by the number
single
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Preserve Sampling Pattern
Disrupt Sampling Pattern
(a) ReIMTS (Ours)
(b) Scaleformer (not designed for IMTS)...
Backbone
Backbone
4644
f b kg
Backbones
split
Backbone
0
Backbone
6
Backbone
Backbone
4
2g 6o
inter-patch
intra-patch
decode
smooth
combine
Specific Backbones
PrimeNet. tPatchGNN...
(d) Warpformer, Hi-Patch, HD-TTS...
Figure 3: Comparison of our method and existing approaches. (a) ReIMTS preserves the original sampling pattern while remaining compatible with most IMTS backbones. (b) Sample-space resam-
pling methods. (c) Patch-based methods for IMTS. (d) Representation space resampling methods.
Table I: Summary of five irregular time series datasets.
Description
MIMIC-III
MIMICIVV
PhysioNet" 12
Human Activity
USHCN
Max length
96
971
47
131
337
# Variable Sample
96
100
36
12
5
21,250
17,874
11,981
1,359
1,114
Avg # obs.
144.6
304.8
308.6
362.2
313.5
Avg # obs. (padding)
9,216.0
92,000.0
1,692.0
1,573.2
1,685.0
Furthermore, Pathformer and MOIRAI require slow transformer-bast layers, whereas ReIMTS can utilize lightweight IMTS backbones such GraFITi (Yalavarthi et al.] (2024) or mTAN (Shukla Marlin 2021a). la). Scaleformer uses resampling to obtain multi-scale inputs, which can disrupt the sampling pattern information, as discussed in Section
of observations makes them not well-suited, as described in Section 4.1
EXPERIMENTS
5.1 EXPERIMENTAL SETUP
5.1.1 DATASETS
Five widely studied irregular multivariate time series datasets, covering healthcare, biomechanics, and climate, are used in the experiments. Their statistics are summarized in Table [ MIMIC-III (Johnson) al. 2016) is clinical database collected from ICU patients during the initial 48 hours of admission, which is rounded for 30 minutes. MIMIC-IV (Johnson et al. 2023) is built upon MIMIC-III, which has higher sampling frequency and data are rounded for I minute. PhysioNet's 12 (Silva al.) 2012) is also clinical database collected during the first 48 hours of ICU stay, rounded for hour. Human Activity includes biomechanical data detailing 3D positional variables, which are rounded for 1 millisecond. USHCN (Menne et al. (2016) includes climate data spanning over 150 years, collected from meteorological stations distributed across the United States. Our analysis focuses on subset of 4 years between 1996 and 2000. For all five datasets, follow the preprocessing setup provided in the publicly available code pipeline PyOmniTS (Li et al.) 2025) v2.0.0, which originated from GraFITi and tPatchGNN (Yalavarthi et al. 2024 Zhang et al. 2024). It splits datasets into training, validation, and test sets adhering to ratios of 8:1:1. a common split setting used previous
works (Zhang et al. 2022
Luo al. 2025).

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Table Experimental results for our method (+ReIMTS) with respective baselines, evaluated by MSE (mean + std) x 10- on five irregular multivariate time series datasets. The best results are indicated in bold. Average improvements (error reductions) are marked with f.
Algorithm
MIMIC-I1I
MIMIC-IV
PhysioNet"l 12
Human Activity
USHCN
Ours
original
9.04 0.00
6,25 0.00
7,93
26.84 0.02
4.57 0.00
PrimeNet
+RIMMSS
4,76
0.19
3,58 = 0.03
3.01 + 0.03
0.82 + 0.02
1.71 0.06
762.3%
original
8.51 0.14
5.09 1 0.12
3,75 +: 0.02
0.89 +: 0.03
5.65 +: 0.67
mTAN
RRIMTS
6.37 0.05
4.04 + 0.10
3,51 0.02
0.89 0.01
1.70 = 0.01
124.3%
TimeCHEAT
original
4,41 +: 0.05
2.50 0.01
3.27 +: 0.11
0.68 0.04
1.73 0.04
+ReIMTS
4.40 1 0.03
2.02 0.03
2.90 +: 0.01
0.52 :: 0.01
1.62 1: 0.06
112.1 %
original
4.75 = 0.04
5.97 + 0.22
3.25 +: 0.00
1.76 + 0.23
2.42 + 0.17
GRU-D
ReIMTS
4.67 1 0.05
3.91 1 0.10
3.25 0.00
0.51 0.01
1.89
0.08
125.8%
Raindrop
original
5.13 0.02
3.41 0.05
3,27 0.01
0.89 0.02
2.04 0.07
ReIMTS
5,05 1 0.06
2.95
0.06
3.14 0.01
0.87 1 0.00
2.01
0.05
14.5%
GraFITi
original
4.08 = 0.02
2.39 + 0.01
2.85 + 0.01
0.43 + 0.00
1.71 = 0.05
ReIMTS
4.07 0.02
1.79 1 0.05
2.83 0.01
0.42 1 0.00
1.66 1 0.02
16.3%
5.1.2 BASELINES
We perform the comparisons also using code pipeline PyOmniTS (Li et al. 2025)
v2.0.0. Twenty-six
baselines included in the benchmark, covering SOTA methods categorized as (1) Multi-scale meth-
ods for IMTS: HD-TTS (Marisca et al.] 2024), Hi-Patch (Luo et al. 2025). Warpformer (Zhang et al.
2023a). (2) Other SOTA methods for IMTS: TimeCHEAT (Liu et al. [2025). GNeuralFlow (Mercatali
et al.ll| 2024), tPatchGNN (Zhang et al. 2024). GraFITi (Yalavatthi et al. 2024). PrimeNet (Chowd-
hury et al. (023). CRU (Schirmer et al.] Raindrop (Zhang et al.) 2022). NeuralFlows (Biloš
et al. (021). mTAA (Shukla & Marlin (021a). SeFT (Horn et al. (020). GRU-D (Che et al.
2018)
(3) Multi-scale methods for regularly sampled time series: ASH-Mr (Shang et al. 2024).
MOIRAI (Woo et al. 2024). TimeMixer (Wang et al.] 2024a). Pathformer (Chen et al.) 2024 Scale-
former (Shabani et al. 2023). (4) Other SOTA methods for regularly sampled time series: Leddam (Ya
et al. 2024), PStchTST (Nie et al. (023), TimesNet (Wu et al.] (2023), Crossformer (Zhang & Yan
2023), Autoformer (Wu et 2021]. We adapt their publicly available codes into the pipeline for
comparisons, where network structures remain unchanged.
5.1.3 IMPLEMENTATION DETAILS
We follow the setting of widely acknowledged Time-Series-Liie Library (Wang et al. 2024b) in learning rate adjustments. All experiments with maximum of 300 epochs and early stopping patience of 10 epochs. To mitigate randomness, we conduct each experiment with five different random seeds ranging from 2024 to 2028 also following Time-Series--ibrrge and standard deviation of the results. MSE is used as the training loss function for models, unless a custom loss function proposed in the original paper is used. When adapting regular time series models for IMTS, masks indicating observed values are included in the MSE calculations during training. The detailed settings for the hyperparameters are provided Appendix E Due to our more fine-grained hyperparameter searches for each experimental settings, baselines can perform better than those reported in previous works (Li et al. 20255 Yalavarthi et al.) (2024] /Zhang et al., 2024). All models are trained on Linux server with Py Torch version 2.7.0 and two NVIDIA GeForce RTX 3090 GPUs, while the efficiency analysis is conducted on another Linux server with Py PyTorch version 2.2.2+cu1 18 and one NVIDIA GeForce RTX 2080Ti GPU.
calculating both the mean
5.2 MAIN RESULTS
compares the ReIMTS version existing IMTS models with respective baselines, and Table shows the models' forecasting performance. Both are evaluated using MSE across five datasets, with the best results highlighted in bold. The visualization of forecasting results can be found in Appendix D The lookback time periods are 36 hours for MIMIC-III MIMIC-VI VI, and PhysioNet" 12, 3000 milliseconds for Human Activity, and 3 years for USHCN. Human Activity uses forecast length of 300 milliseconds, and the rest. datasets use the next 3 timestamps forecast targets, following
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Table Experimental results for other state-of-the-art regular and irregular baselines on five irregular multivariate time series datasets evaluated by MSE (mean + std) x x10 The best and second-best results are indicated in bold and underlined, respectively. 'ME' indicates memory error.
