TVNet: A Novel Time Series Analysis Method Based on Dynamic Convolution and 3D-Variation
Authors: Chenghan Li
Mingchen Li
Ruisheng Diao
Venue: ICLR 2025 Poster (2025)
Keywords: Time series Analysis
Dynamic convolution
Deep Learning
Primary area: learning on time series and dynamical systems
TL;DR: New time series modeling perspective based 3D-variation and new analysis framework based dynamic convolution

Abstract: With the recent development and advancement of Transformer and MLP architectures, significant strides have been made in time series analysis. Conversely, the performance of Convolutional Neural Networks (CNNs) in time series analysis has fallen short of expectations, diminishing their potential for future applications. Our research aims to enhance the representational capacity of Convolutional Neural Networks (CNNs) in time series analysis by introducing novel perspectives and design innovations. To be specific, We introduce a novel time series reshaping technique that considers the inter-patch, intra-patch, and cross-variable dimensions. Consequently, we propose TVNet, a dynamic convolutional network leveraging a 3D perspective to employ time series analysis. TVNet retains the computational efficiency of CNNs and achieves state-of-the-art results in five key time series analysis tasks, offering a superior balance of efficiency and performance over the state-of-the-art Transformer-based and MLP-based models. Additionally, our findings suggest that TVNet exhibits enhanced transferability and robustness. Therefore, it provides a new perspective for applying CNN in advanced time series analysis tasks.

Published as a conference paper at ICLR 2025
TVNET: A NOVEL TIME SERIES ANALYSIS METHOD BASED ON DYNAMIC CONVOLUTION AND 3D- VARIATION
Chenghan Li Mingehen Li & Ruisheng Diao
Shenzhen International Graduate Schoo(SSGGS).Tsinggn University
'The Hong Kong University of Science and Technology (Guangzhou)
3 +ZJU-UIUC Institute, Zhejiang University
1 1ich24@mails t singhua edu. en; m1173 ml17368connect. hkust-ga seduuu edu..edduc..m en;
rui ruishengdiao@@ne i f... edu.
ABSTRACT
At present, the research on time series often focuses on the use Transformer- based and MLP-based Conversll.. the performance of Convolutional Neu- ral Networks (CNNs) in time series analysis has fallen short of expectations, di- minishing their potential for future applications. Our research aims to enhance the representational capacity of Convolutional Neural Networks (CNNs) in time series analysis by introducing novel perspectives and design innovations. To be specific, We introduce novel time series reshaping technique that considers the inter-patch, intra-patch, and cross-variable dimensions. Consequently, we pro- pose TVNet, dynamic convolutional network leveraging a 3D perspective to employ time series analysis. TVNet retains the computational efficiency CNNs and achieves state-of-the-art results in five key time series analysis tasks, offering a superior balance of efficiency and performance over the state-of-the- art Transformer-bast
and MLP-based models. Additionally, our findings suggest that TVNet exhibits enhanced transfcrability and robustness. Therefore, pro- vides perspective for applying CNN in advanced time series analysis tasks.
INTRODUCTION
Time series analysis plays crucial role in many domains(Alfare & Nazeeruddin 2002). such as anomaly detection(Pang al. [222]) in industry signal and generation predication of renewable en- ergy sources (Zhng et al. 2014), 4). recent years, remarkable progress has been made in this area (Wu) let al. 2 (Luo & Wang 2024). In particular, the .MM.MPP.. basedd and Transformer-batt
architecture has been fully explored in the field of time series analysis (Wu et al.) (2021). (Zhou et al. 2022). (Zhou al. 2021). ). WW al. 2022b). (Li al. 2023a), (Challu al. 2023). However, Transformers hibit relatively low computational resource efficiency in time series tasks. MLP- models often struggle to effectively capture the complex dependencies among variables and RNN-based models face challenges in modeling global temporal correlations. In previous studies Wang et al. 2024a), CNNs have been shown to be neural network architecture that can balance efficiency and effectiveness. However, in the past, CNN architecture was often focused on video and images, and its application and research in time series predication and analysis are relatively limited.
Time series data constitute records of continuous temporal changes, analogous to how video footage captures continuous visual transformations frame by frame both capturing temporal continuity in their respective domains. Unlike certain sequential data types such as language(Lim & Zohren, 2021), time series data inherently reflect continuous phenomena. Much as a single video frame typ- ically fails to convey the complete narrative of scene, isolated timestamp in a sequence usually lacks sufficient context for comprehensive analysis. This connection inspires us to leverage CNNs to
"Equal contribution. Corresponding author.

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Published as a conference paper at ICLR 2025
Patragatah
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Figure I: the context of time series analysis, the three-dimensional variation encompasses intra- patch, inter-patch, and cross-variale variaba interactions.
capture multiple dependencies(L.. volutions frequently employed video processing, to attempt comprehensive capture of complex temporal patterns in time series data.
Lai et al. 2018 Luo & Wang 2024), particularly the dynamic con-
Modeling one-dimensional time variations can be complex task due to the intricate patterns volved. Real-world time series often exhibit complex characteristics that require thorough analysis to interpret short-term fluctuations, long-term trends, and temporal pattern changes. Concurrently, the cross-variable dependencies within multivariate time series must be considered. To extract these crucial relationships from time series data, we specifically select intra-patch, inter-patch, and cross- variable(Figure) [T) dependencies, derived from time series characteristics. These three types of em- beddings encompass many significant information flows present in time series data. data.(Liang 2014 Havačková et al. 2007
Motivated by the above considerations, we introduce a novel analytical approach within the realm of time series analysis by integrating dynamic convolution. Specifically, we introduce 3D-Embedding technique to convert one-dimensional time series tensors into three-dimensional tensors. Subse- quently, we propose a network architecture, termed TVNet (Time-Video Net), which leverages dynamic convolution to effectively capture intra-patch, inter- inter-patch, and cross- cross-variable dependen- cies comprehensive time series analysis. We assessed the performance of TVNet across five benchmark analytical tasks: long-term and short-term forecasting, imputation, classification, and anomaly detection. Notably, despite being a purely convolution-basee model, TVNet consistently achieves state-of-the- the-att results in these domains. Importantly, TVNet retains the efficiency inherent to dynamic convolution models, thereby achieving a superior balance between efficiency and per- formance, providing practical and effective solution for time series analysis. Our contributions are as follows:
A novel modeling approach that captures intra- inter-patch and cross-variale variables fea- tures by converting time series data into 3D shape tensor proposed.
TVNet implements consistent state-of-the-ee performance time series analysis tasks across multiple mainstreams, demonstrating excellent task generalization.
T'NNet offers better balance between efficiency and performance. It maintains the effi- ciency benefits convolution based models while competing or even better with the most advanced base models in terms of performance.
RELATED WORK
2.1 TIME SERIES ANALYSIS
Traditional time series analysis methods, such ARIMA (Anderson, 1976) and Holt-Winters mod-
els (Hyndman 2018), despite their solid theoretical underpinnings, are insufficient for datasets ex-
hibiting intricate temporal patterns. In recent years, deep learning approaches, particularly MLP.
based and Transformer baaeeer--aedd models, have achieved significant advancements in this domain (Li
al. 2023a Challu al. 2023 Liu al. 2021
Zhang & Yan 2023 Zhou al. 2022
Wu
2

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Published as a conference paper at ICLR 2025
et al. 2021: Liu et al. 2023 MLP-based models have garnered increasing attention in time ries analysis due to their low computational complexity. For instance, the Dlinear model (Li et al, 2023a) achieves efficient time series prediction by integrating decomposition techniques with MLP. However, current ML. models still struggle with capturing multi-period characteristics of time se- ries and the relationship between different variables. Concurrently, Transformer-basee models have demonstrated formidable performance in time series. Their self-attention mechanisms enable the capture of both long-term dependencies and critical global information. Nevertheless, their scalabil- ity and efficiency are constrained by the quadratic complexity of attention mechanisms. To mitigate this, researchers have introduced techniques to diminish the computational load of Transformers. For example, Pyraformer (Liu et al., 2021) enhances the model architecture with pyramid atten- tion design, facilitating connections across different scales. The recent PatchTST (Nie et al. 2022) employs block-based strategy, enhancing both local feature capture and long-term prediction accu- racy. Despite these innovations, existing Transformer- based methods, which predominantly model ID temporal variations, continue to encounter substantial computational challenges in long-term time series analysis.
2.2 CONVOLUTION IN TIME SERIES ANALYSIS
As deep learning techniques advance, Transformer-basee and MLP-based models have achieved notable success in time series analysis, overshadowing traditional convolutional methods. Yet, in- novative research is revitalizing convolution for time series analysis. The MICN model (Wang) et al. 2023) integrates local features and global correlations by employing a multi-scale convolution structure. SCINet (Liu al. 2022a) innovates by discarding causal convolution in favor of recur- sive downsample-convolun these models have made strides in capturing long-tern dependencies, they are challenged in the generality of time series tasks. TimesNet (Wu et al.) (202aa) uniquely transforms one-dimensional time series into 2D forms, leveraging two-dimensional convolutional techniques from computer vi- sion to enhance information representation. Modern (Luo & Wang (024) extends the scope of convolutional technology by utilizing large convolution kernels to capture global time series fea- tures. However, these models predominantly focus on feature analysis within a single time window, neglecting the comprehensive integration of global, local, and cross-variable interactions.
interaction architecture to handle complex temporal dynamics. While
2.3 DYNAMIC CONVOLUTION IN VIDEO
Dynamic convolution, characterized by their adaptive weight module adjustments, exhibit struc- tural flexibility in response to content variations. These networks incorporate dynamic filtering or convolution mechanisms (MJaa al. 2016), (Yang et al. 2019)). They demonstrate superior process- ing capabilities and enhanced performance relative to conventional static networks. In the domain of video understanding, dynamic networks have also proven effective. For instance, dynamic filter- ing techniques and temporal aggregation methods adeptly capture temporal dynamics within videos, thereby augmenting the models' capacity to represent time series data. ((Meng al. 2021), (Li et al.,
2020h)
3 TVNET
Based on the inter-patch, intra and cross-variable features of the time series mentioned above, this paper proposes TVNett to capture the features of the time series. Specifically, we first design the 3D- 3DD-embedding module so that the ID time series can be converted to 3D time series tensor, and a 3D) block designed to model the three types of properties finter-patch,inte through dynamic convolution. Finally, time series representations extracted by 3D-blocks to get different task outputs through the linear layer. Figure 2 shows the structure of TVNet.
and cross- variablaraa
3.1 3D-EMBEDDING
In this section, propose unique embedding way(3D-Embedding) This method takes into account the inter,patch, intra-patch and cross- variable for time series. We denote Xin E R means the length of time C means the dimensions of time series.
cross-variable
3

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Published as a conference paper at ICLR 2025
hood
Time jerizs inpat glac
OutaEeshadding
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Figure 2: The overarching architecture of TVNet constructed by stacking 3D-blocks in a residual way, which enables the capture of inter-patch, intra- and cross-varialle features from the time series 3D tensor.
M
20
30
15
25
Fani Del
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Figure 3: A univariate time series example is segmented into four distinct patches and the odd and even components specifically for Patchl (ETTh1).
We first embed the input along the feature dimensions to C. and get Xin E R.L..., where C. the embedding the dimensionality of the representation space into which each time point is projected. After embed- ding the input data along the feature dimension to obtain Xin RLCC,., we proceed to segment the embedded data into patches using a one-dimensional convolutional layer (Conv D). Specifically, we configure the Conv ID layer with kernel size P, which defines the length of each patch. This config- uration allows the Conv ID layer to divide the input sequence into N patches, where N is calculated based on the total length T., the patch length P(In the absence of overlapping patches, The output of this Conv11 operation is tensor Xemb E N PxCm. with each N representing the number of patches, P representing the length of each patch, and Cm representing the embed- ding dimensions. Thenn
dimension Cm is crucial hyperparameter that dictates
T./ T./)).
use odd-even split[Liu et al. (022a)) the patch length demisions to get Xodd and Xeven E ( then stacking Xods and Xeven to get Xemb E IR N (P/ Figure 3 illustrates an example of patches and odd-even components applied to a univariate time sere Algorithm
Xemb 3D-Embedding((X,,
(1)
3.2 3D-BLOCK
Time dynamic weight: Previous research, as detailed Wang et al. (2023). has highlighted both consistencies and discrepancies within time series data, particularly in the phenomenon known as mode In response to these observations and inspired by dynamic convolution work the video field(Huang et al.) 2021), Regarding the 3D-Embedding technique mentioned earlier, we employ a dynamic convolutional method to capture the temporal dynamics within each patch. To clarify, collection of individual patches, denoted as (x), (I), n. The weight associated with the i-th patch, denoted as W,, is hypothesized to be decomposable into the product of constant time base weight W.. which is common across all
the embedded representation Xemb is envisioned

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Published as a conference paper at ICLR 2025
patches, and time varying weight ag, which is unique to each patch.
I W.-at 22 (aq W6) -E,
(2)
Time varying weight generation: To more accurately model the temporal dynamics of patches, the time-varying weight a; must account for all patches. Based the above starting point, we design an adaptive Tire-varying weight generation that fully considers the interaction between inter- patch and intra-patch.It can be articulated as a; ((Xemb). Here, denotes the generation function for the time-varying weight. To efficiently handle both inter-patch and intra-patch relationships and manage pre-training weights effectively, the weights of the 31D-block can be initialized akin to standard convolutional layers. This initialization is realized by setting the weights of F(Viner) + F F(Vinna) and augmenting the formulation with constant vector of ones(1). The Figure 4 shows the flow chart for Time varing weight generation.
a2 = (XXemb = +++ F(Vinee) + F(Vintra)
(3)
In this way, at the initial state, W; W.
The function Finint captures intra-patch features. Initially, we apply 3D Adaptive Average Pool- ing the embedded representation Xemb to obtain intra-patch description vectors Vinta which en- capsulate the essential features of each patch. These vectors are of dimension IR C.. xN This opera- tion is described by the following equation:
Vintra Adaptive/vv@PooBdd
Subsequently, for intra-patch channel modeling, we employ single-layer Conv denoted as Fintras on Vintra
Finm (Vintm) DC (Vinta))
Here, ô represents ReLU activation, and BN denotes Batch Normalization.
The function F(Vinte) is tasked with capturing features for inter- suter-pachee. We employ Adaptive Average Pooling 1D on Vintaa to derive Viner- This process can be expressed as:
Vinter E Cm x1 AdaptiicAvggooolld(r.
(6)
Subsequently, for inter-patch channel modeling, single-layer Conv ID, denoted as Finter is applied to Vinteri
Fineer (miter) 6(Conv 1 C-C (Vinter)
Here, d denotes the ReLU activation function.
(V
F inter
R.
Caitt
R
Gm
X
+1
Figure 4: The Time varying weight generation flow chart
3.3 OVERALL STRUCTURE
Following the 3D-Emeddding process, the embedded representation Xemb be permuted to the
form Xemb E C xN (P/2) which is then input into the 3D-block architecture. The purpose of this step is to learn effective representations of the time series, denoted X3D E CR X xNx2x(P/2) Subsequently, X3D is reshaped into X E R(N P)xP.. and passed through linear layer, also referred as the task-linear head, accommodate the specific requirements of various tasks.
X3D TVNet(X.mb)
TVNet(-) is the stacked 3D-blocks Each 3D-block is organized in residual way. The forward process in the i-th 3D block is:
3D = 3D-blockXX + X
(9)
where XTD (RCxxNx2x(PP2)) is the i-th block's (sse Algorithm
5

