T1: One-to-One Channel-Head Binding for Multivariate Time-Series Imputation
Authors: Dongik Park
Hyunwoo Ryu
Suahn Bae
Keondo Park
Hyung-Sin Kim
Venue: ICLR 2026 Poster (2026)
Keywords: Time Series
Imputation
Primary area: learning on time series and dynamical systems
TL;DR: T1 is a CNN-Transformer hybrid that binds channels to attention heads for robust time series imputation, achieving 46% better performance than existing methods, especially under extreme missingness.

Abstract: Imputing missing values in multivariate time series remains challenging, especially under diverse missing patterns and heavy missingness. Existing methods suffer from suboptimal performance as corrupted temporal features hinder effective cross-variable information transfer, amplifying reconstruction errors. Robust imputation requires both extracting temporal patterns from sparse observations within each variable and selectively transferring information across variables—yet current approaches excel at one while compromising the other. We introduce T1 (Time series imputation with 1-to-1 channel-head binding), a CNN-Transformer hybrid architecture that achieves robust imputation through Channel-Head Binding—a mechanism creating one-to-one correspondence between CNN channels and attention heads. This design enables selective information transfer: when missingness corrupts certain temporal patterns, their corresponding attention pathways adaptively down-weight based on remaining observable patterns while preserving reliable cross-variable connections through unaffected channels. Experiments on 11 benchmark datasets demonstrate that T1 achieves state-of-the-art performance, reducing MSE by 46% on average compared to the second-best baseline, with particularly strong gains under extreme sparsity (70% missing ratio). The model generalizes to unseen missing patterns without retraining and uses a consistent hyperparameter configuration across all datasets. The code is available at https://github.com/Oppenheimerdinger/T1.

T1: ONE-TO-ONE CHANNEL-HEAD BINDING FOR MULTIVARIATE TIME-SERIES IMPUTATION
Dongik Park, Hyunwoo Ryu, Suahn Bae, Keondo Park, and Hyung-Sin Kimj Graduate School of Data Science, Seoul National University (breadsora, yahhallong, snubbb, gundo01 02, hyungkim) (angkimmmesm..... ac kr
ABSTRACT
Imputing missing values in multivariate time series remains challenging, espe- cially under diverse missing patterns and heavy missingness. Existing methods suffer from suboptimal performance as corrupted temporal features hinder effee- tive cross-variable information transfer, amplifying reconstruction errors. Ro- bust imputation requires both extracting temporal patterns from sparse observa- tions within each variable and selectively transferring information across vari- ables-yet current approaches excel at one while compromising the other. We introduce T1 (Time series imputation with 1-to-1 channel- -hand binding), CNN- Transformer hybrid architecture that achieves robust imputation through Channel- Head Binding-2 mechanism creating one-to-one correspondence between CNN channels and attention heads. This design enables selective information trans- fer: attention pathways adapt based on observable patterns, down- weightint cor- rupted channels while maintaining reliable cross-variable connections. Experi- ments on 11 benchmark datasstss demonstrate that Tl achieves state-of-the-ar per- formance, reducing MSE by 46% average compared to the second-best base- line, with particularly strong gains under extreme sparsity (70% missing ratio). The model generalizes to unseen missing patterns without retraining and a consistent hyperparameter configuration across all datasets. The code is available at htttts: http::/:////gttttbb....ooo//// Ottp//pppeeeeeeeee me rd m ngge/Ti
INTRODUCTION
Multivariate time-series data underpin decision making in healthcare (Ghassemi et al. 2015 Lee
& Hauskrecht] 2021 Lee et al. 2025). finance (Niu et al.] 2020), climate (Nketiah et al., 2023]
Chen & Dong 2025 and industrial monitoring (Sharma al. 2022). Yet measurements
tinely incomplete: sensors fail, transmissions drop, sampling is irregular, and entire windows go missing (Little & Rubin 2019 Silva al. 2012) Yi et al. 2016). Before any downstream task- forecasting, anomaly detection, classification can succeed, we must impute these gaps with high fidelity. Formally, given X E MxT (M variables with sequence length T) and an observation mask 52 C [M] [T], the goal is to impute X on I2" using only the observed entries X This is challenging because imputation must simultaneously (I) reconstruct temporal structure from sparse, evegularll-samplee observations within each variable and (2) transfer complementary information across variables without importing noise. When temporal features are corrupted by missingness, cross-variable information transfer amplifies errors; when this transfer is naive, it ignores which variables are informative under the current mask.
Current methods for time-series imputation leave gap for robust, efficient processing under heavy missingness. As illustrated in (i)-(iv) of Figure Tal, existing approaches make architectural compro- mises that limit their effectiveness. (i) Time-axt -xis tokenization approaches (Wu et al. (02T] suffer from fundamental limitations: Vanilla Transformers (Vaswani et al.) (017) mix all variables at each timestep token where missing values directly corrupt the representation, allowing corrupted features to contaminate all computations. While methods using diagonally-maste maskedd attention (Du et al. 2023) improve temporal modeling, they inherit the same tokenization mobsem-mmssing values degrade token representations that propagate through attention layers. (ii) Variable-axis tokenization (Liu
Corresponding author.

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Attention
DW Core
Corv
Vertable
PW Comy
Allenion
PW Cony
Time
Channel
Linear
Allention
(i) Time tokenisation
Variable axis tokenization
Dual-xxis Tokeniztionn
Temporal CNN
T1 (Ours)
(a) Comparison between T1 and previous approaches
Value
Oh
head
Ver
Temporal
chc 7
Time
CHead Attention
Convolution
Fibarc
ch
M
(b) CHead Attention: Tight binding between CNN channel and Attention head
Figure 1: TI introduces CNN- Transformer hybrid architecture that effectively processes information by strategically assigning CNN attention the temporal, feature, and variable dimensions using depthwise (DW) and pointwise (PW) convolutions. In our novel mechanism, CHead Attention, each channel encoded by shared CNN directly aligned with single attention head. facilitates cross- variable information exchange, ensuring that interactions occur only between semantically similar temporal features. (revised)
al. 2024) addresses this but fuses all temporal patterns through single representation, losing feature-level selectivity. (iii) Dual-axis tokenization methods (Nie et al. (202)) employ attention on both temporal and variable axes, but struggle to transfer information across both dimensions when
missing values block intermediate pathways. (iv) Temporal Convolutional Neural Network (CNN)
approaches (Wu al.) 2023) Luo Wang 2024) efficiently extract multi-scale temporal features
but provide limited cross variaba information transfer.
We show that robust imputation benefits from task-aligned urchiteture-sspecialieed temporal and cross-variable components whose information transfer accounts for their interdependencies. We propose T1 (Time series imputation with 1-to-1 channel-head binding), a hybrid architecture where CNNs extract temporal features from incomplete observations within variables and attention per- forms selective cross-variable information transfer ((V) in Figure Tap. TI employs modernized tem- poral convolutions (Luo & Wang 2024). leveraging the inherent property of CNNs where each channel learns to capture distinct temporal patterns from the observed data. This process effectively encodes the input into of diverse feature maps, yielding variable tokens that directly parame- terize query, key, and value representations for cross-variable attention. This design leverages each architecture's s strengths for imputation: the convolutional modules excel at building robust temporal representations from sparse observations, while variable-wise attention dynamically identifies infor- mative variables based on their observed patterns. However, a naïve combination of these modules is insufficient. When missingness corrupts specific temporal features, treating each variable single token forces all its channels mix, preventing isolation of corrupted features from reliable ones during information transfer. This necessitates architectural refinement for feature-specific control.
Our key mechanism, Chamnel-Head Binding (CHead Attention, Figure 1b). seamlessly integrates CNNs and inter-variable attention, by creating a one-to-one correspondence between CNN channels and attention heads. Each CNN channel captures distinct temporal feature while each attention head processes only its corresponding chamnel across variables, enabling fine mee-graiddd feature-level information transfer pathways. This feature-level binding enables robust imputation: when miss- ingness prevents a channel from observing its specialized pattern, the feature it extracts becomes less informative. Consequently, corresponding attention head can temper its reliance that chan-
2

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nel during information transfer, while feature-level selectivity prevents these localized uncertainties from contaminating other channels.
In extensive experiments across 11 benchmark datasets, TI achieves state-of-the-art perfor- mance, demonstrating its effectiveness in diverse scenarios including point, block, and naturally occurring missingness. Furthermore, a model trained with a single missing ratio maintains perfor- mance when tested on both higher and lower ratios, a crucial property for real-world applications. These results are achieved using a consistent hyperparameter configuration across all datasets, sug- gesting robustness to hyperparameter choices.
Our main contributions summarized as follows:
We introduce TI, CNN-Transformer hybrid architecture that tackles imputation through com- plementary specialization: CNNs for robust temporal feature extraction under missingness, and Transformers for selective information transfer across informative variables.
We propose Channel- Head Binding (CHead Attention), an architectural mechanism that creates one-to-one correspondence between CNN channels and attention heads, enabling robust imputa- tion by isolating feature-specific information transfer pathways that adapt to varying missingness patterns.
We demonstrate that TI achieves state-of-the-ar performance across 11 datasets, reducing MSE by 46% average and maintaining this advantage under extreme missingness (70% missing ratio), while generalizing to unseen missing patterns without retraining.
2 RELATED WORK
Time-series Imputation. Time-series imputation has evolved from statistical methods (Dempster eet al. 1977 Van Buuren &
2011) to deep learning approaches. RNN-based methods like BRITS (Cao al. (2018) and M-RNN (Yoon al. 2019) model bidirectional temporal dependencies. Transformer-basee approaches including SAITS (Du et al., 2023) and ImputeFormer (Nie al. 2024) leverage self-attention mechanisms with masked training objectives capture long-range dependencies. Generative models, particularly diffusion based CSDI (Tashiro et al.) 2021]. SSSD (Alcaraz Strodthoff] (023), and PriSTI (Liu et al., (023a), achieve high quality through iterative refinement but with prohibitive inference latency. Graph methods like GRIN (Cini al. 2022) and SPIN (Marisca et al.) 2022) model inter variable relationships via message passing but rely static graphs that cannot adapt to instance-specific missingness.
Temporal and Cross-variable Modeling. Effective imputation requires both robust temporal ex- traction and selective cross-variable fusion, yet existing methods excel at one while compromis- ing the other. For temporal modeling, linear models (DLinear, NLinear) decompose via projec- tions (Zeng al.] (023). Vanilla Transformers (Vaswani et al. (017)) tokenize all variables each timestep, while extended versions like PStchTST (Nie et al. 2023), Autoformer (Wu et al., 2021) and FEDformer (Zhou et al. (002)) apply temporal attention with decomposition strategies. CNN- based Methoos-TTCN (Bai et al. 2018), TimesNet (Wu et all 2023), and notably ModernTCN (Luo) multi-scale features through dilated or large-kernel depthwise convolu- tions. While powerful for temporal patterns, these methods lack dynamic cross-variable relation- ships. For cross-variable modeling, Crossformer (Zhang Yan (023) attempts across temporal and variable dimensions but still entangles representations. Transtormer (Liu et al.) (2024) achieves pure variable-axis attention by inverting dimensions, treating each variable's sequence as a single token for clean cross-variable fusion. However, these compress enlangle temporul information. Mean- while, convolutional approaches like ModernTCN effectively capture temporal patterns but rely on static varsabe mixing that cannot adapt to missing patterns. Tl combines these strengths through shared depthwise convolutions and variable-axis attention for cross-variable fusion. The shared convolutions ensure each channel extracts the same pattern type across all variables, while mask-aware embeddings and CHead Attention enable dynamic, validity- information transfer.
& Wann
3 THE T1 ARCHITECTURE FOR TIME SERIES IMPUTATION
We address the problem of time series imputation. Let a multivariate time series be represented by TR. MxT where M denotes the number of variables and T' is the sequence
X (2(11) (20) z
3