Algorithm
MIMIC-III
MIMIC-IV
PhysioNet'l 12
Human Activity
USHCN
MOIRAI
8.66 1 0.00
4.29 - 0.00
4.92 + 0.00
1.08 + 0.00
12.14 + 0.00
Ada-MSHyper
6.16 1 0.01
1.89:0.00
4.06 1.02
1,48 1 0.04
2 0.07
Autoformer
7.08 + 0.08
5.45
4.14 0.04
0.98 + 0.07
4.12 0.29
Scaleformer
5.50 + 0.07
4.13
4.02
1.11 0.05
5.18 0.96
Regular
TimesNet
5.78 + 0.01
3.82
4.08 108+0.01
1.21 +
+200
NHITS
5,83 1 0.01
3,95 0.01
3,84
0,98
3.09 1.19
Pyraformer
5.69 1 0.02
4.08 1 0.04
3,82 0.00
1
1.90 0.03
PStchTST
5.68 + 0.01
2.94 + 0.01
3,40
0.68 +
2.18 0.07
Leddam
5.93 + 0.00
3.70 + 0.02
3,75 0.03
0.91 0.91 0.01
2.38 + 0.10
Pathformer
+ +
ME
3,46 0.01
0.91
5.69 + 1.39
Crossformer
$.37:0000
3.00
3.39 0.05
1
1.87 + 0.05
TimeMixer
5.67 167:0.00 0.05
3.54
3.25 0.01
0.67
2.92 0.54
SeFT
9.23 0.01
+ 0.00
7.67 0.01
13.76
4.12 0.02
NeuralFlows
1
0.02
4.20 4.00
1.68
3.89 0.04
Irregular
CRU
7.07
4.35
6.01
1.04
2.35
GNeuralFlow
6.95
5.01
3.88 0.03
1.70
2.59
IPatchGNN
4.07
0.02
3,22 0.02
0.01
2.11
Hi-Patch
4.35
2.36 0.02
3.11
0,48
2.34 0.11
Warpformer
4.09 0.01
2.42 0.02
2.88 0.01
0.54
1.77 0.03
HD-TTS
4.17::0001
2.36 0.00
2.83
0.01
0.00
1.66 0.04
ReIMTS (Ours)
4.07 1: 0.02
1.79 1 0.05
2.83
0.01
0.42 1 0.00
1.66 + 0.02
the settings in existing works (Bilos et al. 2021 De Brouwer et al. 2019). Results evaluated using MAE are detailed in Appendix|B.2 and an analysis of varying forecast horizons can be found in Appendix B.4 As be seen, method ReIMTS boosts the performance of six existing IMTS models by an average of 27.1 %,, including well-known models and SOTA ones. When using GraFITi as the backbone, ReIMTS achieves the overall best performance compared all bascline models. Compared to existing multi-scale methods for IMTS such as Hi-Patch, Warpformer, and HD-TTS, ReIMTS demonstrates superior extensibility by integrating multi-scale techniques without requiring dedicated multi-scale module within the backbone. We also observe that older methods, such as mTAN and GRU-D, can also achieve performance improvements and even outperform more recent models. This demonstrates the potential of enhancing classic methods for IMTS forecasting with our approach. PrimeNet demonstrates significant performance improvements after applying ReIMTS, which may suggest that its pretraining wecraining-fiiettninn approach require more input samples achieve optimal performance, and we further discuss it in Appendix B.4] As for regularly sampled time series models, some of them surpass relatively old IMTS models, which shows the necessity of comprehensive comparisons.
Table Ablation results of ReIMTS and its four variants on five irregular multivariate time series datasets using GraFITi as the backbone.
Ablation
MIMIC-III
MIMIC-IV
PhysioNet'12
Human Activity
USHCN
ReIMTS
4.07 0.02
1.79 + 0.05
2.83 + 0.01
0.42 + 0.00
1.66 + 0.02
rp sample
4.99 + 0.05
1.92 + 0.04
2.83 + 0.01
0.45 0.01
1.69 + 0.03
rp split
5.02 0.04
2.36 0.03
3.20
0.61 0.02
2.31 0.09
pp IARF
4.20 + 0.02
1.84 0.02
2.79
0.47 0.01
1.89 - 0.05
w/o IARF
4.77 0.08
2.07 0.04
3.06 0.00
0.54
1.69 0.04
5.3 EFFICIENCY ANALYSIS
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We compare the efficiency of our method ReIMTS with existing multi-scale methods for IMTS. namely Warpformer (Zhang et al. 2023a), HD-TTS (Marisca et al. 2024), and Hi-Patch (Luo et al. 2025). GraFITi Yalavarthi et al. 2024) is used the backbone in ReIMTS, and we also perform a comparison with it. Models are assessed based on their MSF, training time, and GPU memory footprint. The training time for one epoch with batch size of 32 is recorded, then divided by the number of batches to determine the training time per iteration. Memory footprints only encompass the model's 's usage instead of representing the entire process. Results on the MIMIC-III dataset are shown in Figure E and results from the remaining datasets are plotted in Figure 6 and discussed in Appendix [B.] As can be seen, ReIMTS runs the fastest and uses the least GPU memory compared to existing multi-scale methods for IMTS, while achieving the lowest MSE. It demonstrates ReIMTS's flexibility using lightweight backbones and scalability performing the best. Compared with the original backbone GraFITi, ReIMTS controls the overhead of multi-scale learning within an acceptable range, without the GPU memory usage being proportional to the number of scale levels.
5.4 ABLATION STUDY
We evaluate the performance of ReIMTS and its four variants across all five datasets. (1) rp sam- ple replaces split subsamples with original sam- ple: (2) rp split splits subsamples based on the number of observations rather than time periods;
GPU Merorry
1.0GB
3.0GB
Hi-Patch 170m 2.2HGD
(3) rp IARF replaces irregularity-awer sentation fusion with addition; (4) w/o IARF re- moves pregularity-awart representation fusion; The ablation results are summarized in Table 4 As can be seen, all model designs are necessary. Results from rp sample and rp split show the necessity of splitting samples, particularly by time periods rather than the number of observa- tions. rp IARF and w/o IARF demonstrate the effectiveness of irregularity- tion fusion, and highlight the necessity of lever- aging both global and local representations.
repre-
MSE+10
HD- HD-TTS
70 23016
Shen 03000
GraFITi
Warpformer 255r A23c0
ReIMTS
40
representa-
29
Training Time (msiiter)
Figure 4: Model efficiency comparison on MIMIC- III, with a 36-hour lookback length, 3 forecast timestamps, 96 variables, and batch size of 32. ReIMTS uses GraFITi as backbone in the figure, which achieves the best efficiency compared to other multi-scal. IMTS methods, including Warp- former, HD-TTS, and Hi-Patch.