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Published as a conference paper at ICLR 2025
Algorithm Training of TVNet.
Require: Input: Training set DD {X, Y)} Look back window E R2 Embedding dimen- sions Cm:number of 3D-blocks L,Patch length P and other training hyperparameter.
Ensure: Output: Trained TVNet
1: Initialize Embedding dimensions and number of 3D-blocks.
2: Sample (X from
3: (3D-Embdding): Xemb Algorithm(X)
4: for for to L do: do
5: a (Xmmb)
6: X & Cono2D(a, Wo. x
7: end for
8: Y + Tass linear head (33)
9: Compute loss L + L(Ý, Y)
10: Update model parameters O via backpropagation
11: until convergence
12: return Trained TVNet
EXPERIMENT
TVNet evaluated across five common analytical tasks, including both long-term and short-term forecasting, data imputation, classification, and anomaly detection, to demonstrate its adaptability in diverse applications.
Baselines: In establishing foundational models for time series analysis, we have extensively in- corporated the most recent and advanced models from the time series community as benchmarks. This includes Transformer-base based models such iTransformer, PatchTST, Crossformer, and FED-
Zhou former(Liv et al. 2023 Nie et al. 2022 Zhang & Yan 2023 Zhou et al. 2022]; MLP-based models like MTSS-Mixer, Dlinear RMI.P, and RLinea((Li et al. 2023b Zeng al. 2023 Li al.) 2023a); and Convolution- based models including TimesNet, MICN, and Modern TCN( et al. 2022a Wang et al.) 2023 Luo & Wang 2024). Additionally, we have included ofate-of-the-art models from each specific task to serve supplementary benchmarks for comprehensive comparison. Our objective is to ensure that our model exhibits competitiveness when benchmarked against these advanced models.
Hyperparameter Setups: The performance model can be influenced by various hyperparam- eter settings. In this study, the hyperparameter ranges for TVNet aligned with those reported in Wu et al. (2022a). A detailed discussion on the impact of each hyperparameter is provided in Appendices Cand D.
Main results: As depicted in Figure 5 T'Nett consistently achieves top-tier performance across five pivotal analytical tasks, showcasing enhanced efficiency. A detailed analysis of the experi-
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Figure 5: Model efficiency comparison under the setting of L(prediction length) =192/720 of ETTm2.

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Published as a conference paper at ICLR 2025
mental results is presented in Section 5.1. The details and outcomes of the experiments for each task are discussed the following subsections. In the tables, the superior results are highlighted bold, while those ranking just below the top indicated with underlined.
4.1 LONG-TERM FORECASTING
Datasets and setups: We performed long-term forecasting experiments on nine well-established real-world benchmarks: Weather(wet), Traffic(pem). Electricity Elletticitt(uuii, Exchange(Lai et al. 2018). ILI(Cdc), and four ETT datasets(Zhou et al. 202 To ensure equitable comparison, we re-executed all baseline models with diverse input lengths, opting for the best outcomes to prevent underestimat- ing their performance. Mean Squared Error (MSE) and Mean Absolute Error (MAE) are adopted as the metrics for evaluating multivariate time series forecast.
Results: Table illustrates the exceptional performance of TVNet in long-term forecasting. Specifically, TVNet outperformed the majority of existing MLP-based, Transformer-based. and Convolution- models across all nine datasets. This outcome suggests that our design signifi- cantly improves the predictive capabilities of time series forecasting via convolution.
Table I: Long-term forecasting results are averaged across four prediction lengths: {24, 36, 48, 60} for ILI and {96. 192, 336, 720} for others. Lower MSE or MAE values indicate superior performance. Refer to Table 28 in the Appendix for comprehensive results, Desults.HHint:Bel (Hint:Baseling results derived from their papers)
Models
TVNet
PushIST p022
Waastormer 2005
Croisfonne
KLinee
MIS Miter
DLinex
TinesNet
MICN
ModamICN
FEaDomer
RMILP
2023
NO2
20130
Metrics
MSB
MAG
MAE
MAB
MSE
MAB
MSE
MSE
MAE
MAB
MSE
MAE
ETTal
0,348
0.379
IL407
0,400
[143]
0.358
0,370
0,305
0.357
0,450
0.303
0.496
0.382
04422
0.369
0.251
0.288
0,332
[0632
0.277
0.325
0.333
0.277
0.336
0.292
0.343
Avg
0.465
0.4%0
Avg
0.076
0.000
0.413
0.437
Blocsicty
Avg
11165
0.111
112033
0.351
0.277
0.177
(0.190
0,295
0.200
0.331
Weshh: Nvg (0.231
0.261
0.264
[1:25
0.278
(1230
(.200)
(0.355
0,272
(1280
01300
(0.25
0.257
0.342
0,215 01224
00310
0.357
Traffic Nvg 01296
0.268
0.364
[1428
0,252
[0535
0.300)
(0.494
0.354
00:34
(0662
0,336
0.535
0,312
0.916
(0:004
0.372
0.406
Euchage
[Av
0.298
0.367
0.357
0.419
[0.600
0,408
[070] 0.633 0.394
(0,373
0.407]
10.97
0,375
(0.416
0.443
00315
0.404
(Q478
0.478
0.345
Aug
1.406
0.766
1.443
0.798
2:141 0.966
(3M61 1.235]
4.269
1-800]
1.885
169
1:041
3.507
1.081
1.410)
0.786
1,990
1.000]
4:300 1.516
4.2 SHORT-TERM FORECASTING
Our benchmark for short-term forecasting is the M4 dataset, as introduced by Makridakis (Makridakis et al.] 2018). We have the input sequence length to be twice that of the forecast horizon Wu et al.) (2022a). For evaluating performance, we utilize key metrics including the Symmetrie Mean Absolute Percentage Error (SMAPE). Mean Absolute Scaled Error (MASE), and Overall Weighted Average (OWA). To enhance our comparative analysis, we have incorporated models such as U-Mixer (Ma et 2024) and N-Hits (Challu et al. 2023).
Datasets and setups:
Results: Table presents the findings. The short-term forecasting task on the M4 dataset is notably challenging due to the varied sources and temporal dynamics the time series data. Neverthe- less, T'Neet retains its top ranking in this rigorous context, demonstrating its enhanced ability for temporal analysis.
The task of short-term forecasting entails evaluating performance across various sub- datasets, each with distinct sampling intervals. The results are presented as a weighted average, with lower metric values signifying enhanced performance. Full results are provided Table 29
Table 2:
Models
TVNet PutcTTST
U-Miser
Crossformer
RI innar
MTS-Mixer 2023b
DlLinem TimesNer
MICN
ModemTCN
FRDformer 2023
N-HITS
(Ours)
2022
2024
2023
2023a
2023b
2022a
2023
2024
2023
SMAPE
11.671
11.807
13,639
11.829
12,840
MSE
1.536
1.590
1.575
1.866
1.677
1.608
2,095
1.885
11,556
1,701
1.613
OWA
0.832
0.851
0.845
0.985
0.898
0.859
1,051
0.851
0.980
0.838
0.918
0.861
7

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Published as a conference paper at ICLR 2025
4.3 IMPUTATION
Datasets and setups: The imputation task is designed to estimate missing values within partially ob- served time series data. Missing values are prevalent in time series due to unforeseen incidents such as equipment failure or communication enrors. Given that missing values can adversely affect the performance of subsequent analyses, the imputation task holds significant practical importance. (Wu et al. (2022a) Subsequently, we concentrate on electricity and weather scenarios, which frequently exhibit data loss issues. We have chosen datasets from these domains as benchmarks, including (Th et al. 2021), Electricity (UCI)uuci) and Weather(wet). To assess the model's capacity under varying degrees of missing data, we randomly introduce data occlusions at ratios of {12.5% 25%, 37.5%, 50%
Results: Table 3 shows TVNet's strong imputation performance despite irregular observations due to missing values. TVNet's top results validate its capability to capture temporal dependencies in complex scenarios. Cross-variable dependencies are key in imputation, aiding in estimating missing values when some variables observed. Methods ignoring these, like PatchTSST(Ni et al.) 2022) and DLinear(Zeny et al. 2023), perform poorly in this task.
Table 3: Average results for the imputation task. Randomly masking {12.5%, 25%, 37.5%, 50% time points to compare the model performance under different missing degrees. seen in 30
Full Full results can be
Modals
TVNe
ParhiST
SCTNee
Droasoomeer
RI RLinear
Fll inear
TimeeNon
MICN
MedaniTCN
RMI P
(Oin)
2022
2012
2015
201//
20224
2015
2012
20
Metrics
MSI
MAR
MSF
MAH
MSI
MAR:
MSR
MAR
MSR
MAR:
MSE
MAR:
MSS:
MAR
MSR
MAR
MSE
MAI
MSSI
MAR:
MSE:
MARl
MSSI
MAR
ETiml
Avg
0
0004
0.33
1.129
0.041
0.345
10000
105
03056
0.154
0.200
Joinn
0.187
0183
(0002
0.177
1003
HTTmn
Avg
(0022
0.066
1.00
0.102
10006
0.34M
0.022
0.107
0.201
0.08
Jo.14
0.240
6.099
0
00.011
0,215
(M002 1.109
(0946
0.145
01104
0.216
(0.152
[0.44]
0.242
0.127
0.236
(107s
0.157
J0.125
0.250
(0.117
0.246
[0.134 0,239
ETTb2
Avg
0.127
(0.06
0.164
[1054
0.168
16.12
0:300
(1.06
0.168
Jo.20
(0:66
0.279
Eloaakaty
Avg
p100
0.100
10001
(1.06
(0.119
0:706
Weathe
Avg (1924
0.019
(103]
D.05
10.066
0.000
Jooss
0:110
(1.00
f00n
0.128
joiose
o.301]
4.4 CLASSIFICATION AND ANOMALY DETECTION
Aver age Accuracy by Model Type
Average F1-score by Model Type
80.0
90
RNNN-
RMMe-based Convolution
77.5
Corvolution
Average Accuracy
75.0
70.0
72.5
71.8
70.5
72.5
11.7
73.6
Outs
70.8
Warsfomeebbeed
70.0
73.0
70.7
73.2
72.5
74.6
Noatoa 1aad 71-score (96]
86
88-
84.7
85.6
85.6
Ours
84.8
84.8
86.8
67.5
57.5
83.5
65.0
82.3
80.5
60.0
LSTHe
LE3R.
Radhel
SCIRe
MCH
Timette
Modernts
DLirear
LiGhTS
MrTS-bber
Ruaway
RMLP
FED.
Fire
Cress.
PatchTS
(WWtrrrars)
80
ScoRe
MBSH
Timeted
ModemtTE
DLiwer
Ams-ather
ALimer
RMLP
PED
Anomatyt
Crask
PatchTT
Figure 6: The results are averaged from several datasets. Higher accuracy and Fl score indicate better
performance. in the Transformer- -assd models indicates the name of former. See Table 31 and 32 in Appendix for full results.
In our classification study, we selected 10 multivariate datasets from the UEA Time Series Classification Archive, introduced by Bagnall (Bagnall et al., 2018)) in 2018. These datasets, which serve as benchmarks, have been standardized using pre-processing practices established by Wu et al. 2022a). To ensure a comprehensive comparison, we have integrated state-of-thh--at methods, including LSTNet (Lai et al.] 2018). Rocket (Dempster et al. 2020), and Flowformer (Wu et al. 2022b), into evaluation framework.
Datasets and setups:
Our analysis covers a range of established benchmarks in the field of anomaly detection, including SMD (Su et al. 2019), SWaT (Mathur & Tippenhauer 2016), PSM (Abdulaal et al. 2021). MSL.,
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and SMAP (Hundman et al.) 2018). To enhance comparative analysis, have incorporated the Anomaly Transformer (Xu et al. 2021) into our baseline models. Our methodology is based on the traditional approach of reconstruction. wherein the deviation from the original, measured by the reconstruction error, the key indicator for detecting anomalies.
The results for time series classification and anomaly detection depicted in Figure 6 In the classification task, TVNet attained the highest performance, with an average accuracy of 74.6%. For the anomaly detection task, TVNet exhibited competitive results 86.8 relative to the previous state-of-the-art.
Results:
MODEL ANALYSIS
5.1
COMPREHENSIV COMPARISON OF PERFORMANCE AND EFFICIENCY
Summary of results: Relative other task-specific models and prior state-of-the-ard benchmarks, TVNet has consistently achieved state-of-the-art performance across five key analytical tasks, high- lighting its exceptional versatility for diverse mission types. Moreover, TVNet'ss efficiency, illus- trated in Figure facilitates a superior balance between efficiency and performance.
Compared with baselines:
TVNet outperforms both Transformer-based and MLP-based models in terms of performance. Concurrently, it achieves faster training speeds and lower memory us- age compared to Transformer-basee models, thereby demonstrating superior efficiency. TVNet's comprehensive consideration of the relationships among time series inter-patch, intra-patch, and crois-variables enhances its representational capacity over the lightweight backbone of MLP mod- els. Compared to ModernTCN, MICN, and TimesNet, TVNet employs dynamic convolution and 3D-Embedding techniques, significantly enhancing its memory efficiency and training speed while achieving the best possible results.
Analysis complexity: TVNet exhibits time complexity of O and a space complexity of O(C)), where Cm denotes the embedding dimension. A comparison of time complexity and memory usage during training and inference phases is presented in Table Relative to Transformer- based models, TVNet demonstrates lower time complexity, and in contrast to convolutional models, maintains independence between space complexity and sequence length.
Table 4: Comparison of different methods in terms of training time and memory complexity.
Methods
Time Complexity
Space complexity
TVNet (Ours)
O O(LO ((L)
O LCC) O(LC2)
MICN Wang et al. 2023)
FEDformer Zhou et 2022
O(L)
Autoformer Wu et al. 202T
(LL L)
(L L) LL L)
Informer Zhou ct al. 202
OL L)
Transformer(Ling et al 2023
O(I2)
O(I")
LSTM
O(L)
O(L)
5.2 ABLATION ANALYSIS
Ablation of inter-pool module: We conducted ablation experiments on the inter-pool module, and the experimental results are shown in the Table It is found in the table that when inter-pool is re- moved, the predicted results will decrease, indicating that inter-pool can increase the representation of the relationship between different patches.
Ablation dynamic convolution: Comparing the dynamic convolution weights to their fixed coun- terparts reveals significant decline in predictive performance without the former. This observation underscores the effectiveness the awwre dynamic convolution proposed in this paper for modeling time series analysis. maablis. The dynamic convolution mechanism allows for more anced capture complex temporal patterns, enhancing the model's 's ability to adapt to varying data distributions and nonlinear relationships.