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Output
VarableM
Reconstruction Upsampling
Instacee
[cl Changl-HHed Atteution (CHind Attention)
Desemmlleriinn
boad
Imegand
Recosstrccion
Upoenppinng
Corv
Variable
11 Block
Attenton
Score
Powlt Shuffle
Layer Nerm
temporal
CHoad
Layer Nerm
Attention
Embedding
tempersi
(b) Temporal Convolutional Q, K, Projection
Cuav QKV
brewer
A
Projector
1
Instance
Nermuloottion
Input
variable
Figure 2: An overview of the Tl architecture. (a) The Mask-Aware Embedding module encodes the input series and its observation mask into a latent representation using ID convolutions. (b) The Temporal Convolutional QKV Projection block employs Depthwise Convolutions extract consis- tent temporal patterns for each channel. The kernel weights are shared across variables, resulting Query, Key, and Value embedding.
in remantically-alignnne tion (CHead Attention) is applied across the variable axis to selectively transfer information. Each head is bound single channel, enabling feature-specific fusion between semantically-aligned patterns. (d) The Reconstruction Upsampler restores the original temporal resolution of the series via a parameter-free ID PixelShuffle operation followed by a final pointwise convolution. (revised)
(c) Our proposed Channel- Atten-
length. The accompanying observation mask Ω E {0, 1JMX indicates whether a value is observed (2m,. = 1) or missing (Dm,. = 0). The objective impute the missing values by leveraging each variable's ' unique temporal patterns and inter-varialle correlations.
3.1 OVERALL ARCHITECTURE
As presented in Figure 2 our novel architecture, T1, comprises three main components: Mask- Aware Embedding, Tl blocks and Reconstruction Upsampler.
Awsk-Aware Embedding, As initial step, instance normalization is applied to each input series To properly handle missing
(m)) computing the normalized series as Z = ((((m))(((m))))))_) data in imputation tasks, the per-instance mean (m)) and standard deviation (mm) are computed solely from observed values (where Pm, 1) and stored for the final denormalization.
To explicitly encode missing value locations, the normalized series and its observation mask are stacked into two-channel input (as presented in Figure 22)) The resulting tensor (e 22*7) is processed by a strided ID convolution with C' filters and augmented with a learnable variable-wise encoding, producing the final embedding (mm E RCLL where L is the latent temporal dimension:
(
(m) Znorm ((())
))
(m) = ConvID
+
(mm) var
(1)
Here (m) CxL is learnable variable-specifie encoding (analogous to positional encoding for tokens).
TI Blocks. The aggregated embedding Z - [1x(1), 211)) ..... (Af) E MxXXL is processed through stacked TI blocks that implement a CNN-Transformer hybrid design. Each variable maintains inde- pendent temporal CNN feature spaces while Channel-Hesd Attention models variable relation- ships. Optionally, downsampling can be applied between blocks to reduce the temporal resolution for subsequent layers. The details of T1 block design are presented in Section 3.2
4

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Reconstruction Upsampler. The final representation from the TI blocks, denoted Zou RMxCXI, is passed to the reconstruction upsampler to generate the final imputed output, as pre- sented in Figure 2d. For the upsampling stage, we employ ID variant of PixelShuffle (Shi et al, 2016), parameter-free operation that rearranges the channel dimension into the temporal dimen- sion. This process reshapes the input from I XxxxCXL to (gMx(C/r)xLLT)) where r = T is the upsampling ratio. Using PixelShuffle avoids the checkerboard artifacts common in transposed convolutions while maintaining efficiency. A subsequent pointwise convolution (PWConv) projects the target dimension:
morm www.eeeeeielillleeiiii. E M
Final imputation ((m)) (m) ((m) + p(() is obtained through denormalization using the stored statistics.
3.2 TI BLOCK
The TI block addresses multivariate imputation through three specialized components: Temporal Convolutional Q. K, V Projection for multi-scale temporal feature extraction, CHead Attention for cross-variable information transfer, and Convolutional Feed-Forward Network (FFN) for channel- wise feature refinement. The shared depthwise convolutions ensure that features are extracted con- sistently across variables, while the 1-to-I channel-head binding mechanism allows the attention to selectively transfer information at the feature level.
Temporal Convolutional Q K, V Projection. To generate the Query, Key, and Value embeddings,
we use a projection block based on depthwise convolutions (DWConv) (as illustrated in Figure 2b).
technique effectively utilized for time-series analysis in ModemTTC (Luo & Wang 2024). This
design choice leverages the inherent property of CNNs where each channel naturally specializes in capturing distinct patterns.
In our architecture, the weights of the DWConv operators are shared across all variables. This straightforward design choice allows each channel to learn consistent feature type from every variable, producing the semantically aligned representations required for the subsequent Channel- Head Attention. Moreover, we employ parallel kernels of different sizes for multi-scale analysis. The projections are formally defined as:
Qm,c DWConV Q cm + DWConv small, Q (m,,);
Km, DWConVturee (e) + DWCCnv small, (Zm,), Vm E CE (1...., C} (3)
Vi,c DWConViarge v (cm DW small, V (Z,,c)
where each DWConv operator
Zm,c R for variable m and channel
CHead Attention for Varis-e Information Transfer. As shown in Figure our Channel- Head Attention creates one-to-one correspondence between CNN channels and attention heads (ni, C), ensuring each head processes a single channel across all variables. This design prevents indiscriminate fuston-instead enabling selective information transfer where each channel indepen- dently identifies and transfers relevant patterns across variables.
For each channel e {L, ..., C'}, the attention operation is:
Qaok? Ve
O. Softmax
where Qc, Ke, V. E X represent channel c's features across all variables.
The output tensor O E MxCxL constructed by concatenating the individual channel outputs [O,,... Oc} along the channel dimension. The refined embedding Zutn- is obtained by applying pointwise convolution to O, followed by layer normalization and residual skip-connection:
Zum = Z LayerNorm(PWCon//C
(5)
Convolutional Feed-Forward Network. Following Channel-Head Attention, we apply convolu- tional feed- forward network for channel-wise feature refinement:
7om 7am (LyeeNN (7aun))
(6)
5

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We use pointwise convolutions rather than linear transformations to preserve the temporal structure inherent in time series data. This design ensures that each temporal position is processed inde- pendently while enabling non-linear interactions across channels. The network follows inverted bottleneck architecture where PWConv, projects to an intermediate dimension and PWConv, maps back to the original channel dimension C. Through stacked T1 blocks, the FFN-mixed features form new channel representations for subsequent layers, enabling progressive feature combination while CHead Attention maintains feature-level selectivity.
4 EXPERIMENTS
In this section, we comprehensively evaluate T1 across various missing data scenarios and bench- mark datasets. We conduct three main experiments to demonstrate the effectiveness of our approach: (I) point missing scenario with varying missing ratios, (2) block missing scenario simulating sen- sor failures, (3) evaluation on naturally occurring missing data. Additionally, we provide detailed representation analysis and ablation studies to better understand the contribution of each component.
4.1 EXPERIMENTAL SETUP
Datasets. We evaluate on widely-used time series benchmark datasets: ETTh1, ETTh2, ETTm1, ETTm2 Zhou et al.
Electricity (Trindade] 2015), Weather (Wetterstation). Illness (CDC). 2018), and PEMSÓ3 (Chen et al. 200T). Additionally, we use two naturally missing datasets: PhysioNet Challenge 2012 (Silva et al. 2012) and AQI36 (Yi al. 2016).
2021).
Exchange (Lai et al.
Baselines. We compare against 11 state-of-the-art methods spanning two categories: (1) Gen-
eral time series and forecasting models: TimeMixer++ (Wang et al. 2024), ModernTN (Luo &
Wang
2024), iTransformer (Liu et al.] 2024), TimesNet (Wu et al., 2023). PatchTST (Nie et al.)
2023 and DLinear (Zeng et al.] (023); y; (2) Specialized imputation models: ImputeFormer (Nie
et al.
2024). SAITS (Du et al.) (023). CSDI (Tashiro et al., (021). BRITS (Cao et al.] 2018). and
PSW-I (Wang et al., 2025a). Architecturally these methods span time-axis tokenization (PatchTST, SAITS), variable-axis tokenization (iTransformer). dual-axis tokenization (ImputeFormer, CSDI), temporal CNN (ModemTCN, TimesNet), RNN-based (BRITS), MLP-based (DLinear). hybrid (TimeMixer++), and optimal transport (PSW-I).
Implementation Details. We set the sequence length to 96 for all experiments. During training, we employ sele-super learning where 40% of observed values are randomly masked and used as reconstruction targets, minimizing MSE loss between predictions and ground truth. For fair com- parison, general time series models are trained under identical conditions to T1, while specialized imputation methods retain their original training protocols; all models are evaluated with the same data splits and random sceds. Performance is evaluated using mean absolute error (MAE) and mean squared error (MSE) following previous studies (Liu et al. 2024, Wang et al.) 2025a). Full train- ing details and loss formulation are provided in Appendix A.2 and experimental results including standard deviations are in Appendix
4.2
MAIN RESULTS
4.2.1
POINT MISSING SCENARIO
Setup. We test on four different missing ratios (0.1, 0.3, 0.5, 0.7) to assess the robustness of each method under various missing conditions.
Table 1: Imputation performance on nine benchmark datasets under point missing scenario. Results are averaged across four missing ratios (0.1, 0.3, 0.5, 0.7), Best results are marked in bold and second best underlined.
Datoes
MSE MAE
TI. (UOrr)
TimeMitzr-+
MSE
MAE
MrNeneTUN
S5SE
MAE
(Transfoener
MSE
MAE
MSE MAE
TimesNet
PacsTS MSE
MAE
MSE
D2Linear
MAE
InguteFbereer MSE
MAE
MSE
SATTS
MAE
MSE
CSDI
MAE
BRITS MSE
MAE
PSW-1 MSE MAE
ETT5
0.138
0:132
0.237
[0.022
0.273
0.223
00.02
0.178
grTha
0
0.052
0.136
0.130
0.388
0.225
0.085
0.034
0.114
0.070
0.647
0.151
ETTa2
0.030
0.099
0.100
0.024
0.128
0.151
0.103
0.035
0.57
0.245
0.001 0.094
Wonter
8.229
084
0.044
0085
0.016
0077
0480
011
0/000
0.079
01092
0.889
0.044
0.064
0.42
0053
0034 01845
0.084
0.942
0.112 0.117
0
0/073
PEMS06
0.21
0,93
0.044
0.143
0.056
0.166 0.048
0.147
0.059
0.171
0U638
0.133
0.294
0.220
0.090
0.175
0.550
0.154
0.882
0.155
0,076
0.178
0.049 0.149
Eachunge
0
0U202
0,023
0.009
0/022
00044
04114
0163
0.02
0.027
6.005
0,044
0.001
0,070
0.150
0.344
0.007
0.244
0.115
0.249
0,031 0.005
Illeas
8338
IL102
0.338
0.201
0.360
0.350
0.305
0.263
0.568
0:45%
0.1
50
0.223
0.145
0.
0.65
0.505
0.614
0,405
586.036
0557
0.426
0.390
0.867 0.123
Elenicit
8043
0.131
00771
0.172
0.121
0.253
0050
11199
105
212
0008
00208
0.191
0,331
0,075
0.177
0.152
0.277
0.144
0.355
0.166
0.244
0. 0.105 0.30S
(0075
0.142
0.172
0.050
0.114
0.193
0.10
10176
0.236
1222
0.174
0302 0.12

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Table 2: Performance comparison under varying test-time missing ratios averaged across all datasets. Models are trained with 0.4 missing ratio and evaluated on different missing intensities.
Missing
(Ours)
Tlmekliscre MAE
ModeesTCN
ITrandfommer
TimesNer
PocchTST
Fompureormerr MAE
SATTS
CSDE
PSW-I MAL MSE MAE
Rato
MSE MAL
MSE
MSE
MAH
MSB MAE.
MAL
MSE MAB
MSE MAB
MAD
0.17
00063
00089
0.15%
0.1100.133 0.23
0.150
1.104
1452
0.344 1.111
6.021 0.129
0.098
0.113
0,088 0.157
0.168
0.200000000 0.122
6,027
0.143
0:168
0.113
0.088 0.1740.172
0.209
40.385
0991 0.168 0.08 0:139
0.049 0.121 (LI1S 0.184
(L335 0.230
(0125 0.210
0.173
L.22 0.176
0.1999 0.270/0.384
0.335
(.299
0.334 21.136 0.745 0.354 0.157
Results. As shown in Table T_ T1 demonstrates superior performance across all datasets. On av- erage, T1 achieves 46% MSE reduction compared to the next best PatchTST baseline and a 56% reduction against the specialized imputer PSW-I. Table 2 further highlights Ti's robustness against increasing data sparsity. At the highest missing ratio of 0.7, where many baselines struggle, TI's MSE is nearly half that of the next best methods, PatchTST (0.049 vs. 0.092), underscoring its resilience in scenarios with severe data loss.
4.2.2 BLOCK MISSING SCENARIO
Setup. To simulate realistic sensor failure scenarios, we introduce two types of missing patterns at test time: (1) 5% probability of point missing for random measurement noise, and (2) 0.15% proba- bility of consecutive block missing with random lengths between 24 to 96 time steps for temporary sensor failures or communication interruptions.
Table 3: Imputation performance under block missing scenario simulating realistic sensor failures.
Test patterns combine 5% point missing and 0.15% block missing (24-96 consecutive timesteps).
Dunaset
MSE
TI (Ours)
MAE
TimeMixrr++ MAE
MSE
MSE
TCN
MAE
iTrnndommer
MSE
MAB
MSE
TimesNe:
MAE
MSE
PatchTST
MAE
MSB
DLinear
MAE
Imputel-vmer
MSB
MAE
MSE
SAITS
MAE
MSE
CSDI
MAE
MSE
BRITS
MAB
ETDa
0.030 0.107
00.115
0.210
0.366
0.172
0.0944
1.305
0.104 0.217
01050
0.151
0.192
0.299
01063
0.155
0.1128
10.00
0.057
0.117
0,856
I1.145
ETTh2
8.027 0.092
0.062
0.153
0.048
0.138
0.050
0.152
0.055
0.156
0.039
0.125
0.078
0.184
0.179
0.228
0.145
0.260
0.074
0.112
0,133
0.250
eTiml
0.030
0,082
0.062
0.131
0,044
0.115
0.145
0.037
0.105
0.202
00036
0.111
0.022
0.087
0.023
0,026
0,099
ETTm2
0.859
0.029
0.090
0.099
0.047
0.075
0.164
PEMS0
0.050
0.180
Exchange
0.003
0.002
0.077
0.266
0.00
0.279
0.037
0.120
Mlless
(.230
0.397
0.237
0.125
0.24
0.588
0.468
0.389
0.401
1182
0.236 0.202
Electiiity
(6008
0.118
0.088
0.180
0.146
0.283
0.080
0.190
0.099
0:212
0.050
0.208
0.302
0.486
0.061
0.152
0.135
0.262
0.133
0.220
0.117 0.244
Avg
[0.026 0.076 00.073
0.141
00.078
0.167
0.071 0.150
00.04
0.164
0.050
0.124
0.114
0.262
001114 0.159
[0.108
0.191
131.4 1.376 0.086 0.166
Results. Tl's strong performance continues in the more challenging block missing scenario. As shown in Table 3 Tl outperforms the next best method, PatchTST, with a 48% reduction in average MSE. This result underscores the effectiveness of T1's cross-variable information transfer when long segments of temporal information are unavailable.
4.2.3 NATURAL MISSING DATASET
Setup. We evaluate on two datasets with naturally occurring missing values using different proto- cols:
PhysioNet Challenge 2012 contains multivariate clinical time series from 4,000 ICU patients with 37 physiological variables and approximately 80% inherent missing values. We add artificial missing patterns (0.1, 0.3, 0.5, 0.7) on top of existing missing values, creating compound missing scenarios with up to 94% total missing rate.
AQ136 consists of air quality measurements from 36 monitoring stations with 15-30% natural missing values due to sensor malfunctions. We evaluate directly on the test set's 's natural missing patterns without additional masking.
Results. Under real-world conditions with naturally occurring missing data, TI proves its practical applicability. On the PhysioNet2012 dataset, T1 demonstrates remarkable stability and achieves 23% performance improvement in average MSE over the next best method, DLinear (Table
This robustness is also demonstrated on the AQI36 dataset, where TI outperforms the next best method, PStchTST, with a 13% reduction in MSE. These results confirm the robustness of our ar- chitecture across diverse and critically sparse data regimes.
7