CONCLUSION
This paper introduces recursive multi-scale method, ReIMTS, to address the IMTS fore- casting problem. ReIMTS recursively divides original IMTS samples into subsamples with shorter time periods while maintaining the orig- inal sampling patterns. By recursively invoking the backbone learn representations at each scale level, ReIMTS retrieves global-to-local multi-scale representations based on the preserved sampling patterns. Moreover, ReIMTS lever- ages an irregularity-awar representation fusion mechanism to adaptively combine global and local representations based on content and sampling patterns, thereby preserving crucial semantics for accurate forecasting. ReIMTS exhibits strong flexibility and improves performance across various existing IMTS backbones, outperforming twenty-six baseline models in our unified code pipeline. Nevertheless, ReIMTS still has more potential in combining with wider range of backbones. Although structurally compatible with most encoder-decoder IMTS models, ODE-based models might need further theoretical explainability when used with our method. Additionally, some diffusion-baal -bsed models predict noisy latent representations in their backbones, which may not be directly compatible with our method. Possible solutions include predicting clean observations during the denoising process, or using ReIMTS within the denoising backbone. We will investigate these challenges further in future work.

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Published as a conference paper at ICLR 2026
ACKNOWLEDGEMENTS
We thank the anonymous reviewers for their helpful feedbacks, and all the donors of the original datasets. The work described in this paper funded by the National Key R&D Program of China (Grant No. 2023YFA101 1601), the National Natural Science Foundation of China (Grant Nos. 62272173, 62273109) the Natural Science Foundation of Guangdong Province (Grant Nos. 2024A1515010089, 2022A15150101701 and the Science and Technology Planning Project of Guangdong Province (Grant No. 2023A0505050106),
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Algorithm 1 ReIMTS:
Learning Recursive Multi-Scale Representations
Require: input IMTS S LR xv binary mask M E {0, 1)2 xV scale level n E (I,..., N), a series of time periods {T") In=1> forecast horizon LQ.
IMTS backbone decoder Faees and a series of encoders IMTS backbones {Fencl 1
Ensure: forecast result 2 E 1
function REIMTS(S" M n, N, (T") 1==1: Lq; (Fe 1 n= Faec, Ha-1)
Ex < Fene LQ)
Equation of the paper
H -- + null then
G Fuse E", H M
Equation
5). and 6 of the paper
else
G E
end
n
N then
Z - F (G", (G",L))
P Base case
return Z
else
S Split(S". Tn+1)
Eqqatiin of the paper
M f- Sp 7n
H" SplitOrDuplicate G")
Equation 99. 110. and
11 of the paper
REIMTS(S"*1 M
" 1, N, 17 J L2, { enc n==11 dec: H Recursive call
J
end if end function
procedure MAIN
Ž < REIMTS(S', M N, (TM) In=l Lq, (Fon NN
n= Faec, null)
return 2 end procedure
A RECURSIVE REPRESENTATION SPLITTING OR DUPLICATION
After E" is fused with the representation from scale level 12-11 to obtain G" as detailed in Section 4.2 for the temporal representation case G := {g]jee (tt))ttt))))) ) where G E Rg." xL" x ReIMTS splits them along the time dimension before passing these global representations scale level. should be noted that in this discussion, 'global' and 'local' are used to describe relative scales between upper and lower levels, rather than considering all N levels. The splitting process is similar to that for original IMTS samples, with split positions determined by time periods:
the lower +
2 time
{giime (t(+t) )
where H time E P x It should be noted that although representations from different levels share the same timestamps, the dependencies they learn differ. Global dependencies Hime learned from time periods of length T", while local ones E correspond shorter time periods of length 7n+11
time
The observation representation case G = (g (t) where G E xXXxX is similar the temporal representation case. We also split them using time periods:
H abs
{get (t)
pat1
(10)
where Hos x2==Ixx=*xxXxXx As for the variable representation case G {gth
(())
pa
where G R XVXD, duplicate the number of representations P scale level for p
pa+1
times, resulting in the same number of representations pa+1 scale level 1:
H
{g (t.
pm11 ]Ik=1
(11)
where H E R x
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B ADDITIONAL EXPERIMENTS
B.1 EFFECT OF SCALE LEVELS
Table 5: Effect of the number of scale levels on five datasets. A larger number of scale levels performs better on datasets with longer maximum lengths and sufficient number of samples.
Scale level
MIMIC-III
MIMIC-IV
PhysioNet' 12
Human Activity
USHCN
4.09 + 0.03
1.79 - 0.05
2.86 0.01
0.42 + 0.00
1.66 = 0.02
3
4.07 + 0.02
1.95 = 0.05
2.83 + 0.01
0.71 + 0.00
1.80 = 0.03
4.10 + 0.02
2.00 = 0.02
2.84 0.01
0.44 0.00
2.01 = 0.02
We assess how the number of scale levels impacts model performance, with results summarized in Table Time periods in different scale levels are 24h, 12h, and 6h for the healtheare datasets MIMIC-II. III MIMIC-IV, and PhysioNet 12, 2000ms, 1000ms, and 500ms for Human Activity, and 2 years, year, and 6 months for USHCN. These chosen time periods are based prior domain knowledge, including cycles in clinical medicine (Lakshman et al.] 2025 Holford 2019) [Morrll al., 2020) and periodic changes in climate (Almazroui et al. 2012). In general, most datasets achieve optimal performance at a scale level of 2, except for PhysioNer" 12 and MIMIC-III. Although the USHCN dataset has relatively long maximum length, it suffers from an insufficient number of samples for training a robust model, as reported in previous work (Yalavarthi et al. 2024).
B.2 EFFECT OF TIME PERIODS
The impact of varying time periods on model performance is demonstrated Figure for all datasets. We the number of scale levels to three on MIMIC-III and PhysioNet' 12, and following the result in Appendix B. We only change the time period at the second scale level. As can be seen, time periods corresponding optimal performance across all datasets are half the total time length when the number of scale levels is two. This is expected given that most IMTS datasets are sparse, exhibiting dependencies over long time periods, as discussed in Appendix B.I] Specifically, for the medical datasets MIMIC-III, MIMIC-IV, and PhysioNet" 12, 24-hour time length corresponds to the daily cycles of patients.
the rest,
B.3 DIFFERENT METRICS
We present the results measured using MAE in Table 6 which follows the same experimental setup as 3 As can be seen, ReIMTS still outperforms all twenty-six baselines across all five datasets. Additionally, it consistently enhances the performance of existing IMTS models under all settings, aligning with the findings from the MSE evaluations discussed in Section 5.2
B.4 VARYING FORECAST HORIZONS
We also evaluate performance across different forecast horizons. We follow the same settings as in existing work (Zhang et al.) 2024) and keep the lookback length settings the same as in Table For MIMIC-III, MIMIC-IV, and PhysioNet" 12, the forecast horizon is set to 12 hours. For Human Activity, the forecast horizon is 1000 milliseconds. For USHCN, the forecast horizon is set year. The results are summarized in Table It is evident that ReIMTS consistently enhances performance across longer forecast lengths. Regarding other baseline models, we have surprisingly noticed that a few models can outperform others in forecasting longer time horizons, as the empirical results have been thoroughly verified. For example, PrimeNet performs better on longer forecast lengths, suggesting that apart from requiring more input samples, its require more training targets in forecast horizons to achieve optimal performance. should be noted that, unlike fully observed MTS, IMTS samples typically split into lookback and forecast window based on time periods rather than the number of observations. The forecast settings here view 75% of the time period as the lookback window, while the remaining 25% as the forecast window.
approach may also
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2.00
MSE (1e-1)
MSE (1e-1)
1.90
4.10
4.05
1.80
4.00
12
24
48
96
1.70
6
12
24
Time Periods (hours)
Time Periods (hours)
(a) MIMIC-III
(b) MIMIC-IV
2.95
0.47
MSE (1e-1)
MSE (1e-1)
2.90
0.45
0.44
2.85
0.43
2.80
300600
1200
Time Periods (hours)
Time Periods (milliseconds)
(c) PhysioNet' 12
(d) Human Activity
MSE (1e-1)
1.5
1.0
2.0
4.0
Time Periods (years)
(c) USHCN
Figure 5: Effect of different time period lengths on PhysioNet' 12, Human Activity, and USHCN.