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Published as a conference paper at ICLR 2025
Table Ablation of inter-pool module in the w/o means without module.
Models
Metrics
Weather
Elecuicity
Trafiic
720
336
192
720
TVNet
0,147
0.194
0.308
0.142
0.164
0.190
0.381
0.198
0.238
W/o intee pool
0.156
0.147
0.212
0.276
0.375
0.220
0.276
0.302
0.284
Table 6: Ablation of dynamic convolution in the TVNet. w/o means without module.
Medel
Woather
Flectricity
Traffic
192
336
95
720
192
3356
TVNe
MSE
6.147
0.194
0.235
0.305
0.142
0.165
0.164
0.190
0.367
0.381
0.395
0.442
0.238
0.277
0.223
0.269
0.264
0.362
0.268
0,290
who dynamic weight
MSE
0.251
0.257
0.291
0.341
0.185
0.201
0.214
0.268
0.391
0.423
0.440
0.507
0.699
0.301
0.370
0.275
0.308
0,316
0.313
5.3 TRANSFER LEARNING
Figures 7 and 8 illustrate the outcomes of our transfer learning experiments. In both direct predic- tion and full-tuning approaches, TVNet outperforms the baseline models, underscoring its superior generalization and transfer capabilities. A pivotal advantage of TVNet is its dynamic weighting mechanism, which adeptly captures intricate temporal dynamics across variety of datasets.
PATSTT
rEDismer
2.40
FaPanii
255
5.692
3,M4
0.487
3.9
0.02
3:39
6:42
6.40
02277
0,227
150
135
720
6:0
112
334
720
E20
152
Figure 7: Transfer learning results for ETTh2.
IT DeDmemer
0.10
E10
Nodille
Podictin
0.05
8:4
5,04
3.49
9283
0/40
620c
0.33X
6.262
640
626
0332
325
6:2
625
192
0:00
720
020
Figure 8: Transfer learning results for ETTm2.
6 CONCLUSION AND FUTURE WORK
This paper introduces a 3D) variational reshaping and dynamic convolution method for general time series analysis. The experimental results demonstrate that T'Nett exhibits excellent versatility across tasks, achieving performance comparable to or surpassing that of the most advanced Transformer- based and MLP-based models. TVNet also preserves the efficiency inherent in Convolution-base models, thus providing optimal balance between performance and efficiency. Future research will focus on large-scale pre-training methods for time series and multi-scale patches, leveraging TVNet the foundational architecture, which anticipated to enhance capabilities across broad spectrum of downstream tasks.
REFERENCES
Cde. illness. URL html Accessed: 2024-08-10.
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Pems. traffic. URL dot cov
Accessed: 2024-08-10.
Uci.
https://archive ics. http.......eeee///aaaaaaattttt.. Elletrrlctty.ooD...gra2222222221
electricity. URL
Accessed: 2024-08-10.
Wetterstation. weather. URL. httph:t/p///wwt www. bgc- jena. wtt.aam....eeeeeteeeeeee Accessed: 2024-
08-10.
Ahmed Abdulaal, Zhuanghua Liu, and Tomer Lancewicki. Practical approach to asynchronous multivariate time series anomaly detection and localization. In Proceedings of the 27th ACM SIGKDD conference knowledge discovery & data mining, pp. 2485-2494, 2021.
Hesham K Alfares and Mohammad Nazeeruddin. Electric load forecasting: literature survey and classification methods. International journal of systems science, 33(1):23-34, 2002.
Oliver Anderson. Time-series. 2nd edn., 1976.
Anthony Bagnall, Hoang Anh Dau, Jason Lines, Michael Flynn, James Large, Aaron Bostrom, Paul Southam, and Eamonn Keogh. The uea multivariate time series classification archive, 2018. arXiv preprint 181 1.00075, 2018.
Cristian Challu, Kin Olivares, Boris N Oreshkin, Federico Garza Ramirez, Max Mergenthaler Canseco, and Artur Dubrawski. Nhits: Neural hierarchical interpolation for time series forecast- ing. In Proceedings of the AAAI conference on artificial intelligence, volume 37, pp. 6989-6997, 2023.
Angus Dempster, François Petitjean, and Geoffrey Webb. Rocket: exceptionally fast and accu- rate time series classification using random convolutional kernels. Data Mining and Knowledge Discovery, 34(5):1454 1491-1955, 2020.
Albert Gu, Karan Goel, and Christopher Ré. Efficiently modeling long sequences with structured state spaces. arXiv preprint arXiv:2111.00396, 2021.
Katerina flaváčková-Schindeee Milan Paluš, Martin Vejmelka, and Joydeep Bhattacharya. Causal- ity detection based information-theowe approaches in time series analysis. Physics Reports, 441(1):1-46, 2007.
Ziyuan Huang, Shiwei Zhang, Liang Pan, Zhiwu Qing, Mingqian Tang, Ziwei Liu, and Marcelo H Ang Jr. Tada! ammorrall--ddaptie convolutions for video understanding. arXiv preprint 10.06721 2021.
Kyle Hundman, Valentino Constantinou, Christopher Laporte, Ian Colwell, and Tom Soderstrom. Detecting spacecraft anomalies using Istms and nonparametric dynamic thresholding. In Pro- ceedings of the 24th ACM SIGKDD international conference on knowledge discovery & data mining, pp. 387-395, 2018
RJ Hyndman. Forecasting: principles and practice. OTexts, 2018
Furong Jia, Kevin Wang. Yixiang Zheng. Defu Cao, and Yan Liu. Gpt4mts: Prompt-basee based large language model for multimodal time-series forecasting. Proceedings of the AAAI Conference Artificial Intelligence, volume 38, pp. 13343-23351, 2024.
Xu Jia, Bert De Brabandere, Tinne Tuytelaars, and Lue V Gool. Dynamic filter networks. Advances in neural information processing systems, 29, 2016.
Ming Jin, Shiyu Wang, Lintao Ma, Zhixuan Chu, James Y Zhang, Xiaoming Shi, Pin- Yu Chen, Yux- uan Liang, Yuan-Fang Li, Shirui Pan, et al. Time-llm: Time series forecasting by reprogramming large language models. arXiv preprint arXiv:2310.01728, 2023.
Diederik Kingma. Adam: A method for stochastic optimization. arXiv preprint arXiv:1412.6988) 2014.
Guokun Lai, Wei-Cheng Chang, Yiming Yang, and Hanxiao Liu. Modeling long-and short-term temporal patterns with deep neural networks. The 41st international ACM SIGIR conference research & development in information retrieval, pp. 95-104 2018.

---

Published as a conference paper at ICLR 2025
Yunsheng Li, Yinpeng Chen, Xiyang Dai, Dongdong Chen, Mengchen Liu, Lu Yuan, Zicheng Liu, Lei Zhang, and Nuno Vasconcelos. Micronet: Towards image recognition with extremely low flops. arXiv preprint arXiv:2011.12288 2020.
Zhe Li, Shiyi Qi, Yiduo Li, and Zenglin Xu. Revisiting long-term time series forecasting: An investigation on linear mapping. arXiv preprint arXivv2305. 10721, 2023a.
Zhe Li, Zhongwen Rao, Lujia Pan, and Zenglin Xu. Mts-mixers: Multivariate time series forecasting via factorized temporal and channel mixing. arXiv preprint (XXi::3302.0500,, 2023b.
San Liang. Unraveling the cause-effect relation between time series. Physical Review E, 90(5): 052150, 2014.
Bryan Lim and Stefan Zohren. Time-series forecasting with deep learning: survey. Philosophical Transactions of the Royal Society A, 379(2194):20200209 2021.
Minhao Liu, Ailing Zeng, Muxi Chen, Zhijian Xu, Qiuxia Lai, Lingna Ma, and Qiang Xu. Scinet: Time series modeling and forecasting with sample convolution and interaction. Advances in Neural Information Processing Systems, 35:5816-5822 2022a.
Shizhan Liu, Hang Yu, Cong Liao, Jianguo Li, Weiyao Lin, Alex X Liu, and Schahram Dustdar. Pyraformer: Low-complexity pyramidal attention for long-range time series modeling and fore- casting. In International conference learning representations, 2021.
Yong Liu, Haixu Wu, Jianmin Wang, and Mingsheng Long. Non-stationary transformers: Exploring the stationarity in time series forecasting. Advances in Neural Information Processing Systems, 35:9881-9988 9893,9 2022b.
Yong Liu, Tengge Hu, Haoran Zhang, Haixu Wu, Shiyu Wang, Lintao Ma, and Mingsheng Long- itransformer: Inverted transformers are effective for time series forecasting. arXiv preprint arXiv:2310.06625 2023.
Donhaao Luo and Xue Wang. Modernten: A modern pure convolution structure for general time series analysis. In The Twelfth International Conference on Learning Representations, 2024.
Xiang Ma, Xuemei Li, Lexin Fang, Tianlong Zhao, and Caiming Zhang. U-mixer: An unet-mixer architecture with stationarity correction for time series forecasting. In Proceedings of the AAAI Conference Artificial Intelligence, volume 38, pp. 14255-14262, 2024.
Spyros Makridakis, Evangelos Spiliotis, and Vassilios Assimakopoulos. The m4 competition: Re- sults, findings, conclusion and way forward. International Journal of forecasting, 34(4):802-808, 2018.
Aditya Mathur and Nils Ole Tippenhauer. Swat: A water treatment testbed for research and training on ics security. In 2016 international workshop on cyber-physical systems for smart water networks (CySWater), pp. 31-36. IEEE, 2016.
Yue Meng, Rameswar Panda, Chung-Ching Lin, Prasanna Sattigeri, Leonid Karlinsky, Kate Saenko, Aude Oliva, and Rogerio Feris. Adafuse: Adaptive temporal fusion network for efficient action recognition. arXiv preprint arXiv:2102.05775. 2021.
Yuqi Nie, Nam H Nguyen, Phanwadee Sinthong, and Jayant Kalagnanam. time series is worth 64 words: Long-term forecasting with transformers. arXiv preprint arXiv:2211.14755 2022.
Zijie Pan, Yushan Jiang, Sahil Garg, Anderson Schneider, Yuriy Nevmyvaka, and Dongjin Song. S2ip-Ilm: Semantic space informed prompt learning with 1lm for time series forecasting, In Forty-first International Conference on Machine Learning. 2024.
Guansong Pang, Chunhua Shen, Longbing Cao, and Anton Van Den Hengel. Deep learning for anomaly detection: A review. ACM computing surveys (CSUR), 54(2):1-38, 2021.
Adam Paszke, Sam Gross, Francisco Massa, Adam Lerer, James Bradbury, Gregory Chanan, Trevor Killeen, Zeming Lin, Natalia Gimelshein, Luca Antiga, et al. Pytorch: An imperative style, high- performance deep learning library. Advances in neural information processing systems, 32, 2019.
12