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Table 4: Performance on naturally missing datasets. PhysioNer2012: compound missing with 80%
inherent + additional masking. AQ136: evaluation on natural test set missing patterns (15-30%).
PhysioNet2012- Natural (8%% Additional Missing
Additioonal Missing Ratio
T1 (Ours)
TimeMixcr++
ModenTCN MAE
(Transfortace
TamesNet MAE
PatchTST
DLinear MSE
Impotieorter
SAITS
MSE
MAB
MSB
MAE
MSE
MSE
MAE
MSE
MSE
MAE
MAE
MSE
MAE
MSE
MAE
0.1 (Total: 82%)
0.049 0.067
0.091
0.107
00092
0.118
0.107
0.128
000882
0.103
0,099
0.116
0.075
0.100
0.078
0.067
0.089
0.070
0.3 (Tama:: 80%)
0.064
0.027
0.372
0.111
0.103
0.121
0.096
0.108
0.106
0.03
0.108
0.000
0.078
0.5 (Total: 90%)
0,081
0.090
0.130
0.117
0.110
0.126
0.120
0.131
0.101
0.116
0.113
0.125
0.104
0.117
0.114
0.091
0.107
0.089
0.7 (Total: 94%)
0.106
0.110
0.236
0.126
0.124
0.134
0.129
0.135
0.114
0.127
0.124
0.132
0.118
0.127
0.151
0.114
0.129
0.106
Avg
0.075
0.086
0.2007
0.115
10.107
0.125
[0.119 0.131
|0.098 0.114
0.114/0.110
0.110
0.123
0.007
0.113
0.108
0.087
0.100
0.086
AQ136
Natural Missing Only (15-30%)
Test Set
0.226 0.226 0.274
0.318 10.281
0.311
[0.314
0.331
J0.337 0.337
0.262
0.303
0.338
0.343
0.447
0.411 00,469 0.400
Mom Attention to Tunget Variable
Madding
Clean
Moan Atteotion to Targest Varalble
Attention Degrasaation Rale
Peuk
8.4%
0.16
Non Poak
2 1 C
11.1%
0.14
High Var
10.4%
Low
7.5%
Time Stop
Missing Ratio of Target Variable
(n) Attention degradation by missing ratio
(b) Head-specific attention patterns by missing type
Figure 3: Representation analysis of TI's attention mechanism. (a) Layer-wise attention weights from other variables to target variable under varying missing ratios (entire ETThl test set). Atten- tion weights decrease with increasing missing ratio, with shallow layers showing more pronounced degradation. (b) Head-specific attention patterns of clean signal and under various missing patterns (peak vs non-peak and high vs low variance, 30% each), showing top-20 heads sorted by clean at- tention weights.
4.2.4 REPRESENTATION ANALYSIS
We conduct two controlled experiments on ETThl qualitatively analyze the effectiveness of CHead Attention.
Missing Response Across Layers. Using the entire ETTh1 test set, we select one variable as target and vary its missing ratio from 0.1 to 0.7 while keeping the missing ratio of all other variables at 0.4. Figure 3h shows attention weights assigned to the target variable decrease with increasing missing ratio. This trend is most noticeable in the shallow layer while deeper layers exhibit reduced sensi- tivity to missingness. Attention weights in the first layer exhibit sharp drop of 46% while weights in the last layer drop by only 6% 10.165-0..153 This suggests partial reconstruction in early layers improves information availability for subsequent layers.
Observable Pattern Dependence. Using single ETTh test sample, we mask 30% of the target variable in regions with different characteristics: peak regions (far from center) versus non-peak regions (near center), and regions with top 30% versus bottom 30% local variance. As shown in left panel of Fig these masks leave fundamentally different temporal patterns in the observed portion of the target variable. The middle panel of Figure 3 visualizes the corresponding attention responses for the top-20 heads, sorted by clean attention weights. Clearly, this visualization reveals distinct response patterns for each masking scenario. Quantitatively, removing high- variance regions reduces attention by 10.4% while removing low- regions reduces it by 7.5%. This indicates that attention modulation depends on which temporal patterns remain observable, not solely on missing ratio. CHead Attention enables each channel to assess whether its corresponding temporal features can be extracted from the observed data.
These results demonstrate that TI learns adaptively down-weight unreliable information path- ways based on both observation density and the extractability of temporal patterns. The layer-wise stabilization and channel-specins responses support our architectural design combining CNN fea- ture extraction with fhannel-boumn attention, contributing to the performance gains observed under structured missingness (Table
8

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4.2.5
ABLATION STUDY
We conduct comprehensive ablation studies to analyze the contribution each component in T1. All experiments are performed on six datasets (ETThl, ETTh2, ETTml, ETTm2, Weather, Electricity) with 40% training mask ratio and evaluated across four test missing ratios (0.1, 0.3, 0.5, 0.7). Table reports averaged results when replacing only the specified component while keeping all others at their default configuration.
Cross-variable Mechanism. Replacing attention with pointwise convolution degrades performance by 12.91% %, demonstrating that adaptive information transfer outperforms fixed patterns. Removing cross-variable modeling entirely results in 56. degradation, confirming that cross-variable in- formation is essential for imputation.
Channel-Heat Head Binding. We evaluate the impact of channel-head grouping by varying the number of channels per attention head: 8, 16, and 32 channels per head (compared our default one-to- one correspondence with 128 channels). Performance degrades by 7.45%, 16.86%, and 14.57% respectively, with 16 channels per head showing the worst degradation. These results confirm that fine-grained, one-to-one channel-head correspondence is crucial for maintaining feature-specific information pathways and preventing the mixing of corrupted and reliable temporal patterns during cross-variable transfer.
Mask-Aware Embedding. Removing the explicit mask channel from input embedding causes 3.64% degradation. This indicates that providing missing patterns directly the model improves its ability to distinguish between observed and missing values during feature extraction.
Reconstruction Method. PixelShuffle outperforms linear upsampling by 3.19%, validating our choice for artifact-free temporal reconstruction.
The substantial gap between convolution (12.91 %) and no cross-variable modeling (56.16%) reveals an important finding: while cross- variable information is crucial, the method of information transfer matters significantly. Our attention mechanism better identifies which variables contain reliable information for imputation compared to fixed convolutional patterns.
Table 5: Comprehensive ablation study on model components (MSE). Each shows the perfor- mance when replacing only the specified component from our full model. The last column shows the percentage increase error relative to our full model.
Component
Alternative
ETThl
ETTH2
ETTm1
ETTm2
Weather
ECL.
Avg
A (%)
T1 (Ours)
0.049
0.036
0.022
0.017
0.029
0.043
0.033
Cross-variable
Conv
0.056
0.040
0.024
0.020
0.029
0.052
0.037
+ 12.91
Component
w/o
0.095
0.064
0.040
0.029
0.031
0.048
0.051
+ 56.16
32 Chns
0.061
0.040
0.030
0.020
0.030
0.044
0.037
+ 14.57
Channel-Head Binding
16 Chns
0.066
0.041
0.028
0.020
0.030
0.045
0.038
+ 16.86
8 Chns
0.055
0.038
0,025
0.019
0.030
0.044
0.035
+ 7.45
Embedding
w/o mask
0.052
0.037
0.023
0.018
0.029
0.044
0.034
+.64
Reconstruction
Linear
0.050
0.036
0.022
0.018
0.030
0.046
0.034
+ +.199
CONCLUSION AND FUTURE WORK
In this paper, we presented T1, a CNN-Transformer hybrid architecture for multivariate time series imputation. By strategically assigning CNNs for temporal feature extraction and attention for cross- variable information transfer, Tl addresses the fundamental challenge of imputation under heavy missingness. Our key innovation, Channel-Head Binding, creates one-to-one correspondences be- tween CNN channels and attention heads, enabling feature-specific information pathways that adapt to varying missingness patterns. Extensive experiments demonstrate that maintains computa- tional efficiency while achieving state-of-the-art performance across diverse datasets and missing scenarios. The architecture's robustness under extreme missing conditions and its stable perfor- mance with a consistent hyperparameter configuration highlight its practical applicability. Looking forward, we will explore extensions to online streaming environments for real-time imputation and active sensing strategies that can guide optimal sensor selection under resource constraints.

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ACKNOWLEDGMENTS
This work was supported in part by Institute of Information communications Technology Planning Evaluation (ITTP) grant funded by the Korea government (MSIT) (RS-2025-25463302) in part by the National Research Foundation (NRF) of Korea grant funded by the Korea government (MSIT) (No. RS-2023-00222663), and in part by AI-Bio Research Grant through Scoul National University.
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A IMPLEMENTATION DETAILS
A.1 DATASET DETAILS
A.1.1 DATASET DESCRIPTIONS
We conduct experiments on 11 multivariate time series datasets spanning diverse domains including energy, transportation, climate, healthcare, and economics. All experiments use a sequence length of 96 timesteps, except for PhysioNer2012 which uses 48 timesteps due its clinical nature and irregular sampling patterns. The datasets are categorized into two groups: complete datasets for ar- tificial missing experiments and naturally missing datasets for realistic evaluation scenarios. Table 6 summarizes the key statistics.
Complete Datasets ETT (Zhou et al. 2021) comprise electricity transformer measurements includ- ing with hourly (ETThI, ETTh2) and 15-minute (ETTml, ETTm2) sampling frequencies. Electric- ity (Trindade) 2015)tracks consumer power consumption. Weather (Wetterstation) contains meteo- rological indicators from the Max Planck Institute weather station. Ilnness (CDC) records CDC in- fluenza surveillance data across US states. Exchange (Lai et al.) 2018)coveers international currency rates from 1990-2016 PEMS03 (Chen et al. 2001) represents highway traffic sensor measurements from California transportation networks.
Naturally Missing Datasets PhysioNet Challenge 2012 (Silva al. 2012) contains ICU patient physiological measurements with 80% inherent missingness due to irregular clinical sampling proto- cols. Experiments are conducted on the 20% observed portions. AQI36 (Yi al., (016) includes air quality monitoring data with 13.3% real missingness from sensor failures: general missing (8.2%) from random transmission errors, spatial block missing (2.2%) from regional power/network out- ages, and temporal block missing (3.5%, 11 timesteps average block length from maintenance peri- ods. These datasets span diverse domains and temporal scales, providing comprehensive evaluation under varying missingness scenarios from dense sensor networks to sparse clinical measurements.
Table Dataset descriptions.
Type
Dataset
Variables
Train
Valid
Test
Frequency
Missing Ratio
ETTh1ETTH2
7
8,545
2.785
2,785
Hourly
ETTmL,ETTm2
7
34,465
11.425
11,425
15min
Electricity
321
18,346
2,621
5,424
Hourly
Complete
Weather
21
36,820
5,260
10,521
10min
Illness
7
609
87
175
Weekly
Exchange
5,245
749
1,499
Daily
PEMS03
358
18,279
2,611
5,223
5min
Naturally Missing
PhysioNet2012 AQ136
37
2,557
640
800
Inregular
80.0%
36
4,422
649
2,548
Hourly
13.3%
A.2 EXPERIMENT DETAILS
A.2.1 CONFIGURATION DETAILS
We maintain consistent architectural design across different datasets, with deterministic sequence- length scaling for kernel sizes when sequence lengths differ from the standard 96 timesteps. Impor- tantly, we use the same model configuration (channel count, layer depth, FFN ratio) regardless of the number of variables each dataset, demonstrating the model's robustness across varying data dimensions.
Standard Configuration. For datasets with sequence length 96, Conv ID embedding with kernel size 2 and stride 1 projects input to 128 channels. The architecture consists of four TI blocks arranged in two hierarchical groups. The first group contains two T1 blocks employing dual-scale depthwise convolutions with kernel sizes 71 and 5, followed by downsampling with kernel size and stride 2. The second group contains two T1 blocks with adjusted kernel sizes and 5, operating on downsampled features. This hierarchical design allows the model to capture multi-scale temporal
14