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Table 6: Experimental results on five irregular multivariate time series datasets, evaluated using MAE
(mean + std) x10-1 The experimental setup is the same in Table 'ME' indicates Memory
Error.
Algorithm
MIMIC-III
MIMIC-IV
PhysioNet') 12
Human Activity
USHCN
Vs Ours
MOIRAL
5.79 0.00
4.00 + 0.00 0.00
4.94 + 0.00
1.91 + 0.00
8.18 0.00
Ada oda-MSHyper
5,22 = 0.00
4.28
4 + 0.00
2.61 + 0.04
3,25 0.07
Autoformer
5,47 = 0.03
5.20
4.50
118:0.00
3.12
Scaleforner
4.93
4.04
0.02
2.25
3.37
Regular
TimesNet
5.03 0.01
4.01
0.01
2.26
1.04
NHITS
4.92 1 0.01
4.13
4.09
2.16 0.01
3.63
Pyraformer
5.08 - 0.00
4.53
4.28
2.28 0.00
3.01 0.01
PatchTST
4.04
3,25
3,90
1.70
3.07 0.06
Leddam
4.83
3.90
0.02
2.00
3.05
Pathformer
4.75 - 0.02
ME
0.01
0.02
Crossformer
4.74 0.00
3,59 - 0.01
0.01
3.95
2.50 0.17
TimeMixer
4.75 0.04
3.88 + 0.02
3.80 0.01
1.66 + 0.03
3
PrimeNet
6.59 = 0.00
5.73
6.79
13.27
4.79
SeFT
6.62 = 0.00
0.01
6.00
9.75
4.00
mTAA
6.19
5.05
0.00
2.18
5.18
NeuralFlows
5.49 0.01
4.79
0.00
3.09
3.39 0.04
Irregular
CRU
5.37 - 0.01
4.56
5.02
2.57
0.06
TimeCHHAT
4.12 - 0.03
+.07
0.00
1.70
+.70
GNeuralFlow
5.35 0.03
4.90
4.38
3.15
3.38 0.04
GRU-D
4.53
5.15
0.01
3.25
2.00
Raindrop
4.44 0.01
3,88
1.01
2.09
3.04 0.12
IPatchGNN
4.18 0.00
3.10
0.02
1.24
287
Hi-Patch
4.08 0.01
2.88
3.71
1.25
2.86
Warpformer
3.90
+.7+
3.54
1.30 0.01
2.74
HD-TTS
3.04
0.01
0.00
1.39 0.04
0.05
GraFITi
3.04
3.07
0.00
1.20 + 0.00
2.75
+mTAN
5.17 0.03
4.05
3,96 0.01
1.01
2.67 0.02
118.3%
ReIMTS
-GR--D
4.29 = 0.00
4.27
3.00
1.43
2.99
116.2%
+ Raindrop
4.40 - 0.02
3.64
0.01
1.97 0.01
3.04
13.5%
+ PrimeNet
4.34 0.00
4.04 0.01
3,64 0.02
2,02 0.00
2.71 0.03
147.6%
+TimeCHEAT
4.10
2,56 1.06
4.00
1.47
2.70 0.08
16.6%
+ +GraFITi
3.69 = 0.01
2.36
3.48 0.01
1.15 1.01 0.01
2.66 - 0.05
16.6%
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Table Experimental results of varying forecast horizons on five irregular multivariate time series datasets evaluated using MSE (mean + std) x x10-1, with the lookback length following Table and forecast horizons set to the rest length of the whole series, which are 12 hours for MIMIC-III MIMIC-IV, and PhysioNet" 12, 1000 milliseconds for Human Activity, and year for USHCN. 'ME' indicates memory error.
Algorithm
MIMIC-III
MIMIC-IV
PhysioNet's 12
Human Activity
USHCN
Vs Ours
MOIRAI
9.68 = 0.00
4.75 + 0.00
5.36 + 0.00
1.02 + 0.00
8.85 0.00
Ada- Hda-Mr
6.73 0.05
4.30
4.6:
1.60 0.01
4.30
Regular
Scaleformer
7.36 =
4.14
4.34
1.54 0.04
4.97 0.06
NHITS
7.43 0.02
5.16
4.60
1.10
4.52 4.09
Pyraformer
6.49 = 0.02
0.00
4.00
1
3,99 1.9 0.03
Patch'T'T
5.90 0.01
3.91
4.28 128+0000 0.04
Pathformer
6.08 = 0.10
ME
3.88
+
6.54
TimeMixer
5.43
3.71 + 0.05
3.76
0.69
5.50
PrimeNet
8.85
0.00
10,94 0.00
7.32 +
mTAA
9.35 0.32
4.12
0.02
1.1
5.63 0.49
TimeCHEAT
4.89 = 0.03
3,02
+.30
0.74
3.96 = 0.03
GNeuralHlow
7.43 - 0.07
+.00
4.39
1.89 + 0.08
4.86 + 0.09
Irregular
GRU-D
5,53 0.05
+.50
+.01
1,83 + 0.23
6.13
Raindrop
5.82
0.55
+.00
0.97
4.49
(PatchGNN
5.90 0.05
2.88
0.01
0.000.001
0.16
Hi-Patch
5.03 0.02
2.97
3.00
4.43 0.18
Warpformer
4.83 = 0.02
+.90
4.01
0.61 0.01
3,90 0.02
HID-TTS
5.62 0.07
2.84
3.78+0.00
0.60+0011
0.23
GraFTTi
4.45
+.72
0.01
0.00
4.25 0.04
+mTAN
6.54 0.02
3,49+0.1
3.94
0.96 0.01
3.76
120.6%
ReIMTS
-GRU-D
5.17 - 0.05
0.12
+
1.39
4.23
115.5%
Raindrop
5,52 = 0.05
3.00
3.04
0.97
0.16
18.4%
PrimeNet
5.17 = 0.03
3.67
0,84
4.29
153,8%
TimeHHAA
4.75 115=000 0.01
2.91
3.01
0.04
3,91 0.05
13.2%
+ GraPITi
4.40
2.50 1 0.01
3.53
0.55 0.00
4.14
14.4%
B.5 ADDITIONAL EFFICIENCY ANALYSIS
We provide additional efficiency comparisons datasets MIMIC-IV, 1 Human Activity, and USHCN, using the same settings as in Table Results are summarized in Figure ReIMTS uses GraFITi its backbones in these comparisons. As can be seen, on most datasets, our method ReIMTS uses significantly fewer GPU memory than other multi-scale IMTS methods, including Warpformer, HD-TTS, and Hi-Patch. The training speed is similar to other multi-scale methods, while ReIMTS can achieve better performance. ReIMTS also has comparable efficiency with the original model GraFITi.