---

Published as a conference paper at ICLR 2025
Ya Su, Youjian Zhao, Chenhao Niu, Rong Liu, Wei Sun, and Dan Pei. Robust anomaly detection for multivariate time series through stochastic recurrent neural network. In Proceedings of the 25th ACM SIGKDD international conference on knowledge discovery & data mining, pp. 2828-2832 2019.
Ao Wang, Hui Chen, Zijia Lin, Jungong Han, and Guiguang Ding. Repvit: Revisiting mobile cnn from vit perspective. In Proceedings of the IEEE/CVE Conference on Computer Vision and Patlern Recognition, pp. 15909-15920, 2024a.
Huiqiang Wang, Jian Peng, Feihu Huang. Jince Wang, Junhui Chen, and Yifei Xiao. Mien: Multi- scale local and global context modeling for long-term series forecasting, In The eleventh interna- tional conference on learning representations, 2023.
Yuxuan Wang. Haixu Wu, Jiaxiang Dong. Yong Liu, Yunzhong Qiu, Haoran Zhang, Jianmin Wang, and Mingsheng Long. Timexer: Empowering transformers for time series forecasting with ex- ogenous variables. arXiv preprint 0rXi::2402.19072 2024b.
Haixu Wu, Jiehui Xu, Jianmin Wang, and Mingsheng Long. Autoformer: Decomposition trans- formers with auto-correlation for long-term series forecasting. Advances neural information processing systems, 24422291222430, 2021.
Haixu Wu, Tengge Hu, Yong Liu, Hang Zhou, Jianmin Wang, and Mingsheng Long. Timesnet: Tem- poral 2d-variation modeling for general time series analysis. arXiv preprint arXiv:2210.02186, 2022a.
Haixu Wu, Jialong Wu, Jichui Xu, Jianmin Wang, and Mingsheng Long. Flowformer: Linearizing transformers with conservation flows. arXiv preprint arXiv:2202.06258, 2022b.
Jiehui Xu, Haixu Wu, Jianmin Wang. and Mingsheng Long. Anomaly transformer: Time series anomaly detection with association discrepancy. arXiv preprint arXiv:21 2021.
Brandon Yang, Gabriel Bender, Quoc V Le, and Jiquan Ngiam. Condconv: Conditionally parame- terized convolutions for efficient inference. Advances neural information processing systems, 32, 2019.
Ailing Zeng, Muxi Chen, Lei Zhang, and Qiang Xu. Are transformers effective for time series forecasting? In Proceedings of the AAAI conference artificial intelligence, volume 37, pp- 11121-11128, 2023.
Tianping Zhang, Yizhuo Zhang, Wei Cao, Jiang Bian, Xiaohan Yi, Shun Zheng, and Jian Li. Less is more: Fast multivariate time series forecasting with light sampling-oriented mip structures. arXiv preprint arXiv:2207.01 2022.
Yao Zhang, Jianxue Wang, and Xifan Wang. Review on probabilistic forecasting of wind power generation. Renewable and Sustainable Energy Reviews, 32:255 270, 2014.
Yunhao Zhang and Junchi Yan. Crossformer: Transformer utilizing cross-dimension dependency for multivariate time series forecasting. The eleventh international conference on learning representations, 2023.
Haoyi Zhou, Shanghang Zhang. Jieqi Peng, Shuai Zhang, Jianxin Li, Hui Xiong, and Wancai Zhang. Informer: Beyond efficient transformer for long sequence time-series forecasting. In Proceedings of the AAAI conference on artificial intelligence, volume 35, pp. 11106-11115, 2021.
Tian Zhou, Ziqing Ma, Qingsong Wen, Xue Wang, Liang Sun, and Rong Jin. Fedformer: Frequency enhanced decomposed transformer for long-term series forecasting. In International conference machine learning. pp. 077266272266... PMLR, 2022.
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A TVNET THEORETICAL DISCUSSIONS
Problem Definition: (Time Series Analysis) Time series analysis encompasses five primary sub- tasks: long-term forecasting, short-term forecasting, interpolation, classification, and anomaly de- tection. Mathematically, these tasks are defined with respect to a look back window X E R2 where L is the window length and C' the number of features. The goal to develop deep- learning model f that minimizes the prediction eтrоr e(Y,J(X)). The target output Y varies by task: For forecasting: Y E I. TeT', where T1 is the forecast horizon and C. is the number of output features. For imputation and anomaly detection: Y E II 1222xC, where T2 is the data length for imputation or anomaly detection and C, is the number of output features. For classification: Y E I where C' represents the number of classification labels.
Algorithm 3DD-mmedding applied to general time series analysis.
Require:
Look back window X E RR4xC, where L, is the length of the time series and C is the number of channels.
1: Embed the input along the feature dimensions C to get X' E LL where C'm is the embed- ding dimension.
2: Use ConviD (kernel size P) divide X' into N patches 2; R PxCm, where N p.
3: for = 1 to do
4: Split each patch 2; by odd and even indices to get addd Tenen
R P/2xCm,
5: Concatenate Iodd and Zeven to get 2; (=2(2//)
6: end for
7: Concatenate all patches get Xemb (RXxXX(P2))XC..
A.1 THEORETICAL ANALYSIS
Theorem B.1: Under appropriate optimization, the dynamic weight model achieves lower error than the fixed weight model, i.e., F. F.y.
Definition:In the context of time series analysis, we can segment dataset into N distinct patches, denoted as I1, #2, UN each with its corresponding true target value y/ Two models are con- sidered for processing these patches:
Fixed Weight Model: This model employs a constant weight Wy to produce the convolution output for each patch The output is calculated follows:
yf W J2
(10)
This model uses variable weights W; for each patch, defined as W; = ag W., where a; is coefficient that can vary with each patch. The convolution output for patch i is then given by:
yd. = W; T2 = (a: Ws) 26
(11)
Proof:
For the fixed weight model, the total error is given by:
Ey
(W, W..x; x. o
(12)
Expanding the square term, we get:
N
Fy
(W, 2W, 24 27 + (vi)
(13)
For the dynamic weight model, the total error is given by:
N
Ed
Σ
((as
Wo xx)) - v6
(14)
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Expanding the square term, get:
Ed = Σ ((a:
W6- =x)²= 2((a W6 xz)) Vi + (vt)²)
(15)
A=1
In the fixed weight model, the error F. is minimized by optimizing the single parameter Wy: dEj a
0 + W = optimal fixed weight
(16)
In the dynamic weight model, the error Ed minimized by optimizing both Wo (shared across patches) and a (specific to each patch). The optimization conditions are:
OEa and dEa
0, Vi
(17)
aW,
da;
Solving for ok;:
Vi
(18)
Wo 24
Substituting this back into Ed, the error is further reduced compared to the fixed weight model.
The dynamic weight model provides additional flexibility by adjusting ag for each patch i. This allows to better approximate the target y resulting in:
Ea Ey
(19)
A.2 COMPUTATIONAL ANALYSIS:
Consider the input time series tensor X3D E C.C where N x P L and represents the time series length. Given that the output dimension of TVNet matches the input dimensions, the computational complexity for 2D convolutions can be described as follows:
FLOPPsConv2D) C. Cm x 122
N x (P/2) C. Cm k2
(20)
Params(Conv2d) = Cm X C. x 12
Om denote the embedding dimensions and & represent the kernel size of the 2D convolutions. In the process generating time-varying weights, the features are initially passed through an intra-pool and subsequently through an inter-pool, which incorporates non- parameerr layer.
FLOPs(Gimtra) Cm x x 2 x P/2 C.
(21)
Params Params(Gsnter) Cm N
In the channel modeling process, two ID convolutions with kernel size of k = 1 are utilized.
FLOPs(chamel) Cm X C'm x k(1) N Cm Cm x k(1) Params(channel) = Om X Om x k(1) + Om X Cm x k(1)
(22)
Subsequently, the time-varying weight matrix E R.C. x.N is multiplied by the temporal weight tensor W E IRC Cm xCn xA2 for 2D convolutions.
FLOPs(multipy) Cm C. x k2 N
(23)
Therefore, the total computational complexity and parameter count are as follows:
FLOPs =FLOPs(CoN2D) + FLOPs(G) FLOPschamee)) + (FLOPsmullppl) =Cm C. L Cm x C. k(1) N
(24)
+ Cm x Gm h(1) Cm x C. x 122 x
Params =Params(Conn22D + Params( + Params(channel)
(25)
Cm C. 2²2 Cm N + C. Cm k(1) Cm x Cm k(1)
Based on the computational analysis, TVNet demonstrates FLOPs of O(L??) and parameter count of OCC2).
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B DATASETS
B.1 LONG-TERM FORECAST AND IMPUTATION DATASETS
Assessments of the long-term forecasting capabilities were conducted using nine widely recog- nized real-world datasets, encompassing domains such as weather, traffic, electricity, exchange rates, infueeza-llike illness (ILD), and the four Electricity Transformer Temperature (ETT) datasets (ETTh1, ETTh2, ETTmI, ETTm2). For the imputation task, benchmarks were established using datasets from weather, electricity, and the four ETT datasets. These datasets, extensively utilized in the field, cover various aspects of daily life.
The characteristics of each dataset, including the total number timesteps, the count of variables, and the sampling frequency, are summarized in Table 7 The datasets are partitioned into training, validation, and testing subsets in chronological order, with the Electricity Transformer Temperature (ETT) dataset employing 6:2:2 ratio and the remaining datasets using 7:1:2 ratio. Normalization to a zero mean is applied to the training, validation, and testing subsets based on the mean and standard deviation of the training subset. Each dataset comprises single, continuous, long-time series, with samples extracted using a sliding window technique.
Further details regarding the datasets
follows:
1. Weather consists of 21 climatic variables, such as humidity and air temperature, recorded in Germany throughout 2020.
2. Traffid includes road occupancy rates collected by 862 sensors across San Francisco Bay area highways over a two-year period, provided by the Californaa Department of Trans- portation.
3. Electricity comprises hourly electricity usage data for 321 consumers from 2012 to 2014.
4. Exchange encompasses daily exchange rates for eight currencies, observed from 1990 to 2016.
5. I which stands for Influenza-Like Illness, contains weekly counts of ILI patients in the United States from 2002 to 2021. It includes seven metrics, such as III patient counts across various age groups and the proportion of ILI patients relative to the total patient population. The data is provided by the Centers for Disease Control and Prevention of the United States.
6. E The Electricity Transformer Temperature (ETT) dataset comprises data from seven sensors across two Chinese counties, featuring load and oil temperature metrics. It includes four subsets: 'ETTh1' and 'ETTh2' for hourly data, and 'ETTml' and 'ETTm2' for 15- minute intervals.
Table 7: Dataset descriptions of long-term forecasting and imputation.
Dataset
Weather
Traffic
Exchange
Electricity
ETThl
ETTh2
ETTml
ETTm2
Dataset Size
52696
17544
7207
26304
966
17420
17420
69680
69680
Variable Number
862
321
Sampling Frequency
10 mins
hour
day
hour
week
hour
hour
mins
15 mins
B.2
SHORT-TERM FORECAST DATASETS
The M4 dataset, which includes 100,000 heterogeneous time series from various domains, poses a unique challenge for short-term forecasting. This attributed to the diverse origins and distinct
hhtps://pems.dol. wtt..aaa..dd...ooooo/
http:///ghhhbb.ooooooooo//on//ae -etpaa/ltiiiiiaaaiiiiieeeeeeeead 12014
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temporal characteristics of the data, which contrast with the uniformity typically found in long-term forecasting datasets. A statistical overview the dataset is provided Table
Table 8: Dataset descriptions of M4 forecasting
Dataset
Sample Numbers (train set, test set)
Variable Number
Prediction Length
M4 Yearly
(23000, 23000)
M4 Quarterly
(24000, 24000)
M4 Monthly
(48000, 48000)
18
M4 Weekly
(359, 359)
13
M4 Daily
(4227, 4227)
I
14
M4 Hourly
(414, 414)
B.3 CLASSIFICATION DATASETS
The UEA dataset comprises diverse collection of time series samples across various domains, designed for classification tasks. encompasses broad spectrum of recognition tasks, including facial, gesture, and action recognition, well audio identification. Furthermore, extends its utility to practical applications in industrial monitoring, health surveillance, and medical diagnostics, with particular emphasis the analysis of cardiac data. Typically, the dataset is organized into offers a detailed overview of the classification statistics for the UEA
10 distinct classes. Table g datasets, underscoring their extensive applicability across multiple domains.
Table 9: Datasets and mapping details of UEA dataset
Dataset
Sample Numbers (train set, test set)
Variable Number
Series Length
DihanolConcenttationn
(261, 263)
1751
FaceDetection
(5890, 3524)
144
62
Handwriting
(150, 850)
I52
Heartbeat
(204, 205)
405
Japanese Vowels
(270, 370)
29
PEMS SF:
(267, 173)
963
144
SelfRegulationSCPI
(268, 293)
896
SelfRegulationSCP2
(200, 180)
7
1152
SpokenArabiicDightt
(6599, 2199)
93
UWWavGGesureLiibrryy
(120, 320)
315
B.4 ANOMALY DETECTION DATASETS
Our benchmarking process utilizes datasets that cover range of domains, such server machinery, spacecraft, and infrastructure systems. These datasets are carefully organized into three distinct phases: training, validation, and testing. Each dataset consists of single, continuous time series, and samples are extracted using uniform, fixed-length sliding window method. Table preesents a comprehensive statistical summary of these datasets, illustrating their structured arrangement and the systematic approach to sample extraction.
presents
Table 10: Dataset sizes and details for anomaly detection datasets
Datasct
Dataset sizes (train set, val set, test set)
Variable Number
Sliding Window Length
SMD
(566724, 141681, 708420)
38
100
MSL
(44653, 11664, 73729)
55
100
SMAP
(108146, 27037, 427617)
25
100
SWaT
(396000, 99000, 449919)
51
100
PSM
(105984, 26497, 87841)
25
100
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B.5 DATASET VISUALIZATION
Figure 10 11
and 12
shows the pairwise correlation among the variables in ETT dataset.
22
28
145
045
439
639
325
96
Mas
Figure 9: Pairwise correlation among the variables(ETTTml.
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1.4
133
250
620
1841
Figure 10: Pairwise correlation among the variables(ETTm2))
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35
Figure 11: Pairwise correlation among the variables(ETTh]]
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341
38
HMLL
Figure 12: Pairwise correlation among the VariablessETThh).
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C
EXPERIMENT DETAILS
Table 11: Model Hyper- and Training Process for Different Tasks/Conigguraions[WWee)
Model
Training Process
(kernel
Layers
Cn
(Paich length)
LR
Loss
Batch Size
Epochs
Long-tam Forecasting
10
MSE
Short-temm Foenciating
10"2
SMAPE
Imputation
3x3
10
MSE
16
Classification
3x3
3
10
Cross Enmppy
16
Anvemaly Detection
3x3
10
MSE
128
10
LR refers to the learning rate, and we have incorporated an early stopping mechanism to enhance the training process. long-term forecasting task, lenght is set to 9 et al. (2022a).
We performed experiments using 5 distinct random seeds: 1111, 333, 2023, 2024, and 2025.
C.I LONG-TERM FORECASTING
Implementation details: Our method utilizes the mean squared error (MSE) loss function and optimized using the ADAM optimizer (Kingma 2014). with an initial learning rate set to 10-4 The training regimen consists of 10 epochs, augmented by an appropriate early stopping mechanism. We employ the mean squared error (MSE) and mean absolute error (MAE) evaluation metrics. The deep learning models are implemented using PyTorch (Paszke et al. 2019) and executed on NVIDIA RTX4090 GPU.
Model parameter: TVNet comprises 3 3DD-blokks, with the embedding dimensions (Cm.) set to 64. The patch length (P) is established at 24, and the kernel size (k) for 2D convolutions is 3 3. The random seed is set to 2024.
The mean square error (MSE) and mean absolute error (MAB) are adopted for long-term forecasting.
Metries:
T
1
MSE
Σ
(2:
x2,)
(26)
T i=0
1 T
MAE = T
Σ
2 xz
(27)
1=0
where T' is the number of observations, Tú is the predicted value, and o; is the actual value for observation i.
C.2 SHORT- FORECASTING
Implementation details: Our method employs the Symmetric Mean Absolute Percentage Error (SMAPE) Joss function and optimized using the ADAM optimizer (Kingmal 2014), with initial learning rate of 10 The training regimen consists of 10 epochs, augmented by appropriate early stopping mechanism. We utilize the SMAPE, Mean Absolute Scaled Error (MASE), and Overall Weighted Average (OWA) as evaluation metrics.
Model parameter: TVNet consists of 3D-blocks, with the embedding dimension C., configured to 64. The patch length P is set to 8, and the kernel size l for 2D convolutions is 3 3.The random seed is set to 2024.
Metrics:
For short-term forecasting, in accordance with Wu et al. 2022a), we utilize the Symmetric Mean Absolute Percentage Error (SMAPE), Mean Absolute Scaled Error (MASE), and Overall Weighted Average (OWA) as the metrics. These metrics can be computed as follows:
T
SMAPE = 200
I
(28)
T
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24 Z4
MASE
(29)
j=p+1 [z 23-
1
SMAPE
MASE MASENaive?
OWA
(30)
2
SMAPF Naive22
where p the periodicity data, is the number of observations, T3 is the predicted value, and x; is the actual value for observation i.
C.3 IMPUTATION
Implementation details: Our method utilizes the mean squared error (MSE) loss function and is optimized using the ADAM optimizer (Kingma, 2014), with an initial learning rate set to 10-3 3 The training regimen consists of 10 epochs, augmented by an appropriate early stopping mechanism. We employ the mean squared error (MSE) and mean absolute error (MAE) as evaluation metrics.