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patterns at different resolutions. FFN expansion ratio is set to 1.0. This configuration remains fixed across all datasets, from 7-variable datasets (ETT series) to 358-variable datasets (PEMS03).
Sequence Length Adaptation. For datasets with different sequence lengths (c.g., PhysioNet with 48 timesteps), we apply deterministic scaling to adjust kernel sizes:
Raddjsstdd L(T ((T96) x kidefuut
where T is the sequence length. This yields 71 - 35 and 31 15 for the large kernels, while small kernels (size 5) remain unchanged. This systematic rule preserves proportional receptive field coverage without dataset-specifie tuning. All other parameters remain identical to the standard configuration.
A.2.2 EXPERIMENT DESIGN
All experiments use five random seeds (102, 202, 302, 402, 502) with mean and standard deviation reported. Experiments were performed on NVIDIA H100 80GB GPUs.
We evaluate models across three missing scenarios to assess generalization capability. Point missing applies independent probability masking at each timestep with varying ratios (10%, 30%, 50%, 70%). Block missing simulates realistic sensor failures by combining 5% point missing with 0.15% probability of initiating consecutive missing blocks spanning 24-96 timesteps. The key experimental principle is training with specific missing ratios and evaluating across multiple missing scenarios.
Complete Datasets TI uses 0.4 point-wise random masking for training in both point missing and block missing experiments. This single trained model evaluated across multiple test scenarios: point missing experiments test ratios of 0.1, 0.3, 0.5, and 0.7 with point-wise patterns, while block missing experiments test on the complex block patterns described above. This design directly tests whether models trained simple point patterns generalize more complex structured missing without specific training.
Naturally Missing Datasets We apply additional artificial missing top of inherent missing pat- terns for imputation training and evaluation. PhysioNet2012 models train with 0.2 point-wise ran- dom masking applied non-missing values, then test on various missing ratios (0.1, 0.3, 0.5, 0.7) applied to non-missing regions. AQI36 models train using real-pattern based artificial missing aug- mented with additional random point-wise masking ratios (0.2, 0.5, 0.8) sampled per batch, while testing uses exclusively the dataset's provided real-pattern based artificial missing patterns.
A.2.3 EVALUATION METRICS
We employ Mean Squared Error (MSE) and Mean Absolute Error (MAE) as primary evaluation metrics for imputation performance:
MSE
1
Σ
(a (m) - Di (m)),
MAE
Σ
(m)
y2 (m))
(7)
M
[M
(m,1))M
(m.t)EM
where M denotes the set of artificially masked positions during evaluation, y/ (m) truth values, and (m())) represents imputed values. Metrics are computed only on artificially masked positions, not on originally missing values, ensuring consistent evaluation across all methods.
represents ground
A.2.4 TRAINING IMPLEMENTATION
We employ self-supervised training strategy where observed values artificially masked during training and the loss is computed only on these masked positions. We distinguish between the orig- inal observation mask Ω {0. 1) M where 1 indicates observed values and 0 indicates missing values, and the training mask V E {0, 1)Mx2 XX where indicates artificially masked positions for training. The model minimizes Mean Squared Error between predictions (.(m) and ground truth Vi (m) at artificially masked locations:
LMSE
Σ
(a/m) y/ (m)) (8)
Em,e I(D(!)) = 0)
()(m= =
15

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This approach ensures the model learns reconstruct values from partial observations without using originally missing data as supervision. We use the Adam optimizer with 31 = 0.9 and 32 = 0.999, learning rate of 0.001 (0.0001 for Weather due to rapid convergence), batch size of 16, and maximum 300 epochs with early stopping patience of 30.
A.3 BASELINE IMPLEMENTATION DETAILS
We evaluate two categories baseline models with distinct configuration strategies to ensure fair and comprehensive comparison. All baseline implementations are based on established frameworks including Time-Series Library] PyPOTS (Du al., 2025), and Awesome-Imputation (Du et al.) 2024 repositories to ensure reproducibility and fair comparison.
General and Forecasting Time Series Models TimeMixer++ (Wang et al. 2024). Mod-
emTCN (Luo & Wang 2024). iTrannformeer (Liu et al. 2024). TimesNet (Wu et al. 2023)
PatchTST (Nie et al., 2023). and DLinear (Zng et al.) (023) adopt identical training protocols
to T1, using 0.4 point- wise random masking during training. MSE loss computed only on masked positions, Adam optimizer with learning rate 0.001, batch size 16, and maximum 300 epochs with early stopping (patience=30). This standardization isolates architectural differences from training strategies. Model architectures follow hierarchical selection priority: official imputation configu- rations for specific datasets when available, configurations from similar variable count imputation tasks, long-ferm forecasting configurations for the same dataset, or forecasting configurations from datasets with similar variable counts.
Specialized Imputation Models ImputeFormer (Nic et al. 2024), SAITS (Du et al. 2023 CSDI (Tashiro et al. 202I), and BRITS (Cao al., 2018) retain their published training proto- cols to leverage model-specific capabilities. These models employ original loss functions (such as CSDI's diffusion loss and BRITS's consistency loss), published optimization schedules, model- specific missing pattern strategies, and architeettur--specffic parameters from official implementa- tions. When exact configurations were unavailable, the same hierarchical priority was applied while preserving each model's 's unique training methodology. Both model categories adapt to natural miss- ing experiments with PhysioNet2012 training using 0.2 point-wise masking on non- mon-missing values, while AQI36 follows the TI protocol with real- ceal-pattern based missing augmentation.
B EFFICIENCY ANALYSIS
Comparison with Baseline Methods. Table presents computational efficiency and performance metries across T1, DLinear (Zeng et al. 2023). ModemTTCN (Luo & Wang 2024), iTransformer (Liu et al. 2024), TimesNet (Wu et al. 2023). PStchTST (Nie et al. 2023), TimeMixer++ (Wang et al., 2024 SAITS (Du et al., 2023), ImputeFormer (Nie al.) 2024), CSDI (Tashiro et al.) (021). achieves the best imputation performance on both ETThl and Weather datasets while maintaining reasonable computational requirements. The comparison reveals significant variations in resource consumption across models, with methods like CSDI and TimeMixer++ requiring substantially higher computational complexity, while lightweight approaches like DLinear sacrifice accuracy for speed. T1 demonstrates effective balance between performance quality and computational ef- ficiency, making it suitable for practical deployment scenarios where both accuracy and resource constraints are important considerations.
https://github.com /emmm www.m///mm-mmmmmm------- leries-
16

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Table 7: Computational efficiency and performance comparison on ETThl and Weather datasets. Params (M): parameters in millions; Memory inference memory: GFLOPs: computational com-
plexity; Train Speed: ms per iteration; MSE: Mean Squared Error (lower is better).
Dataset Model
Params (M)
Memory
GFI.P%;
Train Speed (ms/iter)
MSF
T1 (Ours)
0.543
356.45
0.156
29.84
0.049
DLinear
0.024
22.36
0,003
10.04
0.18
MCdemTTN
1.716
120.99
0.039
13.7
0.083
iTransformer
0.223
22.71
0.003
13.95
0.129
TimesNet
0.588
157.78
0.176
39.18
0.13
PatchTST
2.185
2571.3
10.042
89.46
0.082
TimeMixer+
2.357
437.84
6.235
158.13
0.132
SAITS
5.273
294.49
0.506
37.01
0.092
ImputeFormer
1.368
1060.11
0.645
34.49
0.223
CSDI
1.195
777.71
19.045
154.45
0.083
T1 (Ours)
0.715
793.49
0.467
34.37
0.029
DLincar
0.051
29.07
0.008
7.4
0.044
MCdemTTN
2.598
316.17
0.125
11.8
0.038
Weather
Trannforrmer
4.827
119.79
0.203
13.97
0.09
TimesNet
4.698
224.82
1,35
34.59
0,04
PatchTST
0.455
443.88
0.48
21.56
0.037
TimeMixer++
2.357
1000.74
18.705
205.87
0.034
SAITS
5,297
296.32
0.509
34.59
0.034
ImputeFormer
1,551
1948.45
1.936
52.97
0.042
CSDI
0.326
1122.19
18.238
109.6
0.084
Computational Overhead of Channel-Head Binding. We clarify that Channel- -ead Binding incurs no additional computational overhead compared to standard Multi-Head Attention (MHA) when the total representation capacity is fixed. Let M denote the number of variables, C' the number of channels, and L the latent temporal dimension. In T1, each of the C heads processes a single channel with feature dimension L. yielding complexity O(M² C L). Standard MHA with fewer heads achieves the same total complexity by increasing the per-head dimension proportionally.
To empirically validate this, we measured FLOPs and GPU memory usage across three datasets with varying variable counts (Table R). We compare Ti's 1-to-1 binding (Mlaads 128) against grouped-head variants (Theads E 8,,8, 16)) while keeping the total channel count fixed at 128.
The results confirm that FLOPs remain identical across configurations, as theoretically expected. For memory usage, T1 shows minor increase smaller datasets (1-4%) due to maintaining sep- arate head computations. However, on the large-scale Electricity dataset (M 321), TI consumes approximately 7.5% less memory than grouped-head variants, as the simplified channel- oper- ations avoid the overhead reshaping and managing grouped head dimensions. This suggests that the 1-to-1 binding becomes increasingly efficient the number of variables grows.
Table 8: Computational overhead comparison across different head configurations. All variants use 128 total channels.
Dataset
Model
Hcads
Channels
FLOPSs
Memory (MB)
T1 (Ours)
128
128
155.6 M
283.2
Grouped (Base)
128
155.6 M
280.8
ETThl (M = 7)
Grouped
128
155.6 M
280.0
Grouped
16
128
155.6 M
279.8
(Ours)
128
466.9
Grouped (Buse)
466.9
712.0
Weather (M 21)
Grouped
128
466.9
709.7
Grouped
128
466.9
709.2
T1 (Ours)
128
128
23.8 G
18,567
Grouped (Base)
128
23.8 G
20,071
Electricity (M 321)
Grouped
128
23.8 G
20,010
Grouped
16
128
23.8 G
20,026
17

---

C HYPERPARAMETER SENSITIVITY
We evaluate the sensitivity of T1 to key hyperparameters: the number of attention heads (corre- sponding to channel dimension C), convolutional kernel size, and FFN expansion ratio. All models are trained with 40% missing ratio and evaluated on test sets with varying missingness (10%, 30%, 50%, 70%). Results show averaged performance across these test conditions on ETT, Weather, and Electricity datasets in Figure TI demonstrates robust performance across all tested configurations.
Number of Attention Heads
Kernel Size
FEN Ratio
6:43
00445
0.015
0/400
MSE.
MSE
0.055
6:055
00755
0.88
0.003
64
128
256
SI
71
DT7
Weather
Electriitty
Figure 4: Hyperparameter Sensitivity analysis with respect to the number of heads, FFN ratio, and kernel size.
The model shows minimal sensitivity to variations in the number of heads (64, 128, 256), kernel sizes (31, 51, 71), and FFN expansion ratios (1, 2, 4) across all datasets. Among these, C=128 pro- vides a reasonable balance across diverse datasets and missing ratios, which motivates our default configuration. This stability suggests that T1's Channel-Head Binding mechanism and architectural constraints provide natural regularization, making the model less dependent on precise hyperpa- rameter tuming while maintaining consistent imputation quality across diverse datasets and missing ratios.
Table 9: Detailed numerical results for the hyperparameter sensitivity analysis on the number of attention heads under varying missing ratios 10 0.3, 0.5, 0.7).
Number of Heads Metric
64
128
256
MSE
MAE
MSE
MAE
MSE
MAE
0.1
0.023
0.102
0.025
0.104
0.027
0.110
ETTh
0.032
0.116
0.033
0.118
0.036
0.124
0.047
0.139
0.048
0.140
0.050
0.144
0.7
0.095
0,196
0.091
0.192
0,083
0.194
Avg
0.049
0.138
0.049
0.139
0.052
0.143
0.1
0.023
0.088
0.024
0.089
0.024
0.091
E17h2
0.028
0.099
0.029
0.100
0.029
0.102
0.5
0.036
0.115
0.037
0.116
0,038
0.117
0.054
0.145
0.055
0.145
0.055
0.146
Avg
0.035
0.111
0.036
0.112
0.057
0.114
0.1
0.013
0.074
0.013
0.073
0.013
0.075
E17ml
0.3
0.016
0.081
0,016
0.080
0,017
0.082
0.022
0.093
0.021
0.092
0,022
0.092
0.7
0.039
0.123
0.037
0.119
0.037
0.120
Avg
0.022
0.091
0.022
0.1
0.012
0.057
0.011
0.055
0,012
0.056
FTTm2
0.062
0.5
0.018
0.074
0,018
0.073
0,018
0.073
0.027
0.092
0.026
0.091
0.026
0.092
Avg
0.018
0.072
0.017
0.070
0.018
0.071
0,023
Weather
0.3
0.025
0.037
0,025
0.036
0.025
0.037
0.5
0.029
0.043
0.028
0.042
0.029
0.043
0.7
0.040
0.063
0.041
0.068
0.041
0.065
Avg
0.029
0.044
0.029
0.045
0.029
0.045
Flectricity
0.1
0.033
0.117
0.032
0.114
0.031
0.111
0.037
0.123
0.037
0.121
0.036
0.119
0.5
0.045
0.1.6
0.045
0.134
0.043
0.132
0.069
0.174
0.070
0.174
0.068
0.172
Avg
0.046
0.138
0.046
0.136
0.044
0.133
Overall Average
0.033
0.099
0.033
0.099
0.034
0.100
18