C BACKBONE DETAILS
We introduce how existing IMTS models servce as backbones in ReIMTS, with modifications potentially including reductions hidden dimension size, layer count, or the removal of specific modules. Also, the structure of decoders and how backbones handle future timestamp queries and irregularities are also explained. We use the same strategy in the search of hyperparameters as compared baseline models, which aims to minimize the loss on validation sets. The number of layers searched within 1, 2, 3, and and the hidden dimension size is searched within 16, 32, 64, 128, 256, and 512. The number of scale levels used by ReIMTS are described in following paragraphs, which differs based on backbones. The time period lengths for all variants follow these settings: (1) MIMIC-III: 48 hours, 24 hours, 12 hours, and 6 hours: (2) MIMIC-IV: 48 hours, 24 hours, 12 hours, and hours; (3) PhysioNet' 12: 48 hours, 24 hours, 12 hours, and 6 hours; (4) Human Activity: 4000 milliseconds, 2000 milliseconds, 1000 milliseconds, and 500 milliseconds; (5) USHCN: 4 years, years, year, and 6 months. In the following descriptions, we use Ls and Lg to denote the maximum number of observations in univariate series in lookback and forecast window, respectively.
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GPU Memrory
315
1.DGB
4.0GB
Hi-Patch
2.10
Para
MSEx10"
MSEX10
Wargformer
GraFITI 100a LETIOS
Hi-Patch HD-TTS
Warpformer Stea SEYCO
GPU Memory
mankyy
GraFITI M6 PACE
ReIMTS
HD-TTS ReIMTS
1,0GB
2.00
Training Time (me/iter)
Training Time (maliter)
(a) MIMIC-IV
(b) PhysioNet" 12
0.55
Memory
Warpformer 68r00.0603
0,5GB
1,0GB
3,0BB
HD-TTS
30000
Hi-Patch otw E5000
MSE+101
MSEx10-1
Hi-Patch
Timn 1.10 GB
14
GraFITi
GraFITi
HD-TTS mw I.MAM
(4tens 14003
ReIMTS
RelMITS Zhe PENTA
0.4
102
Training Time (meilter)
Training Time (ms/lter)
(c) Human Activity
(d) USHCN
Figure 6: Efficiency comparisons on MIMIC-IV, PhysioNet') 12, Human Activity, and USHCN with batch size 32. ReIMTS demonstrates significantly lower GPU memory usage than other multi-scale methods Warpformer, HD-TTS, and Hi-Patch on most datasets, while maintaining similar training time. Compared the original backbone GraFITi, ReIMTS achieves comparable efficiency.
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ReIMTS+ uses mTAN (Shukla & Marlin 202 backbones. mTAN encodes input IMTS into temporal representations at a fixed set of reference points, described in Figure 2(b) of its paper. Therefore, it belongs to the case E" = Blime in Eq. g and we pass these temporal representations from top to bottom within the ReIMTS architecture to learn multi-scale temporal representations. For the decoder of m'TAN, it consists of a GRU, multi-head attention, and MLP sequentially. It maps temporal representations of shape Lg x D into time series LQ x V. Future timestamps are used as queries in the multi-head attention, and the number of variables corresponds the output dimension of the MLP. As for the hyperparameters, the hidden dimension size is set to 128, the number of reference points is 32, and the number of scale levels used by ReIMTS 2 on all five datasets. The learning rate is 1 x 10
ReIMTS GRU-D uses GRU-D (Che et al. 2018) as backbones. GRU-D encodes input IMTS into temporal representations for both lookback and future timestamps, as described in Eq. 16 of its paper. Therefore, it belongs to the case E Eimee in Eq. 9 and learns multi-scale temporal representations. For the decoder of GRU-D, it consists of an MLP MLPmaaps temporal representations of shape (Ing + [Q) D into time series (I.g + [Q) x V. Therefore, future timestamps are included in the temporal representations, and the number of variables corresponds to the output dimension of the linear layer. To handle irregularities. GRU-D replaces padding values with the last observed values before processing through a GRU unit. After generating the predicted series, it uses a mask to retain only the observed and predicted values. As for the hyperparameters, since the original paper of GRU-D set the hidden dimension size to 100, we additionally include this setting during hyperparameter searching. The hidden dimension size is set to 100, 64, 64, 64, and 32 on dataset MIMIC-II III MIMIC-IV, PhysioNet" 12, Human Activity, and USHCN, respectively. The number of scale levels used by ReIMTS is set to 2 on all datasets except MIMIC-III III, which adopts 3 levels instead. The learning rate is 1 x 10
Raindro uses Raindrop (Zhang et al. 2022) as backbones. Raindrop encodes input IMTS into observation representations, as described in Eq.2 of its paper. Therefore, it belongs to the case E = Ebe in Eq. during implementation and learns multi-scale observational representations. Other modifications include reducing the number of propagation layers from two to one and removing the final transformer encoder layer. For the decoder of Raindrop, it a linear layer that maps then rearranges variable representations of shape V D into time series with shape Le x V. The variable IDs are learned within these representations, and the forecast length is the output dimension of the linear layer. To handle irregularities, it employs the mask on learned representations to retain only the positions corresponding to actual input observations. As for the hyperparameters, the number of layers used by Raindrop backbone is set to 2 all five datasets. The hidden dimension size is set to 64, 1, 16, 64, and 16 on dataset MIMIC-II, MIMIC-IV, PhysioNet' 12, Human Activity, and USHCN, respectively. The number of scale levels used by ReIMTS is set to 2 on all five datasets. The learning rate is 1 x 10-3
uses PrimeNet (Chowdhury et al. 2023) as backbones. PrimeNet encodes input IMTS into temporal representations for both lookback and future timestamps, as described in Eq.2 in its paper. Therefore, it belongs to the case E E in Eq. p and learns multi-scale temporal representations. We disable the patch splitting operation in the original PrimeNet. For the decoder of PrimeNet, it is also an MLP maps temporal representations of shape (Ls LQ) x D into time series (Ls + LQ) x V. Future timestamps are included in the temporal representations, and the number of variables corresponds to the output dimension of the linear layer. To handle irregularities, it retains only the observed and predicted values after obtaining output series by applying the mask. As for the hyperparameters, the hidden dimension size is set to 256, 256, 256, 256, and 128 on dataset MIMIC-III, MIMIC-IV, PhysioNet' 12, Human Activity and USHCN, respectively. The number of scale levels used by ReIMTS is set to 2 on all five datasets. The learning rate is 1 10-4.
ReIMTS++PimeNe
ReIMTS TiMACHEAT uses TimeCHEAT (Luu et al. 2025) as backbones. TimeCHEAT is based on GraFITi (Yalavarthi et al. 2024 and simultaneously learns temporal, variable, and observation representations, as described from Eq.3 to Eq.10 10 of its paper. We found that sharing variable embeddings across different scale levels is sufficient during experiments. Therefore, it belongs to the case E" = E in Eq. [ during implementation and learns multi-scale variable representations. The patch splitting operation orginal TimeCHEAT is disabled, and the final transformer encoding
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is discarded. Other settings remain the same. For the decoder of TimeCHEAT, it is linear layer that decodes and squeezes representations of shape (Ls + LQ) x V x (3D) into time series obtained by concatenating temporal, variable, and observational representations along the hidden dimension, each repeated and expanded to shape (I.g f.q) V x D. Therefore, future timestamps are included in the temporal representations, while variable IDs are included in the variable ones. To handle irregularities, uses a bipartite graph approach like GraFITi, which removes all padding values and transform inputs into bipartite graphs. As for the hyperparameters, the number of layers is set to 2, 2, 4, 4, and on dataset MIMIC-III, MIMIC-IV, PhysioNet' 12, Human Activity and USHCN, respectively. The hidden dimension size is set to 128, 64, 32, 64, and 64 on dataset MIMIC-III, MIMIC-IV, PhysioNet' 12, Human Activity, and USHCN, respectively. The number of scale levels used by ReIMTS set to on five datasets. The learning rate is 1 x 10-3
(Ls + LQ) x V. These representations
GeIMTS+GraFTIE uses GraFITi (Yalavarthi et al. 2024) as backbones. GraFITi simultaneously learns temporal, variable, and observation representations, as described from Eq. to Eq. 13 of its paper. During our implementation, we only transfer variable representations across different scale levels. Therefore, it belongs to the case E" E, in Eq. II during implementation and learns multi-scale variable representations. For the decoder of GraFITi, please refer to the descriptions of TimeCHEAT's decoder above. To handle irregularities, uses bipartite graph approach that removes all padding values and transform inputs into bipartite graphs. As for the hyperparameterss the number of layers is set to 4, 1, 1, 2, and I on dataset MIMIC-III, MIMIC-IV, PhysioNet" 12, Human Activity, and USHCN, respectively. The hidden dimension size set to 128, 32, 256, 128, and 32 on dataset MIMIC-III, MIMIC-IV, PhysioNet' 12, Human Activity, and USHCN, respectively. The number of scale levels used by ReIMTS is set 2 on all datasets except PhysioNet' 12 and MIMIC-III, which adopt 3 levels instead. The learning rate is 1 x 10-3
D VISUALIZATION
D.I FORECASTING RESULTS
Takts
grar Owr
-02
-06
(a) MIMIC-III
(b) MIMIC-IV
gouedrc
gLactcch
22 oum
(c) PhysioNet
(d) Human Activity
(c) USHCN
Figure 7: Visualization of forecast results all five datasets, under the same settings as in Table 2 Compared to original backbone GraFITi (in green), ReIMTS (in orange) is closer to the ground truth (in blue).