Model parameter: TVNet has blocks. The patch length set to to avoid mixing the masked and unmasked tokens, with the embedding dimension Cm configured to 64.The random seed is set to 2024
C.4 CLASSIFICATION
Our method employs the Cross-Entropy Loss and is optimized using the ADAM optimizer, initialized with a learning rate 10-3 The training regimen consists 30 epochs, complemented by appropriate early stopping mechanism. Classification accuracy serves as the metric for evaluation.
Implementation details:
Model parameter: By default, TVNet comprises blocks. The equation determines the channel number The random seed is set to 2024.
Cm min max (2llogz M1 dmmin) dmaxx) d
(31)
where dmni is 32 and dmax 64, accordance with the predefined criteria. The patch length established at 1.
Metries: For classification, the accuracy is calculated as the metric.
C.5 ANOMALY DETECTION
Implementation details: In the classical reconstruction task, we employ MSE loss for training. The ADAM optimizer is utilized, initialized with learning rate of x x10- The training regimen consists of 10 epochs, complemented by appropriate early stopping mechanism. The reconstruction error, quantified as the Mean Squared Error (MSE), serves as the criterion for anomaly detection. The F1-S F1-Score is adopted the metric.
Model parameter: By default, TVNet comprises 3 blocks. The channel number Cm is determined by the equation
Cm min max (2) logg MI dmain) dmax
(32)
where dmin is 32 and dmax is 128, in accordance with the predefined criteria. The patch length P is established at
Metrics: For anomaly detection, we adopt the F1-score, which is the harmonic mean of precision and recall.
D HYPERPARAMETER SENSITIVITY
D.1 MODEL HYPERPARAMETERS
In this section, we assess the robustness of TVNet by examining its sensitivity to model hyperpa- rameters. We will meticulously assess the impact of hyperparameter tuning long-term forecasting
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models, focusing the embedding dimensions(Cm)) the number of blocks, and the patch length P) and kernel size(k) to enhance the accuracy of our predictions.
Embedding Dimensions and Number of blocks:Figure
shows the different effect about 32, 64, 128, 512) and the number of 3D-blocks(1, 2, 3, 4, 5)
DataEmbedding dimension(C,, on ETT datasets(Predicttoon length 96). Table T2 shows the effects of different on the three data sets(ETTh1, Weather Weetherr and Electricity) for long-term prediction tasks of different prediction lengths. Cmn, with the increase of dimension, MSE and MAE show an upward trend on ETThl and Weather datasets, but decrease first and then increase on Electricity datasets. In general, we can see that for different Cms although the value of forecasting varies over the long term, the overall volatility is small.
We tested the influence of different 3D-Blocks(L) on task prediction results in long-term purecasting.shor--terr forecasting and Anomaly detection.(Tabl T3ble Table [5] For long- term forecasting and short-term forecasting,
2, 3, is tested; for Anomaly detection, is tested. The selection of Lis based Table [I] The results show that as the number of 3D- block layers increases, the accuracy of prediction and anomaly detection generally increases slightly, which indicates that single 3D-block has good time series characterization ability without relying on deep stacking. According to the above results, the model shows better robustness for DataEm- bedding Dimension Cn and the number of 3D-Blocks.
4, 5,
0.40
0.40
ETTm1
MAE
0.35
ETTm2
0.35
EfTml
0.30
ETTh1
0.30
ETTm2
ETTh1
ETTh2
0,25
0.25
ETTh2
2
5
100
200
300
400
500
layer number
Embedding dim
Figure 13: Hyperparameter sensitivity concerning the dimension of DataEmbedding and number of blocks
Table 12: Impact of different DataEmbedding dimension. A lower MSE MAE indicates better performance.
Models
Metrics
ETThl
Weather
Electricity
96
192
336
720
96
192
336
720
96
192
336
720
Cm = 32
MSB
0.369
0.399
0.403
0.460
0.149
0.192
0.235
0.306
0.139
0.168
0.162
0.189
MAE
0.407
0.409
0.414
0.457
0.195
0.237
0.281
0.336
0.228
0.246
0.265
0.287
MSE
0.371
0.398
0.401
0.458
0.147
0.194
0.235
0.308
0.142
0.165
0.164
0.190
MAE
0.408
0.409
0.409
0.459
0.198
0.238
0.277
0.331
0.223
0.241
0.269
0.284
C... 128
MSE
0.365
0.389
0.395
0.451
0.153
0.187
0.240
0.306
0.140
0.157
0.166
0.182
MAE
0.404
0.403
0.406
0.453
0.196
0.235
0.276
0.329
0.219
0.238
0.270
0.285
Table 13: Impact of different number of 3D-Blocks(L). A lower MSE or MAE indicates a better performance.
Models
Metries
E
Weather
Electricity
96
192
336
720
96
192
336
720
96
192
336
720
== 2
MSE
0.380
0.412
0.413
0.479
0.153
0.199
0.242
0.316
0.146
0.169
0.168
0.197
MAE
0.410
0.419
0.417
0.475
0.202
0.244
0.285
0.339
0.230
0.247
0.275
0.291
3
MSF
0.371
0.398
0.401
0.458
0.147
0.194
0.235
0.308
0.142
0.165
0.164
0.190
MAE
0.408
0.409
0.459
0.198
0.238
0.277
0.331
0.223
0.241
0.284
MSE
0.360
0.382
0.387
0.435
0.143
0.190
0.229
0.299
0.139
0.161
0.159
0.185
MAE
0.399
0.402
0.399
0.443
0.194
0.232
0.275
0.321
0.216
0.235
0.269
0.277
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Table 14: Impact of different number of 3D-Blocks(() for short-term forecasting
Models
Yearly
Quarterly
Monhly
Others
SMAPE
MASE
OWA
SMAEP
MASE
OWA
SMAPE
MASE
OWA
SMAPE
MASE
OWA
13.596
3.124
0.826
10.941
1.305
1,064
12.729
0.951
0.885
4.951
3.121
1.035
13.217
2,899
0.768
9,986
1.199
0.876
12.493
0.921
0.866
4.764
2,986
0.969
L == 4
13.199
2.871
0.754
9.981
1.522
0.876
12.490
0.923
0.867
4.752
2.981
0.965
Table 15: Impact of different number of 3D-Blocks(L) for Anomaly detection(F1)
Dataset
Model
SMD
MSL
SMAP
SWaT
PSM
4
Ours
84.93
85.10
71.21
93.54
97.45
5
Ours
85.75
85.16
71.64
93.72
97.53
Ours
85.79
85.20
71.59
93.8T
97.67
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Patch length and Kernel size: In this section, conducted experiments long-term forecasting tasks by varying the Patch length (P) and Kernel size (k). We tested four distinct values for Patch length (8, 12, 24, 32) long-term forecasting.Furthee Further, test different Patch lengths (P) in long- term forecasting and short-term forecasting(Tatt
Table 16), and the results show that TVNett is robust when moderate Patch length is selected. Different P has significant influence the sult. To maintain the dimensionality of each feature map layer, we employed zero-padding equivalent (kernel size 1). The results presented in Table [8 indicate that both extremely small and large convolution kernels negatively impact the prediction accuracy. This study advocates for the adoption of 3 convolution kernel, which strikes balance between capturing local features and maintaining computational efficiency. For the Patch length (P), our findings indicate that both smaller and larger values can degrade the forecasting performance.
the context of long-term fore- casting, we recommend setting the Patch length to 24, it offers an optimal balance for prediction accuracy. For short term forecasting, is recommended for patch-length.
ETTm2
0.35
0.3325
0.256
0.34
0.3300
0.254
1.0
20
10
20
30
10
20
30
100
20
Puich length
Patch lengih
Patch length
Puich length
Figure 14: Hyperparameter sensitivity concerning patch length(prediction length=96)
Table 16: Impact of different Patch length. lower MSE or MAE indicates a better performance.
Models
Metrics
ETTh1
Weather
Electricity
96
192
336
720
96
192
336
720
96
192
336
720
P=8
MSE
0.384
0.406
0.404
0.463
0.153
0.197
0.236
0.309
0.147
0.163
0.172
0.193
MAE
0.413
0.417
0.412
0.463
0.204
0.251
0.286
0.334
0.226
0,247
0.272
0.289
P 12
MSE
0.369
0.404
0.402
0.449
0.153
0.205
0.237
0.311
0.146
0.170
0.163
0.191
0.406
0.411
0.412
0,463
0,209
0.245
0.287
0.332
0,227
0,246
0.265
0,280
24
MSE
0.371
0.398
0.401
0,458
0,147
0.194
0,235
0.308
0,142
0.165
0.164
0.190
MAE
0.408
0.409
0.409
0.459
0.198
0.238
0.277
0.331
0.223
0.241
0.269
0.284
P 32
MSR
0.368
0.395
0.399
0.454
0.150
0.192
0.311
0.145
0.167
0.155
0.192
MAE
0.401
0.407
0.420
0.457
0.205
0.239
0.277
0.332
0.227
0.242
0.252
0.288
Table 17: Impact of different Patch length(P) for short-term forecasting
Models
Metrics
Yearly
Quarterly
Monthly
Others
SMAPE
MASE
OWA
SMAEP
MASE
OWA
SMAPE
MASE
OWA
SMAPE
MASE
OWA
13.151
2.925
0.765
10.056
1.155
0.885
12,382
0.926
0.859
4.792
2.965
0.977
P= 8
13.217
2,899
0.768
9.986
1.159
0.876
12,493
0.921
0.866
4.764
2.986
0.969
0.754
9,903
1.147
0.873
12.348
0.854
4.664
0.955
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Table 18: Impact of different kernel sizes. A lower MSE or MAE indicates better performance.
Models
Metrics
ETTh1
ETTml
Electricity
96
192
720
96
192
336
720
96
192
336
MSE
0.375
0.407
0.405
0.464
0.293
0.327
0.371
0.412
0.143
0.171
0.169
0.196
MAE
0.413
0.417
0.415
0.464
0.358
0.371
0.392
0.419
0.221
0.249
0.265
0.302
MSE
0.371
0.398
0.401
0.458
0.288
0.326
0.365
0.412
0.142
0.165
0.164
0.190
MAE
0.408
0.409
0.409
0.459
0.343
0.367
0.391
0.413
0.223
0.241
0.269
0.284
MSE
0.369
0.396
0.399
0.454
0.289
0.324
0.367
0.417
0.146
0.168
0.165
0.187
MAE
0.405
0.408
0.409
0.457
0.339
0.362
0.390
0.415
0.220
0.240
0,264
0.279
7
MSE
0.370
0.399
0.398
0.450
0.291
0.325
0.368
0.420
0.147
0.167
0.164
0.189
MAR
0.406
0.409
0.409
0.462
0.341
0.360
0.391
0.426
0.225
0.239
0.267
0.281
k
9
MSE
0.386
0.413
0.407
0.474
0.302
0.349
0.403
0.419
0.157
0.189
0.194
0.212
MAE
0.437
0.444
0.439
0.485
0.372
0.396
0.410
0.432
0,230
0,271
0.285
0.314
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D.2 TRANING PROCESS HYPERPARAMETERS
Furthermore, acknowledging that hyperparameterss such as learning rate and batch size influence the results, present experimental results inclusive of standard deviation. We explore batch sizes ranging from 32 to 512, learning rates from 10-5 to 0.05, five seeds (1111111,330 111,33,,002,
2024,2025) and training epochs from 10 100. The findings are summarized in Table I Table 20 and Tablc21 for long-term forecasting. shrttg..shottttmm forecasting and Anomaly detection. From the above results, we can find that for different training process Settings, the standard deviation of the results of different time series tasks is smaller, indicating that the model shows high robustness for different training Settings.
Table 19: Detailed performance of TVNet. We report MSE/MAE and standard deviation different forecasting horizons (24, 36, 48, 60) for ILI and (96, 192, 336, 720) for others. H1, H2, H3, H4 means the horizons.
Horizon
Electricity
ETTh2
Exchange
MSE
MAE
MSE
MAE
MSE
MAE
+ 0.002 0.223 + 0.003
0.263
0.003
0.329 0.003
0.080
0.002
0.195
0.003
HF2
0,165 + 0.002
0.241 + 0.006
0.319 0.003 0.372 = 0.002
0.163
+ 0.001
0.285 + 0.002
H33
0.164 + 0.003 0.269 + 0.002
0.311
0.004 0.373 +: 0.002
0.291
+ 0.003
0.394 + 0.003
0.005
0.284
0.401
0.004
0.658
0.007 0.594
Horizon
Traffic
Weather
MSE
MAR
MSE
MAE
MSE
MAE
HI
1.324 +: 0.006
0.712 + 0.001
0.367
0.003 0.252 + 0.003
0.1/7 : 0.005
0.198 = 0.001
0.020 0.772
0.018
0.381
0.004
0.194
0.003
0.238
113
1.456 + 0.015
0.782 + 0.001
0.395
0.001
0.268 = 0.003
0.233 + 0.005
0.277 + 0.005
H4
1.632 + 0.022 0.796 + 0.005
0.442 0.004 0.290 0.006
0.308 + 0.003
0.331 + 0.003
Table 20: Detailed performance of TVNet. We report standard deviation short-term forecasting
SMAFFE
OWA
MASE
SMARE
SXCAPE
MASE
OBA p0 1111
TVNE
11217 605
2900- 101
1100
1.19 GoKe
13.40 DoKa
0001 6000
1:00
1000
Table 21: Detailed performance of TVNet. We report standard deviation on Anomaly detection(F1)
Datieee
Model
SMD
MSL
SMAP
SWaT
Anomaly Desoction(E))
Ours
0.06
H5.16
0.04
+
0.05
97.55
0.00
Anemaly Detection R)
Ours
$3.40 4 0.02
80.47 J. 0.03
58. 26
0.02
96
0.05
0.04 98.30
96 76
Anomally Desoctiont P)
Ours
88.03 1 0.03
83.91 1 1.05
92.64 0.06
91.26
0.01
0.01
E MORE ABLATION EXPERIMENTS
E INTER-POOL MODULE
In this section, we further conducted ablation studies on the tasks of short-term forecasting and time series anomaly detection, and presented the results. 23)
E.2 RESHAPE REPRESENTATION
The existing representations for time series include 1D, 2D (inter-pool, cross-dimensinn cross-dimenssons)), and 3D Linter-pool, intra-pool pool, and coss-dimensiions.. To demonstrate the effectiveness of the 3D- embedding (3) proposed in this paper, ID-embeddiing E (labell @ )and 2D-embedding Xemb E NxXxxC (label @2) designed following the same rationale. the time series analysis length
task using fixed weight convolution for different methods, long-term forecasting(Prediccie =192) is tested. Table 24 shows the result.It can be seen from the results that the error is smaller than that of -D-Embedding and Branbeedding.D-Emeeeddd indicating that 3D-Embedding can better represent time series.
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Table 22: Ablation of Inter Inter-pool Module.AAnonaly detection(F1) and Short-term (OW)))
Dataset
Model
SMD
MSL
SMAP
SWaT
PSM
Anomaly Detection
Ours
85.75
85.16 67.34
71.64 59.82
93.72 82.74
97.53
w/o
78.61
86.27
Dataset
Model
Yearly
Quarterly
Monthly
Others
Short-term forecasting
Ours
0.768 0.809
0.876 1.231
0.969 1.205
w/o
0.929
Table 23: Different Embedding ways for Anomaly-detection and short-term forecasting.
Dataset
Model
SMD
MSL
SMAP
SWaT
PSM
Anomaly Detection
67.38
70.29
65.43
75.41
85.77
70.60
65.95
$2.09
76.54
82.05
80.21
83.24
69.41
87.65
92.34
Dataset
Model
Yearly
Quarterly
Monthly
Others
Short-term forecasting
①
1.043
1.576
1.132
1.574
0.904
1.589
1.076
1.322
0.839
1.375
1.034
1.323
Table 24: Different Embedding ways for long-term forecasting.
Embedding
Electricity
ETTh2
Exchange
MSE
MAE
MSE
MAE
MSE
MAE
0.214
0.318
0.347
0.391
0.185
0.320
0.209
0.304
0.333
0.386
0.171
0.312
0.201
0.296
0.330
0.381
0.164
0.296
Embedding
ETTml
Traffic
Weather
MSF
MAF
MSR
MAF
MSF
MAR
0.357
0.392
0.440
0.349
0.271
0.292
0.332
0.383
0..277
0.320
0.262
0.271
0.336
0.385
0.423
0.313
0.257
0.269
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E.3 TRAINING SPEED AND MEMORY
Considering that the hyperparameters set during different training processes and the look-back win- dow can affect the number of model parameters and running speed, make fairer comparison of the parameters and training speed of different models, we selected three typical models: PatchTST (Transformer-baseel) based), Dlinear (MLP-based), and ModemTTN (CNN-based), well as the model proposed in this paper for comparison. We unified the training hyperparameters as shown in Table The results for different input lengths on ETTm2 (prediction length fixed at 96) are shown in From the figure, it can be observed that in terms of running speed, as the input length increases, the training time of PStchTST increases, and the memory usage of Modern increases significantly. In contrast, the training time and memory usage of the TVNet proposed in this paper increase slowly with the increase of input length, proving the superiority of the proposed model in terms of efficiency and effectiveness.
11
Figure 15
Tr Training Time epoch
GPU Memory Usage
PaichTST ModemTCN
ModemTON
120
Dilnear
Dlinear
TV/ee
TVitet
40
GPU
20
192
336 back Window
720
192
532
720
Look back Window
Figure 15: Params and GPU Memory for different input length(ETTm2)
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F MORE EXTRA EXPERIMENTS STUDIES
We have conducted additional experiments and analyses.
F.1 INPUT LENGTH
In time series forecasting, the input length dictates the extent of histori- cal data available for the algorithm's analysis. Typically, models that excel at capturing long-term dependencies tend to exhibit superior performance with increasing input lengths. To substantiate this, we evaluated our model across range of input lengths while maintaining constant prediction lengths. Figure 16 illustrates that the performance of transformer-base longer inputs due to the prevalence of repetitive short-term patterns. Conversely, TVNet's predictive accuracy consistently improves with extended input lengths, suggesting its proficiency in capturing long-term dependencies and extracting meaningful information effectively.
Impact of input length:
models diminishes with
E1Th1
Er
Weather
PatchTST
PatchTST
MSF
Ttansformnt Crossformar
MSE
Tirursoommrr
Crossformer
MSE
hachTST
monsformer
TVNet
0.4
TVWet
0.18
Crosstormer
720
Figure 16: The MSE results with different input lengths and same prediction lengths(ETThi,ETTT) and Weather) prediction length(L)=192
F.2 MODEL ROBUSTNESS
We employ straightforward noise injection technique ascertain the robustness of our model. Specifically, we randomly select a proportion of data from the original input sequence and in- troduce random perturbations within the range [-2X,, 2X,,], where X; represents the original data values. The perturbed data is subsequently utilized for training, and the mean squared error (MSE) and mean absolute error (MAB) metries are documented. The findings are presented in Table 25 An increase in the perturbation ratio leads to marginal rise in both MSE and MAE, indicating that TVNet demonstrates commendable robustness against mild noise (up to 10%) and excels at handling significant data anomalies, such those caused by equipment malfunctions in power data.
Table 25: Different indicates different proportions of noise injection.
Models
Merrics
Weather
Flectricity
Traftic
96
192
336
336
720
336
720
TVNo
MSE
MAF
0.198
0.238
0.369
0.252
0.290
1%
MSF
0.146
0.192
0.238
0.305
0.142
0.165
0.167
0.191
0.365
0.383
0.396
0.444
MAE
0.197
0.236
0.280
0.332
0.225
0.244
0.271
0.286
0.255
0.260
0.267
0.292
5%
MSE
0.150
0.196
0,238
0 0.307
0.148
0.170
0.166
0.191
0.369
0.380
0.399
0.145
0.195
10%
MSE
0.159
0.207
0.245
0.310
0.149
0.176
0.177
0.194
0.405
0.451
MAE
0.205
0.247
0.289
0.336
0.229
0.24.5
0.279
0.283
0.265
0.271
0.278
0.294
31