---

Table details the sensitivity analysis for the number of attention heads (nz), which determines channel capacity (nA, = C) under our binding mechanism. Results indicate that n = 128 provides favorable balance that ensures robust generalization across diverse data scales and missing ratios. While a larger capacity (ne, = 256) yields marginal benefits on high-dimensional datasets such as Electricity, it compromises stability on smaller ones. Conversely, a reduced capacity (n/, 64) limits the representation of fine-grained series such as the ETTm datasets. This evidence justifies our choice of 128 universal default and confirms that TI achieves robust imputation independent of dataset-specift parameter tuning.
D ADDITIONAL EXPERIMENTS AND ANALYSIS
D.1 IMPACT OF HEAD SCALING
To distinguish the contribution of the Channel-Head Binding mechanism from the effect of simply increasing the attention head count, we performed scalability analysis using iTraasffrmmr baseline. We examined whether augmenting the number of heads Tlbaad in standard Multi-Head Attention could reproduce the performance gains observed in TI.
The evaluation encompassed two scaling strategies designed to match the head capacity of Tl at 128 heads. In the first configuration, we increased Theads while maintaining constant model dimension, which results in reduced head dimension dy. In the second configuration, we increased Nheads while fixing the head dimension, a setup that scales the model dimension dmmaeel proportionally.
As detailed in Tables TO and 11 increasing the head count in standard Multi-Head Attention does not consistently improve performance. For datasets such as ETTh1 and ETTm2, performance tends to plateau or deteriorate under configurations with high head counts. This trend may stem from optimization challenges or overfitting associated with the excessive fragmentation of the feature space or the rapid growth in parameters.
Most importantly, even the optimal iTransformer configuration yields an MSE of 0.072 on Weather, which remains considerably higher than the 0.029 MSE achieved by T1. These results suggest that the performance advantage of TI derives from the structural efficacy of the Channel-Head Bind- ing mechanism in ensuring semantically aligned information transfer, rather than merely from the increased quantity of attention heads.
Table 10: Impact of increasing the number of attention heads (Rheads) ) in i'ransformer while keeping the model dimension (dmodal) fixed. Best results for each dataset are highlighted in bold.
Configuration
0.1 MSE
0.3
U.S
0.7
Avg MSE
Dutasct
dundal
dg
MAE
MSE
MAE
MSE
MAE
MSE
MAE
MAE
128
16
0.089 0.203
0.102
0.215
0.128
0.239
0.203
0.292
0.131 0.237
ETTh1
16
128
8
0.093
0.208
0.104 0.219
0.130
0.240
0.202
0.292
0.132 0.240
32
128
0.095
0.211 0.106
0.220
0.1
0.241
0.202
0.292
0.133 0.241
128
0.097
0.214 0.110
0.225
0.133
0.244
0.211
0.298
0.138 0.245
128
128
0.099
0.216 0.110 0.225
0.135
0.245
0.212
0.298
0.139 0.246
128
0.024
0.095
0.027
0.101
0.033
0.113 0.049
0.140
0.033 0,112
ETTm2
128
0.025 0.096 0.027 0.102
0.033
0.113 0.048
0.139
0.033 0.113
128
0.025
0.098 0.028
0.303
0.033
0.113 0.047
0.138 0.033 0.1
64
128
0.026
0,100 0.028 0.104
0.033
0.114 0.047 0.137 0.034 0.114
128
128
0.026 0. 100 0.029
105
0.033
0.114
0.047
0.136 0.034
0.114
512
64
0.087
0.1 0.089
0.1
0.090
0.140
0.093
0.142
0.090 0.140
Weather
16
512
32
0.1
0.6
0. 12 0.6
113
0.1 05 0.7 0.113 0.177
32
512
16
0.081
0.130
0.082
0.131
0.083
0.132 0.088
0.136 0.083 0.132
64
512
8
0.086
0.136 0.087
0.137 0.088
0.137 0.091
0,1 0.088 0.137
128
512
4
0.069
0.110
0.070
0.110
0.072
0.112
0.077
0.116
0.072 0.112
19

---

Table 11: Impact of increasing the number of attention heads (1hhaads ) in iTransformer while keeping the head dimension (dz) fixed. Best results for each dataset are highlighted in bold.
Configuration danddl
0.3
0.5
0.7 MSE
Avg MSE MAE
Datasel
Tlaadds
de
MSE
MAE
MSE
MAE
MSE
MAE
MAE
128
16
0.089 0.203
0.102 0.215
0.128 0.239 0.203 0.292 0.131 0.237
256
0.090 0.206
0.103 0.217
0.130 0.240 0.216 0.300
0.135 0.241
32
512
16
0.109 0.227
0.120
0.237
0.146
0.257 0.239 0.318
0.154 0.260
64
1024
16
0.129 0.248
0.144
0.259
0.171
0.279 0.256
0.329
0.175 0.279
128
2048
16
0.323 0.379
0.330
0.383
0.347
0.391
0.389
0,410
0.347 0.391
128
16
0.024 0.095 0.027
0.101 0.033
0.113 0.049
0,140
0.033 0.112
ETTm2
16
256
16
0.025 0.097 0.028
0.103 0.033
0.114 0.051 0,144 0.034 0.114
32
512
16 0.029 0.
0.032
1. 0.037
0. 0.050
1.141 0.037 0.1
64
1024
16
0.060 0,158 0.061
0.159 0.063
0.162 0.069
06169 0.063 0.162
128
2048
16
0.067
0.171 0.069
0.172
0.071 0.174 0.075
0.1
0.071 0.174
8
512
64
0.087 0.139
0.089 0.139 0.090
0.140 0.093
0.142
0.090 0.140
Weather
16
1024
64
0.088 0.138 0.087 0.138 0.089 0.139 0.092 0.140
0.089 0.139
2048
0.113 0.176
0.113 0.176 0.114 0.177 0.115 0.177
0.114 0.177
4096
0.113 0.176
0.113
0.176 0.114
0.177 0.115 0.177
0.113 0.177
128
8192
0.113
0.176
0.113
0.177
0.114
0.177
0.115
0.178
0.114
0.177
D.2 SENSITIVITY ANALYSIS ON TRAINING MASK RATIOS
In practical deployment scenarios, test-time missing ratios are often unknown and dynamic. To vali- date the robustness of our training strategy, we conducted comprehensive ablation study by training Ti with various masking ratios (0.1, 0.3, 0.5, 0.7) and evaluating them across a comprehensive range of test ratios.
Table 12:
Impact of training mask ratios on generalization performance. Bold indicates the best performance for each test condition.
Training Missing Ratio Metric
0.7
MSE
MAE
MSE
MAE
MSE
MAE
MSE
MAE
0.1
0.023 0.102 0.023
0.103
0.006
0.109
0.034
0.124
ET
0.3
0.038 0.126 0.033
0.118
0.035
0.122
0.040
0.133
0.5
0.074 0.168 0.051
0.145
0.050
0.142
0.052
0.148
0.7
0.192 0.260 0.106
0.208
00.000
0.181
0.076
0.177
Avg
[0.082 0.164 0.053
0.143
0.004
0.139
0.139|0.051
0.051
0.145
0.1
0.023 0.090 0.024
0.091
0.026
0.096
0.029
0.108
B1
0,3
0.030 0.105 0.030
0.103
0.030
0.105
0.032
0.113
0.5
0.044 0.129 0.039
0.121
0.038
0.119
0.039
0.124
0.7
0.074 0,173 0.063
0.159
0.054
0.145
0.052
0.143
Avg
[0.043 0.124 0.039
0. 18
0.037
0.116
0.038
0.122
0.1
0.013 0.074 0.013
0.073
0.013
0.076
0.016
0.083
ET7ml
0.3
0.018 0.086 0.016 0.080
0.016
0.082
0.018
0.087
0.5
0.033 0.112 0.022 0.093
0.021
0.092
0.022 0.094
0.7
0.096 0.181 0.038
0.122
0.033
0.113
0.031
0.111
Avg
[0.040 0.113 0.022 0.092
0.021
0.090
0.022 0.094
0.1
0.012 0.059 0.012 0.059
0.012
0.060
0.014 0.068
BTTm2
0.3
0.016 0.069 0.015 0.068
0.067
0.016 0.072
0.5
0.023 0.087 0.020
0.080
0.019
0.077
0.019 0.079
0.7
0.041 0.122 0.030
0.102
0.027
0.094
0.026 0.093
Avg
|0.023 0.084 0.019
0.077
0.018
0.075
0.019 0.078
0.1
0.002 0.034 0.021
0.031
0..04
0.068
0.030
0.058
Weather
0.3
0.028 0.046 0.024
0.034
0.031
0.055
0.029
0.051
0.5
0.040
0.028
0.055
0.048
0.7
0.064 0.110 0.038
0.057
0.047
0.078
0.035
0.052
Avg
[0.039 0.065 0.028
0.041
[0.036
0.064
(0003
0.052
Eleatricity
0.1
0.034 0.117 0.037
0.123
0.044
0.140
0.053
0.154
0.3
0,042 0.132 0.042
0.131
0.046
0.140
0.056
0.157
0.5
0.070 0.176 0.052
0.148
0.052
0.147
0.059
0.159
0.7
0.240
0.347 0.115
0.230
0.071
0.177
0.068
0.168
Avg
[0:097 0.193 0.061
0.158
0.053
0.151
0.059 0.160
20

---

Table 12 presents the detailed results across six datasets. As expected, models generally achieve optimal performance when the training missing ratio closely aligns with the test ratio. However, the results demonstrate that TI maintains high robustness even under distribution shifts; performance degradation significant only when there an extreme discrepancy between training and testing conditions (e.g., training at 0.1 and testing at 0.7).
These findings support our choice masking level, it provides reasonable coverage across both sparse and dense conditions without requiring prior knowledge of test-time missing distributions. This allows a single TI model to be deployed across diverse missing patterns without instance-specific tuning.
0.4 training mask ratio as a practical default. As a moderate
D.3 COMPARISON WITH DIFFUSION-BASE BASED MODEL
We compare TI against SSSD AAcaaaaz & Strodthoff 2023). diffusion- -based imputation model that achieves strong performance through iterative stochastic refinement.
presents the comparison across seven datasets under varying missing ratios. Tl achieves lower MSE on most configurations, with notable improvements on ETTm2 (83.18% average MSE reduction) and Illness (81.70%).
Imputation Performance. Table 13
Table 13: Performance comparison between TI and the diffusion based model SSSD across varying missing ratios.
Models Metric
(Ours)
SSSD
Improvement (%)
MSE
MAE
MSB
MAE
MSE
MAE
0.024
0.104
0.028
ETThi
0.033
0.118
0.037
0.130
11.2
9.75
0.5
0,048
0.139
0.052
0.152
9.1
8.35
0.7
0.093
0.193
0.087
0.193
-6.7
0.39
Avg
0,049
0.138
0.051
0.148
6.44
7.03
0.1
0,024
0.089
0.043
0.132
45.21
32.04
BTTh2
0.3
0,029
0.100
0.056
0,150
48.76
33.40
0.5
0.037
0.116
0.087
0.187
57.05
37.80
0.7
0.055
0.146
0,214
0.294
74.18
50.40
Avg
0.036
0.113
0.100
0.191
56.30
38.41
0.1
0.013
0.073
0.018
0.092
30.16
20.52
ET1ml
0.016
0.080
0.025
0.103
35.96
22.28
0.021
0.122
44,21
25.20
0.037
0.120
0.080
0.169
53.89
29.29
Avg
0.022
0.091
0.040
0.122
41.05
24.32
0.011
0.056
0.044
0.133
$8.16
ETTm2
0.3
0.014
0.063
0.071
0.172
80.39
63.64
0.5
0,018
0.073
0.131
0.238
86.28
69.39
0.7
0,026
0.091
0.330
0.383
92.06
76.25
Avg
0.017
0.070
0.144
0.231
83.18
66.86
0.1
0.023
0.034
0.026
0.031
12.05
-9,83
Weather
0.3
0,025
0,037
0.030
0.039
15.2
13.86
0.5
0.029
0.043
0.036
0.048
20.3
39.86
0.7
0.041
0.066
0.051
0.069
19.76
3.87
Avg
0.029
0.045
0.036
0.047
16.84
1.94
0.1
0.001
0.014
0.003
0.035
54.25
59.34
Exchange
0.002
0.016
0.004
0.041
53.80
61.40
0.002
0.019
71.78
67.19
0.7
0.003
0.025
0.024
0.103
89.04
75.86
Avg
0.002
0.018
0.009
0.059
67.22
65.95
0.016
0.073
0.109
0.166
85.59
55.83
Illness
0.3
0.020
0.081
0.141
0.193
86.06
58.27
0.5
0.031
0.098
0.195
0.231
84.10
57.50
0.7
0.085
0.157
0.293
0.293
71.05
46.47
Avg
0.038
0.102
0.184
0.221
81,70
54.52
21