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We visualize the forecasting results of our proposed ReIMTS when using GraFITi its backbone, and also ones from the original GraFITi model. as depicted in Figure 7 The forecast settings are exactly the same in Table 2 which means the lookback window length is set to 36 hours for MIMIC-III MIMIC-IV, and PhysioNet' 12, 3000 milliseconds for Human Activity, and 3 years for USHCN. The goal is to predict next 300ms for Human Activity, and 3 timestamps for other datasets. As can be seen, ReIMTS is closer to the ground truth value.
D.2 MULTI-SCALE REPRESENTATIONS
(a) w/o ReIMTS
(b) ReIMTS
Figure 8: The t-SNE visualization of multi-scale representations in ReIMTS+GRU-D classification dataset PAM. Red boxs indicate the region of interest, which mainly contain samples from class 2. (a) Without ReIMTS, samples from class 2 very close ones from class 5 and 7. (b) After applying ReIMTS, samples from class 2 are more distant from others, leading to improved performance. It should be noted that class and class have similar colors, where samples from class are mostly outside of the region of interest.
Since it's hard visualize the relationships between learned representations and forecasting accuracy, we train ReIMTS+GRU-D on classification task instead for visualization, as depicted in Figure B where colored points represent test set samples. GraFITi not originally designed for classification task, so we choose the classic and widely acknowledged GRU-D as backbones for ReIMTS. Widely studied dataset PAM (Reiss & Stricker 2012) used, which contains 8 class labels. We follow the preprocessing scripts of Raindrop (Zhang et al. (002) and split the train/val/test sets adhere to ratio 8:1:1. Other training protocols are the same as forecasting training in Table 3 As can be seen in Figure 8 (a), when learning without ReIMTS, samples from class 2 are very close ones from class and The test set performance is 84. 14% in precision, 78.04% in recall, and 75.03% FI. After applying ReIMTS in Figure 8 (b), samples from class are more distant from others multi-scale representations. The test set performance is improved to 86.74% precision, 84.04% in recall, and 82.44% in F1.
E BASELINE DETAILS
We briefly introduce each baseline model along with their key hyperparameter settings here. The search of hyperparameters aims to minimize the loss on validation sets. The number of layers is searched within 1, 2, 3, and 4, the hidden dimension size is searched within 16, 32, 64, 128, 256, and 512. Unless otherwise specified, we use a batch size of 16 for USHCN, and 32 for others. However, if the model cannot be trained using 24 GB of GPU memory, we recursively halve the batch size until training is possible. Number of epochs, early stopping patience, random seeds, and learning rates have been described in Section 5.1.3 We aim to use the same hyperparameters for learning rate and special loss functions, as specified in their original papers and codes, whenever available. For all classification models, replace the final softmax layer with linear layer enable forecasting.
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E.1 METHODS FOR MTS
Woo et al. 2024) is a pretraining model for time series forecasting. We use the small version of the provided pretrained configurations and weights, comprising 6 layers with hidden dimension 384. We finetune the model on IMTS datasets with learning rate of x 10-1
MOIRAI
Ada-MSHyper (Shang et al. 2024) uses hypergraphs for temporal multi scall learning in MTS forecasting. The window size for multiscale is 4. The learning rate is 1 x 10-3, We also use its node and hyperedge constrainted loss function for training. The number layers is set to 1, 1, 2, 1, and 1 on dataset MIMIC-III, MIMIC-IV, PhysioNet') 12, Human Activity, and USHCN, respectively. The hidden dimension size is set to 32, 256, 256, 512, and 64 on dataset MIMIC-III, MIMIC-IV, PhysioNet' 12, Human Activity, and USHCN, respectively.
Autoformer (Wu et al., 2021) is a transformer variant with auto-correlation decomposition for MTS forecasting. The attention factor is 3. The learning rate is x 10-3 The number of layers is set to 2, 1. 1, and I on dataset MIMIC-III, MIMIC-IV, PhysioNet' 12, Human Activity, and USHCN, respectively. The hidden dimension size is set 32, 32, 64, 512, and 128 on dataset MIMIC-III MIMIC-IV, PhysioNet' 12, Human Activity, and USHCN, respectively.
Scaleformer (Shabani et al., 2023) is a coarse-to-fine multi-scale framework for transformer models in MTS forecasting. We adopt its best-performing backbone evaluated in original paper, Autoformer, in our benchmark. The scale factor is 2. The attention factor is 3. The number of encoder layers is 4 dataset USHCN, and 2 on the rest. The number of decoder layers is 1. The hidden dimension size set to 1 128, 256, 64, 256, and 16 on dataset MIMIC-III MIMIC-IV, PhysioNet 12, Human Activity, and USHCN, respectively. The learning rate 1 x 10-3
TimesNet (Wu et al.
2023 uses 2-D variantion modeling for MTS analysis. The attention factor 3. The dimension for FCN is 32. The learning rate x 10-3, The number of encoder layers is set to 2. The hidden dimension size is set to 256, 128, 128, 32, and 128 on dataset MIMIC-III, MIMIC-IV, PhysioNet' 12, Human Activity, and USHCN, respectively.
NHITS (Challu et al. 2023) is multi-scale model with hierarchical interpolation technique for MTS forecasting. The learning rate is x 10-3, 3, The hidden dimension size is set to 64, 32, 32, 512, and 128 on dataset MIMIC-III, MIMIC-IV, PhysioNet' 12, Human Activity, and USHCN, respectively.
PatchTST Nie al. 2023 leverages patching in transformer for MTS forecasting. The patch lengths are 12, 90, 6, 300 and 10 for MIMIC-III, MIMIC-IV, PhysioNet' 12, Human Activity, and USHCN, respectively. The number of encoder layers is on USHCN, and on the rest. The attention factor is 3. The number of heads in attention is 8 on USHCN, and 16 on the rest. The learning rate x 10-4, The hidden dimension size set to 128, 128, 256, 512, and 32 on dataset MIMIC-III, MIMIC-IV, PhysioNet" 12, Human Activity, and USHCN, respectively.
Leddam Yu et al. 2024) uses learnable ceasonal-trent decomposition for MTS forecasting. The learning rate is 1 x 10 3 The number of layers is set to 2, 4. 2, 1, and 4 on dataset MIMIC-III, MIMIC-IV, PhysioNet' 12, Human Activity and USHCN, respectively. The hidden dimension size is set to 32, 32, 128, 512, and 64 on dataset MIMIC-III, MIMIC-IV, PhysioNet' 12, Human Activity, and USHCN, respectively.