---

Published as a conference paper at ICLR 2025
F.3 UNIVARIATE LONG-TERM FORECASTING RESULTS
Table 26 shows the Univariate long-term forecasting results.
Table 26: Following PatchTS (Nie et al. 2022 input length is fixed as 336 and prediction lengths T (96, 192, 336, 7203. The best results are in bold.
Models
Metrics
TVNet
PaccTTTT
DLincar
FEDformer
Autoformer
LogTIrass
MSE
MAE
MSE
MAB
MSE
MAE
MSE
MAE
MSE
MAE
MSE
MAE
MSE
MAE
0.053
0.179
0.056
0.377
192
0.067
0.202
0,071
0.205
0,071
0.204
0.104
0.245
0.114
0.262
0.217
0.295
0.234
0.409
ETTh1
0.071
0.210
0.220
0.098
0.270
720
0.083
0.229
0.087
0.236
0.087
0.359
0.142
0.299
0.126
0.283
0.183
0.355
0.475
0.629
0.121
0.282
0.271
0.373
192
0.164
0.320
0.168
0.328
0.176
0.329
0.185
0.330
0,204
0.351
0.227
0.387
0.281
0.429
ETTb2
336
0.171
0.333
0.171
0.336
0.209
0.367
0.231
0.378
0.246
0.389
0,408
0.293
0.437
720
0.219
0.380
0.223
0.380
0.276
0.426
0.278
0.420
0.268
0.409
0.291
0.439
0.218
0.387
0.024
0.121
0.028
0.033
0.140
0.056
0.277
0.218
0.387
192
0.038
0.150
0.039
0,150
0.045
0.156
0.058
0. 0.186
0.081
0.216
0.151
0.310
0.157
0.317
ETTml
336
0.053
0.173
0.053
0,173
0.061
0.182
0.084
0.231
0.076
0.218
0.427
0.591
0.289
0.459
720
0.072
0,203
0.073
0.206
0,080
0,210
0.102
0.250
0.110
0.267
0.438
0.586
0.430
0.579
0.063
0,183
0.065
0,186
0.063
0.183
0.067
0.198
0.065
0.989
0.088
0.225
0.075
0.208
ETTm2
192
0.089
0.227
0.093
0.231
0.092
0.227
0.102
0.245
0.118
0.256
0.132
0.283
0.129
0.275
336
0.119
0.261
0,120
0.265
0.119
0.261
0,130
0.279
0.154
0.305
0.180
0.336
0.154
0.302
720
0.170
0.322
0.171
0.322
0.175
0.320
0.178
0.325
0.182
0.335
0.300
0.435
0.160
0.321
32

---

Published as a conference paper at ICLR 2025
F.4 LLM AND MORE BASELINES
For the long-term forecasting task, we have added some new Baselines (LLM-Based and TMixer). the results, from which we can see that TVNet has shown good performance in most of the forecasting results.
Table 27: The complete results for long-term forecasting are detailed baselines focused on LLM), demonstrating thorough comparison among various competitive models across four distinct forecast horizons. The Avg metric indicates the average performance across these forecast horizons.
Models
TVNet (Ours)
S2I--LLM 2024
TimeLLM 2025
GPTITS 2024
TimeMiaer (2024b)
Metrics
MSE
MAE
MSE
MAE
0.258
0.343
0.288
0.346
0.311
0.365
0.292
0.346
0.320
0.357
192
0.326
0.367
0.325
0.365
0.364
0.395
0.332
0.372
0.361
0.381
336
0.365
0.391
0.389
0.390
0.369
0.398
0.366
0.394
0.390
0.404
720
0.412
0.413
0.403
0.418
0.416
0.425
0.417
0,421
0.454
0.441
Avg
0.348
0.379
0.343
0.379
0.365
0.395
0.388
0.403
0.381
0.395
0.161
0.254
0.165
0.257
0.170
0.262
0.173
0.262
0.175
0.258
E11m2
0.220
0.299
0,303
0.229
0.301
0.237
336
0.272
0.316
0.277
0.330
0.281
0.335
0.286
0.341
0.298
0.340
720
0.349
0.379
0.363
0. 0.390
0.379
0,448
0.378
0.401
0.391
0,396
Avg
0.251
0.319
0.264
0.339
0.275
96
0.371
0.408
0.366
0.396
0.380
0.406
0.376
0.397
0.375
0.400
192
0.39%
0.409
0.401
0.420
0.426
0.438
0.416
0.418
0.429
0.421
0.401
0,409
0.412
0.431
0.437
0.451
0.442
0.433
0.484
0.458
720
0.458
0,459
0.440
01:4%%
0.515
0.509
0.477
0.456
0.498
0,482
Avg
0.407
0.421
0.406
0.427
0.439
0.451
0.465
0.455
0.447
0,440
0,263
0.339
0.178
0.340
0,306
0.362
0.285
0.342
0.289
0.341
0.319
0,373
0.346
0.385
0.346
0.389
0,372
336
0.311
0.373
0.367
0.486
0.393
0,422
0.373
0.407
0.386
0.414
720
0.401
0.414
07400
0,436
0.397
0.433
0,405
0,441
0,412
0.434
Avg.
0.324
0.347
0.391
0.360
0,412
0.364
0.395
Elecrriity
0.142
0.223
0.135
0.230
0.140
0.246
0.139
0.238
0.153
0.247
192
0.165
0.241
0.149
0.247
0.155
0.253
0.153
0.251
0.166
0.256
336
0.164
0.369
0.167
0.266
0.175
0,279
0.169
0.266
0.185
0.277
0.190
0,284
0.210
0.287
0.204
0,305
0,203
0.297
0.225
0,310
Avg.
0.165
0.254
0.161
0.257
0.168
0.270
0.167
0.263
0.182
0.272
Wealher
0.194
0.147
0,238
0.198
0.145
0.238
0.195
0.148
0.194
0.197
0.162
0.248
0.212
0,163
0.208
0,209
336
0.235
0.277
0.243
0.280
0.248
0.285
0.254
0.286
0.251
0.287
720
0.308
0.331
0.312
0. 1.326
0.317
0,332
0.326
0.337
0.339
0,341
Avg.
0.221
0,261
0.222
0.259
0.226
0.265
0.237
0.270
0.240
0.271
96
0.367
0.253
0.379
0.274
0.383
0.280
0.388
0,282
0.462
0.285
Tuille
192
0
0,263
0.397
0 0.242
0.399
0.294
0.407
0,290
0.473
0.296
3.56
0.395
0.368
0.407
0.289
0.41
0.306
0.412
0.294
0.498
0.296
0.442
0,290
0.440
0.448
0.319
0.450
0.312
0.506
0.313
Avg
0.39%
0.268
0.40X
0.286
0.440
0.301
0.414
0.294
0.484
0.297
33

---

Published as a conference paper at ICLR 2025
F.5 EXOGENOUS VARIABLE FORECASTING
As discussed in Timexer Wang et al. 2024b). forecasting exogenous variables is crucial in various domains, including load forecasting. Our experiments the ETT dataset also focused on predicting such variables. Figures 17 demonstrate that TVNet consistently outperforms the optimal baseline model exogenous variable forecasting.
2958
(a) ETThl
(b) ETTh2
8558
(c) ETTml
(d) ETTm2
Figure 17: Exogenous variable learning results for ETT dataset.
34