---

Computational Efficiency. Table 14 compares computational requirements. TI's single-pass chitecture provides substantial efficiency gains: approximately 1,344x faster inference and 4,295 x faster training compared to SSSD's multi-step denoising process. TI also requires significantly fewer parameters (0.54M vs. 48. IM) and less memory (234MB vs. 5,646MB), making it more practical for resource-constrained deployment scenarios.
Table 14: Computational efficiency comparison between TI and SSSD.
Metric
T1 (Ours)
SSSD
Ratio
Parameters (M)
0.54
48.11
89x smaller
GFLOPs
0.155
1.863
12x less
Training Memory (MB)
234
5646
24x less
Inference (ms/sample)
0.60
811
1,344x faster
Training (ms/iter)
47
201,845
4,295 faster
22

---

D.4 VISUALIZATION CROSS- VARIABLE ATTENTION PATTERNS
Clean
Moun Are 2ie Tugg:: Totare
Peak
Nar-Pak
Time
Time series with masking and attention heatmap target variablle (var4)
Clmm
(b) Inter-variable atiention maps (7x7) for top 10 heads
Non-Peat
(c) Attention difference from clean condition
Figure 5: Extended attention analysis under varying missingness patterns (expansion of Figure 3(b)). (a) Left: Example time series (var4 from ETTh1) with four masking strategies targeting peak, non- peak, high-variance, and low-variance regions. Right: Mean attention weights the target variable across 10 heads and conditions. (b) Full 7x7 inter-variable attention maps for the top-10 10p-10 heads (sorted by clean attention weights). Magenta lines indicate the target variable (var4). (c) Atten- tion difference from the clean condition, showing how each head adapts its attention distribution in response to different missing patterns. Red indicates increased attention; blue indicates decreased attention.
To provide quantitative illustration of Channel- Head Binding effects, extend Figure B with detailed attention maps. While Figure 3(b) visualizes the top-20 20 heads, here we focus on the top-10 heads for clearer presentation of attention dynamics under different masking conditions.
23

---

We use single ETTh1 test sample with 7 variables. Following the experimental setup in Sec- tion 4.2.4 we mask 30% of the target variable (var4) using four strategies targeting different tem- poral characteristics: peak regions, non-peak regions, high-variance segments, and low-variance segments.
Figure 5 5)b) reveals that different heads learn specialized attention patterns. Some heads exhibit strong diagonal patterns indicating velf-bariable focus, while others develop off-diagonal connec- tions capturing cross-variable dependencies.
Figure c demonstrates that these attention patterns adapt to the missingness configuration rather than remaining static. When var4 is masked, many heads reduce their atfention var4 and redis- tribute it to other variables. This indicates that the model recognizes unreliable sources and seeks information from alternative variables, enabled by Channel-Head Binding.
E
CASE STUDY OF PHYSIONET2012
E.1 DATASET CHARACTERIZATION
PhysioNet Challenge 2012 contains multivariate clinical time series from 4,000 ICU patients with 37 physiological variables recorded approximately 48 hours. The dataset exhibits substantial variable-level heterogeneity in missing rates, reflecting real-world clinical measurement protocols. Vital signs (13 variables) range from 19% 94% missing, where continuously monitored signals (e.g., HR at 19%) contrast sharply with intermittently recorded ones (e.g., NISysABP at 94%). Lab measurements (23 variables) range from 51% to 100% missing, as they require explicit sample collection. This heterogeneity- whhee missing rates vary by an order of magnitude even within the same category- PhysioNer2012 an ideal testbed for evaluating T1's 's imputation robustness under realistic, non-uniform missingness.
Table 15: PhysioNet2012 variable-level missing rate distribution by category.
Category
Vars
Missing Rate
Examples
Vital Signs
13
0.19 0.94
HR (0.19), Urine (0.37), Temp (0.67), NISysABP (0.94)
Lab Measurements
23
0.51 1.00
Mg (0.51), PaO2 (0.90), Cholesterol (1.00)
E.2
PER- VER-VVAIBBLE IMPUTATION PERFORMANCE
To examine per-variable imputation behavior, we report MSE and MAE for six representative vari- ables spanning diverse missing rates (0.19 to 0.91) under the 0.5 additional masking condition (total 900% missing). Table 16 presents results for both vital signs (HR, Urine, Temp) and lab mea- surements (Mg, PaO2, HCT). Variables were selected to represent diverse missing rates across both categories.
Table 16: Per-variable imputation performance on PhysioNet2012 under 0.5 additional masking. Variables span diverse missing rates (0. (0.19-). across vital signs and lab measurements. Best results are in red bold, and second best are blue underlined.
Variable
Category
Natural Missing Rate
TI (Ours)
TimesNet MSE
DLineur MSE
ImputeFormer MSE
SAITS MSE
PatchTST
MSB
MAE
MAE
MAE
MSE
MAE
HR
Vital
0.19
0.189
0.296
0.237
0.347
0.245
0.356
0.392
0.431
0.208
0.309
0.351
0.439
Urine
Vital
0.37
0.364
0.297
0.408
0.318
0.408
0.322
01.458
0.330
0.426
0.279
0.420
0.332
Temp
0.67
0.239
0.306
0.222
0.300
0.214
0.339
0.186
0.327
0.186
0.317
0.227
Mg
Lab
0.51
0.126
0.171
0.190
0.225
0.195
0.228
0.207
0.203
0.133
0.165
0.299
0.321
PaO2
Lab
0.90
0.067
0.085
0.082
0.118
0.083
0.117
0.094
0.077
0.094
0.079
0.091
0.120
0.087
0.094
0.128
0.127
0.097
0.076
0.097
0.095
0.127
TI achieves the lowest MSE across all six variables, demonstrating consistent improvements regard- less of the inherent missing rate. Notably, the model maintains its performance advantage even for variables with extremely high missing rates (e.g.. PaO2, HCT), confirming its capability to robustly reconstruct dynamics from sparse, irregular observations where baseline methods often struggle.
24

---

E.3 QUALITATIVE VISUALIZATION
To provide a clear comparison among different models, we present imputation showcases for three representative variables in Figures 6 which produced by the following models: TI. Times- Net (Wu et al. ).23). PStchTST (Nie et al. 2023), DLinear (Zeng et al., 2023). ImputeFormer (Nic) al. 2024), and SAITS (Du al. 2023). All results shown under 50% additional masking.
Among the compared models, TI produces the most accurate imputations across various sparsity levels.
TimesNet
PatchTST
SoundTuuh
22-
Greandhuu
294
Aeticii Misino
2--
Anhad Mosie
2.-
54-
39
1.0
DLinear
ImputeFormer
SAITS
2.4
Fred cSan
Dtooved
34
Natural Massin
1%
Naruraa
1.5
Netural Masinng
63
3.
Figure 6: Visualization of imputation results PhysioNet2012 for HR.
Brssnchthh AdFicii Wasligg
Ore PraaniTuus
Ocsereed
Artifical
TUTURI Waiiig
Ratural
-2.
-25-
DLinsar
ImputeFormer
SAITS
Prodiction
Anticcal Mooding
3.
Figure 7: Visualization of imputation results PhysioNet2211 for Temp.
25