Pathformer Chen et al. 2024) is multi-scale transformer with multi patch size aggregation. Since Pathformer does not support splitting irregular time series into patches of different lengths, the number of layers is fixed as The hidden dimension size is set to 32, 16, 32, 16, and 16 on dataset MIMIC-III, MIMIC-IV, PhysioNet') 12, Human Activity, and USHCN, respectively. The patch lengths are 24, 720, 12, 1000, and 50 for MIMIC-III, MIMIC-IV, PhysioNet' 12, Human Activity, and USHCN, respectively. The learning rate is 1 x 1
Crossformer Zhang& & Yan 2023) learns cross- diosessimmssional dependencies for MTS forecasting. The segment lengths are 12, 360, 6, 300, and 12 for MIMIC-III, MIMIC-IV, PhysioNet' 12, Human
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Activity, and USHCN respectively. The learning rate is x 10 The number of encoder layers is set to 8 on USHCN, and on the rest. The hidden dimension size is set to 32, 32, 128, 512, and 64 on dataset MIMIC-III, MIMIC-IV, PhysioNet' 12, Human Activity, and USHCN, respectively.
TimeMixer Wang al. 2024a) uses seasonal-trent decomposition each sampling scale level. The down sampling windows are 24, 720, 12, 300, and 50 for MIMIC-III, MIMIC-IV, PhysioNet" 12, Human Activity, and USHCN, respectively. The number of encoder layer 8 on USHCN, and on the rest. The dimension for ferd-forward layer is 16 on USHCN, and 32 on the rest. The learning rate 1 x 10-2. The number of downsampling layers is set to 1. The hidden dimension size is set to 32, 32, 64, 16, and 256 dataset MIMIC-III, MIMIC-IV, PhysioNet' 12, Human Activity, and USHCN, respectively.
E.2 METHODS FOR IMTS
PrimeNet (Chowdhury al. 2023 is an IMTS pretraining model. Since the provided weights are specific to datasets with 41 variables, we retrain the model on all datasets. The patch lengths are 12, 180, 6, 300, and for MIMIC-III, MIMIC-IV, PhysioNet" 12, Human Activity, and USHCN respectively. The number of heads in attention is 1. The learning rate is 1 x 10 The hidden dimension size is set to 32, 32, 128, 128, and 64 on dataset MIMIC-II, MIMIC-IV, PhysioNet" 12, Human Activity, and USHCN, respectively.
SeFT (Horn et al. 2020 is a set-based method for IMTS classification. The dropout rate is 0.1. The learning rate is 1 X 10 10-3. 3, The number of layers is set to 2, 2, 4, 4, and 4 on dataset MIMIC-III, MIMIC-IV, PhysioNet's 12, Human Activity, and USHCN, respectively. The hidden dimension size set to 256, 64, 32, 128, and 16 on dataset MIMIC-III, MIMIC-IV, PhysioNet' 12, Human Activity, and USHCN, respectively.
mTAN Shhukla & Marlin 202 converts IMTS to reference points for IMTS classification. The number of reference points 32 on MIMIC-III, 128 on USHCN, and 8 on the rest datasets. The hidden dimension size is set to 32, 64, 64, 64, and 256 on dataset MIMIC-III, MIMIC-IV, PhysioNet' 12, Human Activity, and USHCN, respectively. The learning rate is x 10-3
NeuralFlows BBilss et al. 2021 is an efficient alternative to Neural ODE in IMTS analysis. The number of flow layers The latent dimension is 20. The hidden dimension for time 8. The number of hidden layers is 3. The learning rate is x 10 10-3
CRU (Schirmer et al. 2022) uses continuous recurrent units for IMTS analysis. The hidden dimension is 20. The learning rate is 1 x 10-3
TimeCHEAT LLuu et al. 2025) uses channel-dependent within patches and
among patches. The patch lengths are 12, 360, 6, 1000, and 50 for MIMIC-II, III, MIMIC-IV Phys- ioNet' 12, Human Activity, and USHCN respectively. The number of attention heads is 8 on USHCN, and 4 on the rest. The learning rate is 1 x 10-3, The number of layers is set to 1, 1, 1, 2, and on dataset MIMIC-II, MIMIC-IV, PhysioNet' 12, Human Activity, and USHCN, respectively. The hid- den dimension size is set to 32, 32. 32, 64, and 128 on dataset MIMIC-III, MIMIC-IV, PhysioNet") 12, Human Activity, and USHCN, respectively.
GNeuralFlow Mercatali et al. 2024 enhances NeuralFlows with graph neural networks for IMTS analysis. The flow model uses ResNet. The number of flow layers is 2. The latent dimension for input is 20. The latent dimension for time is 8. The number of hidden layers is 3. The learning rate is 1 x 10-3
Che et al. 2018) adapts GRUs for IMTS classification. The learning rate is x 10 - Since the original paper of GRU-D set the hidden dimension size to 100, we additionally include this setting during hyperparameter searching. The hidden dimension size is set to 100, 32, 100, 100, and 128 dataset MIMIC-III, MIMIC-IV, PhysioNet"s 12, Human Activity, and USHCN, respectively.
GRU-D
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Raindrop Zhang al. 2022) models time- ainevaayyigg variable dependencies for IMTS classification. The learning rate is 1 x 10 The number of layers set to 1, 1, 1, and 2 on dataset MIMIC-III, MIMIC-IV, PhysioNet' 12, Human Activity, and USHCN, respectively. The hidden dimension size is set to 32.
1PatchGGNN Zhang al., 2024) processes IMTS into patches and use graph neural networks for IMTS forecasting. The patch lengths are 12, 360, 6, 300, and 10 for MIMIC-III, MIMIC-IV, PhysioNet' 12, Human Activity, and USHCN, respectively. The number of heads in attention 4 on USHCN, and I the rest. The learning rate is 10-3. The number of layers is set to 4, 2, 4, 4, and on dataset MIMIC-III, MIMIC-IV, PhysioNet's 12, Human Activity, and USHCN, respectively. The hidden dimension size is set to 64, 32, 64, 64, and 32 dataset MIMIC-III MIMIC-IV, PhysioNet' 12, Human Activity, and USHCN, respectively.
Hi-Patch (uoo al. 2025) implements hierarchical graph fusion inside backbone. The patch lengths are 12, 90, 6, 500, and for MIMIC-III, MIMIC-IV, PhysioNet' 12, Human Activity, and USHCN, respectively. The number of attention heads is USHCN and on the rest. The learning rate is 1 x 10-3. The number of layers is set to 4, 1, 4, 4, and 4 on dataset MIMIC-III, MIMIC-IV, PhysioNet' 12, Human Activity, and USHCN, respectively. The hidden dimension size is set to 32, 64, 32, 128, and 32 on dataset MIMIC-III, MIMIC-IV, PhysioNet' 12, Human Activity, and USHCN, respectively.
Warpformer Zhang al. 2023a uses warping for multiscale modeling in IMTS classification. The number of heads is 1. The dropout rate is 0. The learning rate x 10-3 The number of layers is set 4, 1, 1, 3, and dataset MIMIC-III, MIMIC-IV, PhysioNet' 12, Human Activity, and USHCN, respectively, The hidden dimension size is set to 64.
HD-TTS (Marisca et al.) 2024) implements both variable and temporal multi-scale inside backbone. The number of mn layers is 4. The number of pooling layers is 1. The learning rate is 1 x 10-3 The hidden dimension size is 64.