---

Published as a conference paper at ICLR 2025
G FULL RESULTS
G.1 LONG-TERM FORECASTING
Table 28: The complete results for long-term forecasting are detailed, demonstrating a thorough comparison among various competitive models across four distinct forecast horizons. The Avg metric indicates the average performance across these forecast horizons.
Model
TYNet
PuchTST
Transfinner
Croufores
RLines
MTS Miter
Diinear
TennsNet
MICN 2013
ModenTCN 2024
FEDiomer
RMLP
(Ours)
2023a
2027a
Metics
MAE
MSE
MAE
MAE
MSE
MAE
MSE
MAE
MAE
MSB
MAE
MSE
MXE
95
0.288
0.361
0.7141
0.342
(0:154
0.968
0.316
0.173
0.931
0.342
0.314
0.188
0.799
0.343
0.318
0.175
0.314
100
0.202
0.345
0.336
0.990
00.7M
192.
0.326
0.167
0.152
0.569
0:377
0.391
0.377
0.111
0.355
0.369
0.354
0.186
0:355
0.165
0:331
0.187
0:359
0.387
1.312
0.165
0.365
0.415
0.344
0.925
336
0,365
0.391
0.366
0.302
0.436
0.420
0.431
0.442
0.370
0.363
0.394
0.405
0.369
0.366
0.410
0,411
0.398
0.413
0.365
0.391
0.392
0.425
0.300
0.410
Arg
0,348
0.361
0.000
0.376
0.355
0.357
0.379
96
0.861
0.354
0.165
0.255
(0.190
0.264
0.164
0.253
0.177
0.259
0.167
0.260
0.157
0.178
0:273
0.166
0.256
0.080
0.27)
[6.174
192
0.220
0.293
0.230
0.202
0.250
0.309
0,505
0.519
0.219
0.290
[.241
0,303
0.224
0.303
0.249
0.309
0.245
0.316
0.222
0.293
0.252
0.318
0.233
0.303
336
0,212
0,316
0.211
0.329
0.311
01345
1.611
0.590
0.233
0.326
11297
0.338
0.251
0,342
0.312
0.151
(1:295
0.250
0,272
0.124
0.324
0.364
0.2291 0.338
0.379
0.362
0.585
0.365
0.397
0.351
0.420
Ang
0.251
0.311
0:255
0.515
0.332
0,925
0.266
0.396
0.253
0.314
00,300
95
0,371
0.405
0.399
(0:766
0.386
0,391
0,372
0.345
0,375
0.3M
0.364
0:427
0.368
0.344
00377
0.415
(0,300
0.410
ETM
193
0.398
0.019
0.415
[1421
00:41
11:136
01:19
0.064
0.004
0/412
01416
0.426
0.005
0.416
0.557
0.436
(0:20
0.453
0.405
0.611
0.423
0.646
(0,430
0.832
336
0.401
0.409
0.422
0.435
0.467
0.455
0.440
0.461
0.420
0/423
0.455
0.449
0.439
0.443
0.491
0.409
0.433
0.45
0.391
0.412
0.444
0.462
0.444
0.443
0.459
0.460
0.472
0.472
0.492
Ang
0.407
0.496
0.433
0.404
0.420
0:454
0.995
0.184
(1240
0.765
0.985
0.110
0.954
ETR
192
0,319
0.372
0.339
0.570
0.310
0.400
0.205
0.624
0.320
0.374
0.374
0.399
0.363
0.418
0.402
0.414
0.438
0.320
0.374
0.407
0.446
0.344
336
0.311
0,373
00.3MM
0.300
014435
11433
11827
0.675
0.325
0.380
1.99%
0.432
0.448
0.465
01445
0.457
01417
0.457
11:11
0.100
00400
0.6477
0.353
0.007
730
0.401
0.494
(0:19
0.422
0.422
0.445
1.111
0.540
(1372
0.421
[1463
0.465
0.605
0.551
0.463
0.46%
0.476
0.473
0.902
0.457
0.412
0.460
0.410 0.440
0.324
0.377
0.330
0.579
0,37M
0.386
0.413
0.431
0.414
0.322
0.379
003388
0.434
Flbemsity
96
0.142
0.223
0.129
0.222
0.235
0.141
0.243
0.153
0.257
0.267
0.129
0.226
10.186
0.502
0.224
192
0.165
0.341
0.142
0.240
00:60
0.25%
0.258
0.154
0.368
0.168
0:361
0.152
0.349
0.154
0.389
0.168
0:379
0.143
0:129
0.197
0.31
0.344
336
0.164
0.269
0.163
0.250
0.178
0.269
0.323
0.369
0.171
0.264
0.176
0.277
0.159
0.267
0.198
0.300
0.106
0.508
0.161
0:259
0.213
0.525
0.066
0.257
720
0,190
0.384
0.197
0.290
0.225
0.317
0.404
0.423
0.259
0.297
0.212
0.308
0.233
0,344
0.220
0,120
0.203
0,312
0.191
0.286
0.233
0,344
0.200
0.291
Arg
0.105
0.254
10.14
0,253
0.277
11.295
01100
0,261
0.173
0.272
0.137
0.274
0.192
00.122
0.202
0.1.6
0.253
10.207
0.301
0.251
96
0.147
0.198
00:40
0.196
00177
0.225
0.156
0.206
0.152
0.236
0.140
0.300
10.231
0.314
(6.149
0.202
Weather
192
0.194
0.338
0.194
0.41
0.221
0.254
0.260
0.199
0.248
0.220
0.262
0.219
0.261
0.220
0,283
0.196
0.245
0.775
0.329
336
0.255
0.277
0.345
0.281
0.278
0.256
0.225
0.311
0.205
0.294
0.249
0.291
0.265
0,319
0.260
0.306
0.275
0.324
1.233
0.272
0.339
0.377
0.243
0.292
720
0,310
0.331
0.314
0.334
0:355
0:347
113318
0.363
11332
0,339
0.336
0,343
0.333
0,362
0.305
0,199
00:11
0.250
0.314
0.354
0.38M
0.409
0.310
0.333
Axg
0,221
0.261
0.226
0.264
(0.258
0.278
0.230
0,200
0.247
0.279
0.235
0,272
0.240
0.300
0.259
0.287
0.242
0.298
0.234
0.264
003100
0:357
60222
0.365
96
0.167
0.252
0.360
0.349
00.705
0.268
0.512
0.290
0.406
0.375
0:462
0.352
0,410
0.262
0.805
0.121
0 0..06
0.501
0.368
0:151
0.576
00380
00.490
0.307
Yrafic
1M2
0.281
0.262
0.37V
0.356
01417
0,377
0.85%
0.354
0.433
0.315
0,37V
0.201
06610
1/66
0.195
0.268
0.392
0.264
(0-433
0.765
0.910
0.517
0.187
0.808
0.100
0.416
0.796
0.679
0.196
(
0.110
0.392
0:300
0.600
0.955
00.470
720
0,442
0.290
0.432
0.256
0-467
0. 0.302
0.535
0.313
0.555
0.396
0.539
0,370
0.466
0.315
0.640
0.390
0.571
0.323
0.440
0.296
0.621
0.595
0.513
0.973
Avg
0.396
0,265
0.339
0.364
(0:438
0,262
11.335
0.300
0.518
0,763
0.494
0.354
0.434
0,295
0.620
0.336
00:355
0,312
0.39
0.270
00.004
0.372
(0,466
0.345
Bichange
95
0.080
8,195
0./91
0.214
(0:096
0.206
0.186
0.146
0.08%
0.101
0.08%
0.000
0.081
0.201
00100
0.354
01
0.100
0.284
0.000
1.196
(1226
(0.083
01200
0.192
0.313
0.296
01185
0.256
0.360
0.292
336
0.291
0.394
0.350
0.432
0.331
0.417
0.783
0.721
0.309
0.401
0.336
0.417
0.305
0.414
0.367
0.443
0.272
0.407
0.307
0.305
0.426
0.464
0.300
720
0.658
0,594
0.911
0.716
0.847
0.691
1.367
0.943
0.817
0.680
0,900
0,715
0.643
0.501
0.964
0.746
0.714
0.658
0.656
0.582
L,000
0.500
(0.116
0.680
Aag
0.754
0.16
00.367
0.419
(0:300
11
01.0%
11.701
0.683
0.945
0,194
0.375
0.417
01.997
0.375
01416
0,441
00:115
0.404
0.302
0.966
10.475
0.476
[0.305
0.394
24
1.324
0.712
1.319
0.754
2.200
1.02
3.040
1.186
4.337
1.507
1.472
0.798
2,215
1,081
2.317
0.934
2,684
1.112
1.347
0.717
22.624
1.005
14.445
1,536
0.772
1.430
3.356
1.481
1,435
1995
19972
0.778
2.516
1.021
4.409
1.159
1.456
0.732
1,553
0.515
2.127
1.004
1.484
1.474
0.822
2.130
1,004
2.238
0.940
1,012
1,388
0.781
2.505
1.041
4.368
60
1,652
0.795
1.470
0.788
2.200
0.096
3,608
1.302
4.278
1.877
1,839
0,912
2.368
1,0%6
2,027
0.925
2,653
1,085
1,774
0.865
2.742
1.123
4.306
1.502
Aag
1,466
0.766
1.443
0.705
22.441
0.906
3.361
1.335
4.259
1,400
1.555
0,919
2,160
1.041
2,139
0.931
2
1.085
L440
0.786
2.590
1.070
4.367
1.516
1st count
21
24
9
3
0
0
3
0
11
12
6
35

---

Published as a conference paper at ICLR 2025
G.2 SHORT-TERM FORECASTING
Table 29: The complete results for the short-term forecasting task in the M4 datasct are presented, utilizing the Weighted Average (WA) the metric.
Models
TVNet PatchTST
M-Mixer
Creeformer
RLinear
MTS-Mixer
DLinner
TimesNet
MICN
ModemTCCN
DTDffomer
N.HITS
(Ours)
2022
2024
2023
2023a
2025b
2023
2022a
2023
2024
2023
2023
Yealy
SMAPE
13.217
132258
13.317
13.392
13.944
13.548
16.965
13.387
14.935
13:226
13.728
13.418
MASE
2.899
2.985
3.006
3.001
3.015
3.091
4.283
2.9%6
3.523
2.957
3,048
3.045
OWA
0.768
0.781
0,786
0.787
0,807
0,803
1,058
0.786
0,900
0.777
0.803
0.793
Monthly Quarterty
SMAPE
9.986
10.197
9.956
16.317
10.702
10.128
12.145
10.100
11.452
9.971
10.792
10.202
MASE
1.159
0.803
1.156
2.197
1,299
1.196
1,520
1.182
1.389
1.167
1.283
1.194
0.803
1.542
0.959
0.896
1.106
0.890
0.878
0.958
0.899
SMAPE
12.641
13:057
12,924
13.363
12.717
13,514
12,670
13.773
12.556
14.260
12.791
MASE
0.921
0,930
1.067
0.966
1.014
0.931
1.037
0.933
1.076
0.917
1.102
0.969
OWA
0.866
0.876
0.976
0.902
0.940
0.879
0.956
0.878
0.983
0.86h
1.012
0.899
Others
SMAPE
766
4.946
4.858
5.493
5.437
4,817
6.709
4,891
6.716
4.715
4.954
5.061
MASE
2,986
2,985
3.195
3,690
3,706
3.255
4,953
3,302
4.717
3.107
3,264
3,216
OWA
0.969
1.044
1.015
1.160
1.157
1.02
1.487
1.035
1.451
0.986
1.036
1,040
SMAPE
11.807
11.740
13.474
12,473
11.892
13.639
11.829
13.130
11.698
12.840
11.927
MASE
1,536
1,590
1.575
1,866
1.677
1,608
2.095
1.585
1.896
11,556
1.701
1.613
OWA
0.832
0.851
0.845
0.985
0.898
0.859
1,051
0.851
0,980
0.838
0.918
0.861
G.3 IMPUTATION
Table 30: The complete results for the imputation task are follows: To assess model performance under varying degrees of missing data, we randomly masked time points at rates of 12.5%, 25%, 37.5%, and 50%.
Models
TVNa
PaddISTT 2022
SCINa 20220
Creafuruaz 2023
MTS-Mieer
Dlince
TimeeNee Anoba
MICN p023]
Med
FEDYomarr 2022
RMLP
(Ouns)
2023u
p0236
2023
2004
2023
Meines
MSB:
MAE:
MSB
MAL
MSE:
MAR
MSB
MAE
MSB
MAN
MSB
MAI
MAl:
12.5%
0.031
0.116
0.087
0.137
0.047
0.137
0.043
0.134
0.065
0.162
0.019
0.092
00009
0.137
0.015
0.082
0.035
0.135
2858
0.016
0.881
0.061
0.10
8.066
0.174
0.098
0.341
0061
0.157
0.011
0.147
0.000
0.191
0023
0.101
0.099
0.170
0.01%
0.08
0000
0.166
(1057
0.184
97.5%
0.019
0.890
0.044
0.133
0.01
0.134
0.041
0.342
0077
0.175
0.060
0.160
0.101
0.219
0.299
0.11
0.000
0.199
0.001
0.095
0.899
0.191
0.97
0.168
8.025
(1.49)
0.052
01006
11195
0.070
0.174
0.133
0.488
00036
0221
Avg
|0.008
0.688
0.030
0.129
(004]
0.343
0.070
0.166
0.056
0.154
[0.003
0.206
0.027
0.107
0.070
0.083
0.000
0.003
0.062
0.137
12.5%
0L018
0.081
0,025
0,992
B1023
0.083
0.0444
0.348
0.006
0.026
0,096
10002
0.106
0.018
0.040
0.000
0.005
0.017
0.876
10056
0.159
(0026
0,0M6
ETTha
25
0.021
0.081
0.027
0.055
0.026
0.100
0.447
0.151
0.030
0.105
0.030
0.103
0.085
0.196
0.020
0.085
0.100
0.216
0,015
0.050
0,050
0.195
0.030
0,105
0,105
0.044
0.345
0.115
0.035
0.110
0.105
0.023
0.163
0.020
0.084
0.034
50%
0.091
0.031
0.111
0.047
0.150
0.030
0.123
0.037
0.115
0.131
0.347
0.026
0.096
0.254
0.343
0,822
0,890
0.156
0.276
0.039
AvE
0.002
0.080
0.025
0.99
[0027
0.102
(0044
0.349
0.002
01108
[0032
0.307
10.065
0.208
0.022
0.085
00.14
0.249
0,019
0.882
00.101
0.215
(0002 0,109
12.5
[.032
0.119
0.094
0.100
[0.59
0.202
00009
0.218
0.008
0.206
0.097
0.209
(0.15)
0.267
0.057
0.159
10,07
0.093
0.085
0.128
(00070
0 100
(0006 0.305
25R
0.039
0.337
0.119
0.225
0.099
0.211
0.125
0.243
0.123
0.229
0.155
0.226
0.180
0.202
0.099
0.178
0.105
0,232
0.042
0.140
0.106
0.236
0.120
0:228
50%
8.064
0.368
0.173
0.271
0.120
0.231
0.155
0.281
0.1881
0.27%
0.060
0.263
0.257
0.347
0.102
0.215
0.185
0,310
0.007
0.178
0.168
0.299
0.176
0,274
Avg
|0.046
0.145
0.133
0.276
[a.
0.216
001122
0.251
00:141
0.242
0.127
0.286
10.301
0.306
0.078
0.187
10.125
0.250
0.060
0.150
[0.117
0.346
(0.14 0.290
12.5%
0.036
0.119
0.057
0.150
[.005
0.161
00103
0.230
0.057
1.152
0.051
0.157
0.100
0.216
0.040
0.130
0.106
0.223
0,037
0.121
0,095
0.212
0.055
0.153
0,038
0.123
01022
0.110
0.229
0.022
11160
0.162
0.127
0.247
0.046
0,040
37.5%
0,040
0.126
0.065
0.165
0.129
0.246
0.068
0.168
0.070
0.17)
0.158
0.276
0.052
0.151
0.220
0.332
0,043
0.134
0.187
0.304
0.070
50%
8.044
0.143
0.076
0.179
(.069)
0.172
0.145
0.205
0.076
0.179
0.075
0.181
0.183
0.299
0.000
0.162
0.334
0.403
0.048
0.143
0.252
0.541
(.075
0,191
Ave
8.0009
0.127
0.065
0
166
[0064
0. 165
0.122
0:340
01000
0.168
0.069
0.166
00.141
0.350
0.049
0.146
00.005
0.307
0.003
(0.163
(
(1.77
(10M6
0.166
12.5%
0.065
0.180
0.073
0.158
0.073
0.185
0.068
0.181
0.079
1.199
0.069
0.182
000022
0.214
0.055
0.202
0.090
0.216
0.859
0.171
0.107
0.237
0.073
0.188
0.081
0.009
0.23
0.833
0.301
0.115
0:347
0.000
0.206
0.108
0.336
57.80
11045
0.1M5
00077
0217
00800
0.207
0.087
0:200
0.151
01262
[0097
0.31
0.114
0.270
0.094
0.313
0.126
0.257
0,877
0.190
0.130
01206
(1107
0.251
4996
0.091
0.310
0.110
0.30
(1099
0.214
0.005
0.312
01:00
0.201
1110
0.231
0.5
0.305
0.100
0.221
01151
0:325
0.086
012000
(0.188
(12554
(1
115
0.283
AvA
0.070
0.194
0.091
0.209
[.006
0.201
[0.033
0.199
0.119
0.246
0.059
0.205
00.32
0.260
0.092
0.210
0.119
0.247
0.873
0.157
0.130
0.259
0.099
0.221
12.5%
[0001
0,004
0.47
(0006
0000
ILUSS
0.052
10.009
0.000
0.025
01145
(11006
0.008
0.001
010000
01041
11107
(1000) 0.051
Weather
25%
6.837
0.051
0.53
0.029
0.000
0005
0,088
0,032
1.034
0.086
0.045
0.100
0.029
0.052
0.44
0.115
0,021
0.041
0.064
0.163
37.5%
8.024
0,040
0.034
8058
6031
0,055
0.085
0,083
0,066
0.052
1.037
0.060
0.067
0.117
0.31
0.057
0.062
0.141
0.027
0.046
0.107
0.229
0.036
0.062
30%
6.028
0.841
0.039
0.066
0.034
0.059
0.038
0,092
0.040
0.067
0.041
0.066
0.066
0.134
0.034
0.062
0.080
0.168
0.031
0.051
0.153
0.312
0.040
0:068
[.024
8,8.9
0,033
0057
(1031
0.083
(00095
0,000
00054
11036
0.05s
0.110
0.000
010566
(10056
00,007
01064
(1,0M
(1.205
(11155
36