---

TimesNet
PatchTST
W
V
W M
M
W
N
wid.attion Ohvereed Hariara nelscin
Chverved Bar Milciinn
Chaarred
DLinear
Imputeformer
SAITS
M
M
M
M
-25
Pinictian GraundPuahh Ar M.30
-.5-
satin CrouncThuss
GrouncTuth
-23-
Artiiica Mausing
Artiical Mustng
-25
Figure 8: Visualization of imputation results on PhysioNer2012 for PaO2.
F FULL RESULTS
Table 17: Full results with point missing ratios( 0.1, 0.3, 0.5, 0.7) across datasets.
Models
(Ours)
TimeMnurre:
Modern TCN
ITTenffomerr
Timonnt
PacchTST
DI inliner
Impusefommer
Saits
CSD MSE
BRITS
Mealc
MSE
MAE
MSE
MAE
MAE
MSE MAE
MSE
MAE
MSE
MAE
MSE
MAE
MAE
MSB MAE
0.161
0.204
0.00
0.229
0.251
0.238
0.065
0.15T
0.089
0.187
0.122
0.290
0.200
0.208
0.300
0.347
0.429
0.2114
0.291
0.14
0.334
0,289
AAg 0.049
0.138
00.122
0.252
[0.053
0.159
66.12
0.236
[1,130
0.237
6.002
0.155
0,1180
0:273|0.223
0.273
0.223
0.266
(0,092
0.17M
0.005
0.178
(0.121
0.223
(0.126
0.231
IU024
0.089
00.057
0.148
[0.041
0.131
10,05]
0.148
10,053
0.155
10,006
0
0.066
0.172
0.132
0.212
10.18
0.254
00005
11110
0.126
0.247
0,035
0.124
Fm12
1.029
0.100
0.060
0.151
0.441
0.130
0.083
0.154
[0,044
0.156
0.009
0.127
0.055
0.156
0.153
0.251
0.185
0.276
0.054
1.127
0.162
0.281
10041
0.133
0.5
I0037
0.116
0.067
0.160
0.043
0.141
0.064
0,166
(0.063
0.167
0.045
0.141
0.067
0.171
0.356
0.342
0.230
0.331
0,075
0.150
0.252
0.357
0.047
0.145
0.7
0.055
0.146
0.067
0.156
[0007
0.178
000055
0,195
[0,092
0.201
0.005
0.178
0.104
0.215
1.047
0.611
0.583
0.507
0.116
0.158
0.385
0,443
(.055
0,165
Arg
0,036
0.161
[0.05]
[0.064
0.165
(0,049
0.073
|.178|0.429
0.178
0.354
00275
0.342
0.075
0.144
(02226
0.327
[1046
0.013
0.242
0.025
10,02
011124
FTT
0.118
0.041
0.001
0.027
0.102
0.037
0.040
0.120
0,021
0.091
0,002
0.125
0003
0.116
00025
10,035
0.001
0.112
0.009
0.188
0.0's
0.158
00058
0122
0.006
0.117
(.053
0.06)
0.048
0,133
0.837
0.120
0//94
01
(0085
0.179
0.110
0.206
10.095
6.187
0.008
0.133
0.279
300
0.205
0.244
0.129
0.210
0.054
0.144
(1158
0.276
(1066
0,158
Arg 0,022 0.091
10:02
0.136
(0040
0.124
10,003
0.159
(0,045
0.130
6.008
0.13910.110
10.132
0:225
00006
0.155
10,051
0.12?
000034
0.114
(0077
0.166
(K.047
0,131
0J811
0.656
0.004
01888
1019
0094
10.004
0.005
[0,021
0,088
10.017
0.044
0.037
0.127
0.061
0.121
100057
0.155
00002
0.067
(1050
0.177
1.016
0.085
FT1e2
0.014
0.063
0.000
00000
(020)
0085
0,021
0.101
(0021
0.050
0.019
0.079
0.028
0.108
0.057
0.132
0.071
0002
0.108
0.225
1001
0,088
0.018
0.073
00000
0009
1020
0099
0,002
0.111
10006
0.095
0.0023
0.077
0.035
0.11
0.100
(1200
01091
(.211
0:318
0002
0,096
0.036
0.091
00:41
0.119
1000
01:2
0.046
0.136
(0.000
1.125
0.006
0111
0.000
100
0.562
0.317
0.190
0.273
0.111
(0.992
0.596
1.0.2
0.110
Arg 0.017
0.070
00000
0.000
[0002
0.099
10,052
(0,02)
1000
10,004
(0040
0.124
01183
00:03
0.201
10:035
(0:245
0.314
Wosterr
0,025
0,023
0.004
0001
0.04
0051
0049
0.008
10,002
0.055
(0.045
0.025
0.093
0.063
0.050
0.05
0003
1004
0.092
0.038
00055
(00026
(UU5T
0,009
0.062
(.090
0,066
0,029
00034
0004
0054
00000
0.138
0.00
0,000
0.09
00000
0.09
(.07%
0.041
0.065
0.045
0.71
0051
00093
0.003
0.140
0.
102
0.049
0.059
0.060
0.10
0.065
0084
0085
0.77
0.099
0.307
0.256
1.1
0.086
Aag 80829
0.045
0.084
0055
[0038
01072
10,000
0.198
10,040
0:079
10.007
(1059)
0.044
0.064
0.042
0053
10.194
000084
IJ:42
(0112
0.117
(0.007
0.072
PPMSOX
0.014
0.015
0.076
0.078
0.085
0.000
0:13
0:131
1044
8054
01129
0. 8.162
0,006
0,029
0.134
0.116
10,048
10,000
0.138
0,160
00,022
0.029
0. 1210
0.136
0.047
0.155
0.269
0.025
0.023
1000
0.009
00049
0005
0.134
01147
0.113
0
0.141
0.147
0L8488
0.155
0.125
0.144
(0044
0.0166
0.142
0.146
1.018
01156
0.096
0.500
0.000
0.155
0L06k
(1174
0.000
0.130
0.006
01175
10106
0.242
0.002
0.206
[0.101
0.150
200
0.216
0.349
0.077
0.181
0.078
0.177
0.125
0.255
(.056
0.159
Aag
01443
0005
2220
0.000
1o.60
0.155
0.176
Exclunge
0,001 0.014
00000
0000
0047
0.003
0/009
(0.00)
0.029
00000
0.033
0.000
0.077
00018
0.042
10090
0.215
00008
0.057
(10034
0.117
(10.2 0.003
I.002 0.016
0.000
0000
0057
0.001
0.011
0.001
0.00%
0.0002
0.033
0.000
0.83
0.066
0.44
0.127
0. 00904
0.006
0.051
(1050
0.175
0.026
0.00%
IU902
0.019
6010
0067
0.004
0.015
00001
0,030
0.001
0.025
0.004
0.05
0.019
0.557
0.184
0.351
0.006
0.053
(1113
0.273
n003
0.006
0.003
0.025
01003
0013
0078
0.000
0.042
[0.005
0.041
0.004
0.057
0.008
0.057
0.071
0.135
(0.311
0.447
0.008
0.050
(1277
0.434
(1039
0.083
Aug RJ802 0.018
10.002
0022
[0000
0.05
10.004
0.004
(0.007
0.012
10.003
0.027
10.005
0.04
0.001
0.070
10.180
944
[0.007
0.054
10.15 0.2400
(0003)
0.006
0,016
0.073
00.167
0.24
0.356
00.
0.225
10.435
(0.
1000000000
0
0:414
0.408
0.608
0.435
0.:99
0.905
11
12.22
(0233 0.291
(.029
0,086
Einco
0.081
0.
0251
01:44
0.256
0.151
0.545
0.468
0.484
0.442
677.8
10.65
0.317
0.341
0.056
0.109
0.208
005885
0.64%
0.515
0.670
0.908
167.9
7,866
(0451
0.419
10:00
0.377
0.500
0.370
0.854
0.565
0.516
0.850
0.600
0.944
0.621
189.5
5.476
(0.701
0.543
0,170
0,835
0.291
(0.205
00.345
0.392
0.636
(0.614
0.495
1566.9
9:057
(0-42
0.399
0.067
Fleatnatt
0,851
0.636
0.119
0.112
10005
0.000
01145
0.153
01124
0088
0.308
10
0,003
0.153
10.05
(0,002
0.213
10
6,000
1.5
0 199
0.162
0.235
0:3W
0.04
0.148
10.133
0.136
0.264
0.250
10.130
0.135
0.336
0.219
0.135
0.242
0.263
(.089
0.196
0,043
0.131
0.064
01165
0085
0.208
0.068
0.174
11.13
0.224
0.07%
0.193
0.121
0.257
0.099
0.171
0.149
0.272
0.145
0.237
0.171
0.305
0.115
0.220
0.063
0.162
00.15
0.226
(1119
0.337
0.180
0.300
10.128
0.215
0.130
0.258
0.302
0.457
0.13
0,247
0,199
0,511
0.167
0.258
0.247
0.378
0.144
0.239
(Ang 0J043 0.131
(0.07]
0.172
[8121
0.253
10,000
0.199
(0.105
0.225
|0,009
0.208
[0.191
0.351
000076
0.177
(0.152
0.277
00.144
01235
00168
0.205
(0.006 0,205
26

---

Table 18: The standard deviation of Table 17
Mexteis
T7 (hur))
MidennTUN
Iiranfommnt
Timeenet
PacchTST
Soite
CS11
BRTTS
PSW-1
Meuse
MSE
MAB
MSE
MAE
MSE
MAE
MSE
MAE
MSE
MAE
MSE
MAE
MSE
MAE
MSE
MAE
MSE
MAE
MSE
MAE
MSE
MAE
MSE MAE
0.001
0.008
10.004
0.005
10.001
0:001
0.000
0.001
(0:00)
0.001
0.007
0.000
0.005
0.02
0.008
0.004
ETT
0.11
0.001
0.002
0.001
0:001
0.000
0.001
0.000
0.001
0.001
0.023
0.005
0.009
0.008
0.04
0.004
0.006
0.004
0.008
0.004
00.00
0.007
0.003
0.002
0.000
0.008
0.001
00003
0.003
0.010
0.004
0.006
AAv
0.001
0.001
[0.015
0.013
10,004
0,004
[0,00]
0,001
[0.00]
0.002
0.002
0.003
[0001
0.001
[0,04
0.029
10.014
0.015
0.006
0,005
[.005
0.007
10,005
0.007
0.000
0000
(00001
0.001
[00001
0.001
000000
0.001
[0000]
0.002
(0:000
0:001
0J091
0:0015
100017
0.01
0.0237
0,00
[1007
0.002
0.000
Fm
0.000
0.001
0.000
0.000
0.000
0.001
0.000
0.000
0.001
0.001
0.000
0.000
0.000
0.000
0.023
0.009
0.017
0.016
0.003
0.002
[,005
0.002
(00065
0.002
0.000
0001
00000
01001
0.000
0:001
0.000
0.000
0.000
0.001 (0:001
0:001
00001
01001
00005
0:006
0.000
0.011
0.012
(10m
0.00
0.00
0000
(0:001
0.001
000001
0.000
0.000
0.001
00000
0.005
(0.00)
0.001
01001
0.001
00009
0.004
0.139
0.063
0.007
0.00
[1001
0.003
(0.00)
0.000
Avg
01000
01001
(0000]
01001
[0,00]
0,001
[0,000
0,001
[0,00] 00002 (0:00) 00001
[1,00
01001
[OOMS
0.015
|0,0M8
0.127
0.000
01000
11005
0,005
[0000
0.000
0.000
10:000
10,001
0.002
10,001
0,001
[00002
0.004
(0:000
00004
01004
100004
10,001
0.008
00002
[1001
0.002
(0.00)
0.000
Em1hl
0.000
0.000
0.000
0.001
0.000
0.001
0.001
0.001
0.003
0.003
00:000
0.000
0.001
0.001
0.013
0.000
0.004
0.001
0.001
0201
(1009
0.000
(0000
0.009
0.000
0.000
0.000
0.001
0,000
0.001
0.001
0.002
0.004
0.003 00:000 0.001
0.001
(..01
0.032
0.001
0.000
0.008
0.002
00003
1.000
0.006
(,000
0.008
0.000
0000
01000
0,0011
0,002
000003
0,0012
(0,009
0.006 (1.015
0:017
[0002
11001
00100
00085
0.009
00000
0.003
010011
[1005
0.000
(00003
0,000
Avgg
01000
0.000
00000
10000
0.002
[0,001
0,001
[0,00]
0,002
[0,004
0.004 (0,005
0.004
[0,002
01000
100005
0.023
10.01]
0.017
0.002
0,002
[U005
0.007
[0,003
0.007
(000)
0.000
100000
0.002
000000
0.000
0,000
0.001
(0:000
0.001
0.00%
0.005
10000
0,005
0.001
0,002
1,005
0.003
(0,003
0.003
ETTha2
0.001
0.000
0.000
0.000
0.000
0,000
0.000
0.007
0,010
0.011
0.001
0.006
0.007
0.000
(0.00]
0,000
0.001
0,000
0,000
[0003]
0.001
(0,000
0.0000
0.021
0.012
[U006
0.002
(0006
AvE 0.000
0.001
[0.00]
0.002
10,000
0,001
[0,000
0,000
|0,000
0.001 (0,000
0.000
(U000)
0,001
[0,029
0.019
10.013
0.014
0.006
0,002
[U005 0.005
10,005
0,005
Weather
0.001
0.000
0.001
0.001
10.000
0.000
0.001
0000)
10002
00000
0.005
0:201
10,000
0.000
0.000
0.000
[0,00]
0.00]
0.003
0.003
0,000
00000
0.001
0.001
0.004
0.001
0,002
01001
00000
0.003
0.004
0.004
10,000
0.000
0.000
0.001
0.092
0.045
0,035
0,035
[,005
[,004
0.010
0.003
(0,005
(00004
0.003
0.010
0.000
8000
0.000
0000
00011
0:00
0:000
0:000
0.001
0.002
(0:00)
0:00
0.001
0.001
0.00
0.011
0.002
0.088
D08t
[1000
0.009
0.000
0.001
000000
0.001
0.000
0.004
0.001
0.000
0.001
0.002 (0.002
0.004
0.001
0.001
000004
0.006
0.002
0.004
0.009
0.061
[1002
0.001
[0.00] 0.001
[0.000
0.001
|0.001
0.003
|0,000
0,000
|0.00] 0.002
[0000
10.003
10.001
0.002
0,042
[1005
0.006
PEMSI4
0.000
0.000
0.000
0.001
[0.00]
0.001
0.000
0.002
10.002
0.001
0.001
0.002
10.001
0.000
0.003
0.001
10,002
0.001
0.005 00:002
0.001 0,000
0.001
0.004
0.001
0.000
0.001
(0.000
10.003
0.002
0.005
0.065
10,000
0.001
0.002
0.001
0.067
0.113
0.141
0.145
0.008
0.009
0.009
0u000
10,005
0,009
0.009
0,000
0.000
0000
01001
0,000
0.001
0.001
0.001
0,002
0.005 (0:000
0.0000
(1000)
11.0000
0.019
0.001
0.005
0.088
0.188
[.003
0:000
(00003
0.000
0.7
01005
0000
(0:0
01000
00000
0.007
000003
0.004
[.006
0.071 (0:000
0.001
(10000
10:000
0000%
0.000
0.007
0.00%
0.008
0.177
[.009
0.007
(0.009
0.000
Avg
0.001
0000
[0:00]
01000
[0,001
0,001
[0,00]
0,002
0.007 (0:00) 0.001] [0,005
[0.001
0.001
[00023
0:028
|0,001
0.005
010003
0.155
[1,07
0.006
[0:007 01000
Eachanez
0:000
0.000
(0:000
0.001
0.011
0.010
0.13
0.008
0,00
0.009
0.000
0.000
0.000
0.000
0.009
0.061
0.001
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.004
0.010
0,010
0.010
0.083
0.005
0.005
0.005
01000
0,000
0,000
000000
0,000
0.000
0.000
00,000
000000
01008
000064
0,000
0.008
0.000
(U009
0.004
(0/00
Aigg 0.000
00000
10,000
0.000
10,000
0,000
10,000
0,000
|0,000
0.000 (0,000 0.000]
[1000)
0,000
[0.023
0:025
|0,005
0.011
0.007
0,054
[U004 0.004
(0,004 0,006
0.001
0.003
00.00
0.043
10007
0:025
10,000
0:084
0.023
0.011
(0:003
0.002
0.023
0.030
0.017
0.004
0.039
596
549
5,643
[UOOS
0.005
10:005
0,005
0.42
0.019
0.01
0:000
0:001
0.010
00:001
0.008
0.011
0.073
0.042
411
691
0.007
0.004
0.044
0,40
0.023
0.015
0.000
0:001
0.016
0.009
(0:00)
0.14
0.009
0.026
0.075
0.038
218
524
9.325
0.006
0.007
(0.006
00004
01031
0.049
0,016
0,009
0,004
0.015
0.006 (0,010
0.001
(1.11
0,012
0000
0:011
0.002
0.045
119.279
3.150
[UBOT
0.006
(0/007
0.002
[0.04]
10.002
0,019
10,002
0,003
J0L018
0.009 00004
0,013
10.075
0.041
(335.336
[L006
0.006
10,006 0.006
Elenleilt
0.000
0.001
10.007
0.008
10,004
0.207
10,002
0,003
[0,00]
0.000
0.001 0.002
0.005
0.004
0.003
0.004
10,003
0.002
0.025
0,019
0.008
0.005
10:005 0.005
0.000
0.000
0.007
0.008
0,002
0.203
0.000
0.000
0,000
0.000
0.000
0.000
0.001
0,602
0,003
0.004
0,002
0
0.021
0.015
[.002
01001
(00022 0.001
0.000
8000
0.008
0.007
0.001
0.007
0.000
0.000
0.000
0.000 00:00) 0.000
0.001
0.001
010044
0.007
0.003
0.002
0.019
0.015
[.00%
(1000
(0/00) 0.002
0.001
0000
0.007
0.007
00001
0.014
0.002
0.002
0.003
0.003 (0:00) 0.001
0.002
00000
0.016
0.000
0.007
0.008
0.016
0.013
[.002
01000
(0:001 0.009
AAvg 0.000
0.001
[0.007
0.007
[0,005
0.005
[0.00]
0.001
[0,00]
0.001
0.000
0.001
[0002
0.002
0.007
00004
0.003
0.020
0,016
[0,04
0.004
[0,004 0.004
Table 19: The standard deviation of Table 3
TI (Ours)
TimeMixert+
ModemTCN I'Transfrmmer MAF
TimesNet
PatchTST
DLiineu
ImputeeFrreer
SAITS
Dataset
MSF
MAF
MSF
MAF
MSF MAF MSF
MSF MAE
MSF
MAF
MSF
MAR
MSF
MAF
MSE
MAF
ETTb1
0.004 0.003
0.010
0.010
0.011
0.008 0.002 0.002
0.003
0.002
0.003
0.003
0.003
0.001
0.008
0.010
0.0022 0,005
BTTh2
0.002 0.001
0.002
0.001
0.004 0.003 0.006 0.002
0.002 0.002
0.000
0.001
0.006
0.003
0.022
0.008
0.014 0.015
ETTm1
0.003 0.001
0.002
0.002
0.003
0.003 0.003 0.002
0.007 0.005
0.000 0.000
0.004
0.005
0.025
0.006
0.004 0.008
BTTm2
0.001 0.001
0.000
0.002
0.001
0.001 0.001
0.001
0.001 0.901
0.001 0.000
0.002
0.001
0.008
0.004
0.010 0.014
Weather
0.001 0.001
0.001
0.001
0.003
0.007 0.001
0.000
0.003 0.003
0.002
0.002
0.001
0.002
0.002
0.004
0.001 0.001
PEMS03
0.000 0.001
0.003
0.004
0.002
0.004 0.001
0.003
0.002 0.005
0.003
0.005
0.001
0.001
0.004
0.008
0.001 0.001
Exchange
0.001 0.001
0.000
0.000
0.000
0.001 0.002
0.001
0.000 0.000
0.001 0.000
0.001
0.000
0.006
0.010
0.007 0.013
Iness
0.011
0.007
0.037
0.038
0.044
0.033 0.007
0.005
0.017
0.007
0.023
0.008
0.038
0.021
0.016
0.008
0.045 0.034
Flectricity
0.002
0.001
0.007
0.007
0.004
0.007 0.002
0.004
0.001
0.000
0.001
0.002
0.006
0.005
0.003
0.004
0.003 0.002
Avg
0.003
0.002
0.007
0.007
00.008
0.007 0.003
0.002
|0.004
0.003
0.004
0.002
0.0007
0.004
0.008
0.007
|0.010 0.010
Table 20: The standard deviation of Table
PhystoNet2012- - Natural (80% + Additional Missing
Additional Missing Ratio
T1 (Ours)
TimeMixer+++
McdemTCNN
iTransforseer
TimesNot
PatchTST
DLincar MSE MAE
ImputeFormer MSE
SAITS
MAG
MAE
MSE MAE
MSE MAE
MAE
MSE MAE
MAE
MAE
0.1 (Total: 82%)
10.033 0.802 0.001
0.001
0.031
0.027 0.012 0.006 0..014
0.006 [0.026 0.018
0.006
0.003 0.010
0.009
10.019
0.002
0.3 (Total: 96%)
0.005 0.002
0.376
0.001
0.029
0.024
0.006
0.005 0.010
0.005
0.018 0.014
0.005
0.003
0.010
0.008
0.010
0.002
0.5 (Total: 90%)
0.004
0.002
0.035
0.001
0.027
0.019
0.011
0.004
0.015
0.006 0.003
0.010
0.007
0.012
0.802
0.7 (Total: 94%%)
0.006
0.002
0.164
0.002
0.018
0.013
0.009
0.005
0..088
0.005 0.012 0.008
0.010
0.005
0.009
0.006
0.010
0.002
Avg
00.004
0.002 0.144
0.001
0.026
0.021 0.010 0.004 |0,010 0.005 |0.018 0.013|0.007 0.003 0.010
0.007
10.013
0.002
AQ136 Natural Missing Only (15-30%)
Test Set
|0.007 0.003
0.003/0.015
[..05
0.005
0.0077
0.004
00.008 0.004
|0.008 0.007 [0.004 0.004
0.000
0.006
0.024
0.024
|0:007 0.907
27