GraFITi Yallvvrthi al. 2024 uses bipartite graphs for IMTS forecasting. The number of heads in attention is 4. The learning rate is 1 x 10 The number of layers is set to 3, 1, 2, 4, and on dataset MIMIC-III MIMIC-IV, PhysioNet' 12, Human Activity and USHCN, respectively. The hidden dimension size is set to 256, 32, 32, 32, and 128 on dataset MIMIC-III, MIMIC-IV, PhysioNet' 12, Human Activity, and USHCN, respectively.
F THE USE OF LARGE LANGUAGE MODELS
We Large Language Models (LLMs) polish writing only. Specifically, we write all contents ourselves, then use LLMs to check for any possible grammar mistakes or incorrect usage of words. We have not used LLMs for any other purpose.
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Reviews:
[{"review_id": "AZYGg00nHb", "reviewer": "Reviewer_MQ28", "summary": "The authors describe a new method to learn multi-scale representations for irregular time series data.", "questions": "What are the limitations of your method, and for which dataset characteristics does it perform well, and for which not?", "limitations": "", "rating": 6, "confidence": 4, "soundness": 2, "presentation": 3, "contribution": 3, "strengths": "- original idea to learn multi-scale representations\n- well written paper\n- good results", "weaknesses": "- state-of-the-art comparison should be extended, especially in extending the discussions on strengths and weaknesses of previous work, clearly specifying the contributions and possible limitations of the new method proposed", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "2PrKoFBpUt", "reviewer": "Reviewer_XY3z", "summary": "This paper proposes ReIMTS, a recursive multi-scale modeling framework for Irregular Multivariate Time Series (IMTS) forecasting. Unlike prior approaches that rely on resampling to generate coarse-grained sequences, ReIMTS preserves the original timestamps and recursively splits each sample into subsamples with progressively shorter time spans. An irregularity-aware fusion mechanism is introduced to integrate information across scales, enabling the model to capture both global and local temporal dependencies without destroying sampling patterns.", "questions": "1. Does the recursive decomposition introduce cumulative error across scales, and if so, how is this controlled or regularized?\n\n2. How does ReIMTS handle dependencies among different variables in IMTS?\n\n3. Could the authors clarify the specific motivation for adopting recursion instead of parallel or hierarchical multi-scale fusion?\n\n4. Since the recursive splitting resembles patch-based segmentation, what distinguishes ReIMTS from existing hierarchical or patch-based multi-scale models?", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. The paper is clearly written and logically structured, providing background on multi-scale modeling for irregular time series.\n\n2. The proposed irregularity-aware fusion is intuitive and aligns well with the challenges of IMTS.\n\n3. Experimental evaluation is comprehensive, covering multiple datasets and models, and demonstrates strong empirical results.", "weaknesses": "1. The novelty of the approach is somewhat limited in that the recursive multi-scale design can be viewed as a restructured version of existing patch-based or hierarchical multi-scale strategies.\n\n2. The motivation for using a recursive structure, as opposed to other multi-scale fusion designs, is not clearly justified.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "4yKAJf9fbr", "reviewer": "Reviewer_rfED", "summary": "This paper proposes ReIMTS, a recursive multi-scale modeling approach for irregular multivariate time series (IMTS) forecasting, which splits samples recursively and employs irregularity-aware representation fusion mechanism", "questions": "I am happy to raise my rating of the paper if the author can address my concerns about **1) notations/equations** and **2) fairness**.", "limitations": "", "rating": 4, "confidence": 3, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "1. The motivation is clear, and the method is novel.\n2. Experimental evaluation is comprehensive.\n3. The method is easily adaptable to different models.", "weaknesses": "1. The notation and equations are not professional and can be largely improved. This paper uses a lot of double subscripts/superscript, and very long subscripts/superscripts, especially in Sec 4.1, from Eq. 2 to Eq. 6. I suggest the author reduce the length of Sec 4.1, and move some interesting experimental results or useful method comparison (Fig. 6) from the supplementary to the main paper.\n2. Potential comparison fairness issues:\n - Backbone models are modified when integrated into ReIMTS (layers reduced, dimensions changed - Appendix B), unclear if these modifications could account for some improvements\n - Is there a difference in hyperparameter settings used for ReIMTS variants vs. baselines?\n3. (minor) This paper could benefit from more discussion on the results. Table 2 shows that the performance improvement achieved by using different backbones is quite different, 62.3% vs. 9.9%. This is somewhat unusual and could benefit from an in-depth analysis.\n4. (minor) Increased memory usage. Figure 3 shows that the available memory has increased by more than 50%(0.390 vs 0.598).", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "rJimstoUVH", "reviewer": "Reviewer_4Jcx", "summary": "The paper addresses the valuable problem of learning multi-scale information from irregular time series. ReIMTS, a multi-scale method based on recursive splitting followed by concatenation, is proposed. Forecasting experiments demonstrate its competitive performance across settings. While the idea is overall well-motivated and novel, more explanatory experiments could further strengthen the claims.", "questions": "1.As mentioned in Weakness 2, is it really necessary to distinguish between $ L^n $ and $ T^n $, two symbols that differ only in the presence of time units? For example, in line 203, why is $ e^1_{\\text{time},0:T^1} $ using the symbol with time units, when it actually belongs to $ R^{L^1 \\times d_{\\text{model}}} $, which uses the symbol without time units?\n\n2.As mentioned in weakness 3, how is the efficiency of ReIMTS when applied to other backbones, like PrimeNet[1] and mTAN[2]?\n\n3.In Section 4.2, the paper introduces a representation fusion method that employs a scoring linear layer to assign weights to global representations. Could the authors provide further insights into this design to clarify how different representations are combined? Specifically, does ReIMTS tend to prioritize the use of local representations or global ones?\n\n4.Representations learned in the classification task are plotted in Figure 8. However, benchmark comparisons have not included metrics from classification. How does ReIMTS perform under other downstream tasks, such as classification?\n\n\n5.The paper's experimental settings follow those from HyperIMTS[3], while the HyperIMTS model is not included in the benchmark comparisons. Why is it not included? Can ReIMTS work with HyperIMTS?\n\n[1] R. R. Chowdhury, J. Li, X. Zhang, D. Hong, R. K. Gupta, and J. Shang; “PrimeNet: Pre-training for Irregular Multivariate Time Series”; AAAI 2023.\n\n[2] S. N. Shukla and B. Marlin; “Multi-Time Attention Networks for Irregularly Sampled Time Series”; ICLR 2021.\n\n[3] B. Li, Y. Luo, Z. Liu, J. Zheng, J. Lv, and Q. Ma; “HyperIMTS: Hypergraph Neural Network for Irregular Multivariate Time Series Forecasting”; ICML 2025.", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1.The paper is well-motivated, and the proposed ReIMTS is an interesting and easily understandable solution to the problem.\n\n2.Benchmark experiments are extensive for the IMTS forecasting task, and the corresponding codes are available.", "weaknesses": "1.Although Figure 1 illustrates a sampling pattern present in the dataset, the term \"sampling pattern\" is rarely used in existing works. More careful explanations of this concept are needed.\n\n2.At line 187, the paper states that $L^n$ and $T^n$ are distinct, with the difference lying in the presence of time units. The notation causes some confusion during reading, raising questions about whether it is necessary to distinguish them using different symbols.\n\n3.Although ReIMTS+GraFITi appears to have good efficiency compared to other multi-scale methods, its training time (66ms) is double that of GraFITi (33ms). This raises doubts about the efficiency of ReIMTS when applied to other backbones.\n\n\n4.The paper is entitled “Learning... Representations...”, which implies that ReIMTS functions as a representation learning booster. While the benchmark experiments on the forecasting task are extensive, additional experiments on the classification task could make the claim more persuasive.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)