Reviews:
[{"review_id": "EVbANM41SI", "reviewer": "Reviewer_tunt", "summary": "This paper proposes a new model for filling in missing values in multivariate time series. Its key innovation is Channel-Head Binding, which creates a direct, one-to-one link between feature-learning CNN channels and information-sharing attention heads. This allows the model to selectively transfer information between variables based on which temporal patterns are reliable, preventing corrupted data from spreading.", "questions": "1. How is the number of  convolution channels chosen, In other words, why set it to 128 while training?", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "1. The one-to-one \"Channel-Head Binding\" is a novel and clever way to fuse CNNs and Transformers for robust imputation.\n2. Extremely thorough testing on diverse datasets and challenging missingness scenarios, with strong results.\n3. The paper is well-structured, the problem is well-motivated, and the model is clearly explained with helpful diagrams.", "weaknesses": "A substantive assessment of the weaknesses of the paper. Focus on constructive and actionable insights on how the work could improve towards its stated goals. Be specific, avoid generic remarks. For example, if you believe the contribution lacks novelty, provide references and an explanation as evidence; if you believe experiments are insufficient, explain why and exactly what is missing, etc.\n1. The number of the convolution channels in T1 is set to 128 during training and is the only hyper-parameter, but no experiment or discussion is provided to explain the reason and the influence of this parameter setting. A simple contrastive experiment would prove the strength of  convolution module better.\n2. The paper only points out the limitations of current convolution and Transformers in imputation, more explanation on the reason or theoretical strength of such combined construction would much improve readers’ understanding.\n3. In section 3, when introducing the architecture of T1, lots of convolution and transformers architecture can be used as analogy, which can help readers familiar with these models to more quickly grasp the structural principles and design innovations of T1.\n4. If I understand it right, in figure 1(a), the output of convolution embedding is described as “Feature”, while all the other places in the paper, this dimension is described as “Channel”, Aligning this term would make it much clearer.", "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": "6BP6Sn7AX8", "reviewer": "Reviewer_4xsq", "summary": "This paper proposes T1, a CNN-Transformer hybrid model for multivariate time-series imputation under heavy and diverse missing patterns. The key innovation is Channel-Head Binding (CHead Attention), which establishes a one-to-one correspondence between CNN channels (for temporal feature extraction) and Transformer attention heads (for cross-variable information transfer). This allows selective, feature-level interactions that mitigate error propagation from corrupted observations. The architecture uses modernized temporal convolutions with depthwise and pointwise operations to handle sparse data robustly. Experiments on 11 benchmark datasets show T1 outperforming baselines, with strong generalization to unseen missing patterns and a single hyperparameter setup across datasets.", "questions": "1. What is the computational overhead of Channel-Head Binding compared to vanilla CNN-Transformers? Ablations on channel/head counts would be useful.", "limitations": "", "rating": 6, "confidence": 3, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "1. Novel Architectural Design: The Channel-Head Binding mechanism is a clever integration of CNNs and Transformers, addressing a clear limitation in prior tokenization strategies (e.g., time-axis, variable-axis, or dual-axis approaches). By aligning channels and heads, it enables fine-grained control over information transfer, which is particularly effective for imputation where missingness corrupts specific temporal patterns. This hybrid approach leverages CNNs for robust local feature extraction and attention for adaptive cross-variable fusion, making it well-suited to real-world sparse data scenarios.\n\n2. Strong Empirical Results: The reported average MSE improvement over the second-best baseline is impressive, especially under extreme missing ratios. The model's ability to generalize to unseen patterns without retraining and its use of a unified hyperparameter configuration highlight its practicality for diverse domains like healthcare, finance, and climate monitoring.\n\n3. Efficiency and Robustness: T1's design emphasizes efficiency through convolutional operations and avoids common pitfalls like naive token mixing, leading to reliable performance in heavy missingness cases where other methods degrade.", "weaknesses": "1. Limited Comparison to Recent Generative Methods: While the baselines cover traditional imputation techniques (e.g., Transformer variants, CNN-based models), the experiments could benefit from comparisons to emerging generative approaches like diffusion models (e.g., CSDI or adaptations from recent works like Winformer) or LLM-based time-series methods. These could provide context on whether T1's gains hold against probabilistic or foundation-model-based alternatives, especially in cross-domain or long-sequence settings.\n\n2. Dataset Diversity and Scale: The 11 benchmarks are solid but somewhat standard in time-series literature; including more recent or larger-scale datasets could strengthen claims of broad applicability. Additionally, while natural missingness is mentioned, deeper analysis of real-world irregular sampling (e.g., via case studies) would enhance the evaluation.\n\n3. Minor Issues:  Figures could include more quantitative illustrations of binding effects (e.g., attention heatmaps under varying missingness).", "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": "yhAdl0UhfQ", "reviewer": "Reviewer_q6Mh", "summary": "The main task of this paper is multivariate time-series missing value imputation. \nIt focuses on how to balance temporal feature extraction and the transfer of cross-variable information, as well as imputation under diverse missing patterns and high missing rates. To solve this problem, the paper proposes T1, a CNN-Transformer hybrid architecture.", "questions": "1. The number of channels used in the experiments is 128, and the authors also discuss different values of channel numbers in the appendix. However, the experimental results show little fluctuation. Is there a possibility of channel number redundancy here? I am curious whether there will be many zero vectors after a time-series segment with 40% missing values undergoes two rounds of convolution. Have the authors considered training under different missing value rates?\n2. Regarding the Dual-axis tokenization method, the authors describe its disadvantage as: \"but struggle to transfer information across both dimensions when missing values block intermediate pathways.\" Will T1 face similar problems, during information transfer between channels?\n3. Other questions are as mentioned in the \"Weaknesses\" section.", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "1. The experiments are comprehensive: a large number of datasets are used, the comparative models basically cover the current sota methods, and different missing scenarios are compared, making the result quite thorough.\n2. The experimental results are abundant and appear reliable.", "weaknesses": "1. The authors summarize different categories of methods in the main text. It would be more intuitive if a similar categorized comparison approach was adopted in the experimental section.\n2. There are certain issues with the figures in the paper: the stacked arrows between channels in Figure 1(b) are misleading; in Figure 2, the direction of the arrow from (b) to (c) is unclear, and Figure 2(c) does not show \"Value\".\n3. The writing and figure drawing may cause misunderstandings. Based on the main text, my understanding is as follows: For a time segment with M variables, one of the variables is processed by CNN to obtain C channels. For each channel, Q, K, and V are calculated using Formula 3. Then, for each channel, the corresponding Q, K, V of the M variables are stacked by category. Next, Formula 4 is used to calculate the attention scores. Finally, the results of the C channels are stacked. This part and the corresponding figures need to be described more clearly.", "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": "ZAm6mf1h2g", "reviewer": "Reviewer_drgA", "summary": "This paper introduces T1, a CNN-Transformer hybrid architecture for multivariate time series imputation. The key contribution is the “Channel-Head Binding” mechanism, which establishes a one-to-one correspondence between CNN channels (capturing temporal features) and attention heads (enabling cross-variable information transfer), allowing feature-level selectivity in imputing missing data.", "questions": "Please see the weaknesses.", "limitations": "", "rating": 4, "confidence": 3, "soundness": 2, "presentation": 3, "contribution": 3, "strengths": "1. The T1 architecture demonstrates superior performance across its experimental settings.\n2. The model shows particular strength in scenarios with heavy missingness.\n3. The paper introduces a novel mechanism.", "weaknesses": "1. The model's core logic relies on the unproven assumption that CNN channels naturally learn distinct temporal patterns. Without an explicit mechanism to enforce this, features may be redundant, which would undermine the \"feature isolation\" claim and allow corrupted information to propagate.\n2. The rigid 1-to-1 binding is a strong constraint that prevents the model from learning combinations of features across different channels. Furthermore, the claim that heads \"adaptively down-weight\" corrupted channels is not mechanistically proven.\n3. The claim of using a \"single hyperparameter configuration\" is exaggerated. The appendix reveals that convolutional kernel sizes were \"proportionally adjusted\" for the PhysioNet.1", "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)