---

Published as a conference paper at ICLR 2025
G.4 CLASSIFICATION
Table 31: Performance comparison of various models on different datasets with accuracy metrics for classification.
Models
RNN based
Convolution based
MLP based
Transformer based
Cross, [02.3]
2018
2021
2000
1022a]
2022a
2023
2024
2023
2023
202.56
2022
2002
200.2
(Ouns)
EltansCConeematiinn
45.2
38.0
FaceDrsection
65.7
66.7
64.7
68.9
05.2
05.6
70.3
68.0
67.5
70.2
56.0
68.3
03.7
67.5
71.2
Handwriing
25.8
24.6
58.8
23.6
25.5
32.1
30.6
27.0
26.1
26.0
25.0
29.6
28.8
33.8
32.7
Heathest
77.1
75.6
74.7
77.6
78.1
Jegmesekowech
96.1
98.4
96.2
96.0
94.5
95.4
98.5
96.2
96.2
94.5
98.4
97.5
99.1
98.9
98.9
PEMS
ScllRegularinnSCPP
$4.0
90.8
90.8
92.5
$6.0
91.8
93.4
87.3
89.8
91.7
85.7
90.7
92,1
92.5
93.7
ScllRequlatioSC.22
53.3
ApokenArahicDDgits:
100.0
100.0
71.2
98.1
97.1
99.0
91.4
100.0
97.4
100.0
98/3
97.9
98.8
99.4
UWaveGesturl Library
87.8
85.9
94.4
85.1
82.8
85.3
86.7
82.1
80.3
83.3
65.3
85.6
85.3
56.5
86.5
Averag Accuracy
72.5
24.2
70.4
73.2
G.S ANOMALY DETECTION
Table 32: Performance comparison of various models on different datasets with Precision (P), Recall (R), and DlddFFFseee Fl-score (F1) metries for annomaly detection.
Datasets
SMD
MSL
SMAP
SWaT
PSM
Avg F1
Models
Metrics
R
H-
P
R
F1
R
F1
P
R
F1
P
R
F1
(98-
SCINet
2022a
85.97
82.57
84.24
84.16
82.61
83.38
93.12
54.81
69.00
87.53
94.95
91.09
97. 97.93
94.15
96.00
84.74
MICN
2023
88.45
83.47
85.89
83.02
83.67
83.34
90.65
61.42
73.23
91.87
95.08
93.45
98.40
88.69
93.29
85.84
TimesNer
2022
88.66
83.14
85.81
83.92
86 32
85.
92.52
58.29
71.52
86.76
97.32
91.74
98.
96.76
97.47
86.34
DLineur
2023
83.62
71.52
77.10
84.34
84.52
84.88
92.32
55.41
69.26
80.91
95.30
87.52
98.
28
89.26
93.55
82.46
LighTTS
2022
87.10
78.42
82.53
82.40
75.78
78.95
92.58
55.27
69.21
91.98
94.72
93.33
98.
95.97
97.15
84.23
MTS Mixer
202.5
88.60
82.92
85.67
85.35
84.13
84.74
93.13
58.01
71.19
84.49
93.81
88.91
98.41
88.63
93.26
84.75
RLLincar
20230
87.79
79.98
83.70
89.26
74.39
81.15
89.94
$4.01
67.49
92.27
93.18
92.73
98.47
94.28
96.33
84.28
RMLP
20250
87.35
78.10
82.46
86.67
65.30
74.48
90.62
52.22 66.26
92.32
93.20
92.76
98.01
93.25
95.57
82.31
Reformer
2021
82.58
69.24
75.32
85.51
83.31
84.40
90.91
57.44
70.40
72.50
96.53
82.80
59.93
95.38
73.61
77.31
Informer
2021
86.60
77.23 81.65
81.77
86.48
84.06
90.11
57.13
69.92
70.29
96.75
81.43
64.27
96.33
77.10
78.83
Anomaly*
2021
88.91
82.23
85.49
79.61
87.37
83.31
91.85
58.11
71.18
72.51
97.32
83.10
68.35
94.72
79:40
80.50
Pyraformer
2021
85.61
80.61
83.04
83.81
85.93 84.86
92.54
57.71
71.09
87.92
96.00
91.78
71/67
96.02
82.08
82.57
Autoformer
2021
88.06
82.35
8
77.27
80.92
79.05
90.40
58.62
71.12
89.85
95.81 92.74
99.08
88.
93.29
84.26
Stationary
20220
88.33
81.21
84.62
68.55
89.14
77.50
89.37
59.02
71.09
68.03
96.75
79.88
97.
96.76
97.29
82.08
FEDfomeer
2022
87.95
82.39
85.08
77.14
80.07
78.57
90.47
58.10
70.76
90,17
96.42 93.17
97.31
97.16
97.23
84.97
Crsssormer
2023
83.06
76.61
79.70
84.68
83.71 84.
92.04
55.37
69.14
88.49
93.48
90.92
97.16
89.73
93.30
83.45
PatchTST
2022
87.42
81.65
84.44
84.07
86.23
85
92.43
57.51
70.91
80.70
94.43 87.24
98.87
93.99
96.37
84.82
ModemTCN
2024
87.86
83.85
85.81
83.94
85.93
84.92
95.17
$7.69
71.26
91.83
95.98
93.86
98.09
96.38
97.23
86.62
TYNet
(Uurs)
88.03
83.49
85.75
83.91
86.47
85.
92.94
58.26
71.64
91.26
96.33
93.72
98.30
96.76
97.53
86.76
37

---

Published as a conference paper at ICLR 2025
H SHOWCASES
Dimonsion 1
Dimansion 2
Di mansion 3
Dimensian
value
Forecattry value
-2
Ground
Truth Dimension 7
Dimenssion 5
Dimension 6
Forcartiigg 13lee
Faecarting Valu
0.5
0.0
0.0
Ground Truth
Ground Truth
Ground Iruth
Dimension 1
Dimension 2
Di miension 3
Dimension 4
Forecasting value
Forecatting vale
0.0
Foreaating
0.0
Forecazting
-2.5
Ground
Truth Dimension 7
Tuth
Dimension 5
Dimension 6
Forccantrg valee
Roncaating vale
0-
0.0
0.5
1.0
-1.5
-1.0
-0.5
0.0
0.5
Ground Thuth
Graind Truth
Ground Thith
Dimension
Dimension 2
Dimension
Dimension 4
Foreraniing oeho
Forecaustigg sole
Eoper www.erattingg unlor
-0.5
Ground Thuth
Ground Thuth
muth
Ground Truth
Dimension
Dimension
Dimension
Ferocastinn val be
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Figure 18: Visualization of ETThl Multivariate forecasting results
38

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Published as a conference paper at ICLR 2025
Drwand Frath Farccading
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Figure 19; Visualization of ETThl Univariate forecasting results
39


Reviews:
[{"review_id": "JNDyITwnHa", "reviewer": "Reviewer_K1xh", "summary": "The paper introduces TVNet, a novel time series analysis method that addresses the limitations of CNNs in capturing complex temporal dynamics by converting 1D time series data into 3D tensors and applying dynamic convolution. This approach achieves state-of-the-art performance across various time series tasks while maintaining efficiency.", "questions": "1. It is recommended to present the inference time and computational load of the model under the same settings.\n2. To effectively demonstrate the capability of long-term forecasting, it is recommended to follow the same settings as the original dataset, for instance: {96, 192, 336, 720}.\n3. More explanation may be needed to justify its complexity, especially in the experimental analysis, where more demonstration of its performance in terms of inter-patch, intra-patch, and cross-variable interpretability is needed.", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "1. The paper introduces TVNet, a novel method for time series analysis that leverages dynamic convolution and 3D transformation, offering a fresh perspective in the field by converting 1D time series data into 3D tensors through a 3D-Embedding technique.\n2. The paper demonstrates the capacity of the model across five critical time series analysis tasks, including long-term and short-term forecasting, imputation, classification, and anomaly detection, showcasing the model's generalization capabilities.\n3. The paper is well-organized, with a logical flow , making it easy to follow and understand.", "weaknesses": "1. Although the paper mentions the efficiency of the model, it does not discuss in detail the consumption of computational resources when running on datasets of different scales. Additionally, different methods have different training strategies, making the training time a poor reflection of the true time consumption of the model. It is recommended to present the inference time and computational load of the model under the same settings.\n2. The experimental results show long-term forecasting, but it seems that the prediction lengths = {24, 36, 48, 60} do not reflect the setting of 'long-term.' It is suggested to follow the same settings as the original dataset, such as: {96, 192, 336, 720}.\n3. In Table 1, it is a very serious error that the values for weather and traffic are identical.\n4. The article's claim of \"achieves top-tier performance across five pivotal analytical tasks\" is overclaimed because the results on long sequences show that the method did not achieve state-of-the-art (SOTA) on multiple datasets, and the improvement in results that did achieve SOTA is very limited (approximately 0.85% to 2.36% on MSE).\n5. Although the paper proposes a powerful model, more explanation may be needed to justify its complexity, especially in the experimental analysis, where more demonstration of its performance in terms of inter-patch, intra-patch, and cross-variable interpretability is needed.", "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": "kTY2TATlf8", "reviewer": "Reviewer_X5hZ", "summary": "The manuscript introduces TVNet, a dynamic convolutional network for time series analysis, employing 3D embedding and convolution mechanisms to handle inter-patch, intra-patch, and cross-variable dependencies. TVNet aims to improve CNN performance in time series tasks and demonstrates its utility across multiple tasks, including long-term and short-term forecasting, classification, anomaly detection, and data imputation.", "questions": "- **Motivation**:\n    - Can the authors elaborate on the specific limitations of RNNs and Transformers in time series analysis that CNNs aim to address? Given the well-known success of Transformers and RNNs, what makes CNNs uniquely suitable for time series tasks?\n- **Rationale Behind 3D-Embedding**:\n    - Why were the inter-patch, intra-patch, and cross-variable embeddings selected? Are there theoretical or empirical justifications for these choices? Could alternative embeddings have been explored, and how would the performance be affected by such variations?", "limitations": "", "rating": 5, "confidence": 4, "soundness": 2, "presentation": 1, "contribution": 2, "strengths": "- The modular design of TVNet is scalable and easily extensible\n- Maintains computational efficiency comparable to CNNs while achieving superior results.\n- Comprehensive experiments covering many tasks, baselines and analysis", "weaknesses": "- **Lack of Strong Motivation**: The paper's motivation could be strengthened. While it aims to “enhance the representational capacity of CNNs for time series analysis,” it does not adequately explain **why** this enhancement is necessary, given the strong performance of RNNs and Transformers for such tasks. It is well understood that different network architectures are suited for different input modalities, based on the inductive biases they introduce [1]. Therefore, further justification is needed to clarify the specific gaps that CNNs can fill in time series analysis.\n- **Insufficient Emphasis on Novelty**: Although the introduction of **3D-embedding** is a core idea, the rationale for choosing the specific three embeddings (inter-patch, intra-patch, and cross-variable) is not adequately explained. A deeper discussion is necessary to understand why these dimensions were prioritized and how they contribute to improved performance. This would help highlight the **novelty** and distinctiveness of the proposed method.\n\n[1] Chiyuan Zhang, Samy Bengio, Moritz Hardt, Michael C. Mozer, Yoram Singer: Identity Crisis: Memorization and Generalization Under Extreme Overparameterization. ICLR 2020", "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": "qUQ68gnvbm", "reviewer": "Reviewer_PJvc", "summary": "This paper presents TVNet, a dynamic convolutional network for time series analysis, utilizing a 3D-Embedding technique and dynamic convolution to capture intra-patch, inter-patch, and cross-variable dependencies. TVNet is evaluated on five tasks and shows state-of-the-art performance, better efficiency than some models, and good transferability and robustness.", "questions": "1. Can the authors provide more details about the choice of hyperparameters and their impact on performance? \n2. Why was there no comparison with some of the latest models such as TimeMixer and models combined with large language models (e.g., S2 IP-LLM, TimeLLM)? What could be the potential implications of such comparisons for the evaluation of TVNet?", "limitations": "", "rating": 6, "confidence": 4, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "1. The proposed 3D-Embedding technique and the consideration of different types of dependencies (intra-patch, inter-patch, cross-variable) are novel and well-motivated.\n2. The experimental evaluation is comprehensive, covering multiple tasks and comparing with a wide range of state-of-the-art models. The consistent top performance across these tasks is a significant strength.", "weaknesses": "1. Some parts of the method description could be made clearer. For example, the generation function for the time-varying weight could be explained in more detail.\n2. The paper does not compare with some of the latest models such as TimeMixer[1] and recent models combined with large language models (e.g., S2 IP-LLM[2], TimeLLM[3]). This omission may lead to an incomplete understanding of the relative performance and novelty of TVNet in the context of the most recent research trends.\n\n[1]Wang S, Wu H, Shi X, et al. Timemixer: Decomposable multiscale mixing for time series forecasting[J]. arXiv preprint arXiv:2405.14616, 2024.\n[2]Pan Z, Jiang Y, Garg S, et al. $ S^ 2$ IP-LLM: Semantic Space Informed Prompt Learning with LLM for Time Series Forecasting[C]//Forty-first International Conference on Machine Learning. 2024.\n[3]Jin M, Wang S, Ma L, et al. Time-llm: Time series forecasting by reprogramming large language models[J]. arXiv preprint arXiv:2310.01728, 2023.", "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": "bnAKIAQ77M", "reviewer": "Reviewer_ZoZa", "summary": "This paper propose a method called TVNet. TVNet can capture intra-patch,inter-patch and cross-variables features by converting 1D time series data into 3D shape tensor.", "questions": "The same to Weaknesses.", "limitations": "", "rating": 8, "confidence": 2, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "To sum up, this is a good paper. They proposed TVNet.\nTVNet captures intra-patch,inter-patch and cross-variables features by converting 1D time series data into 3D shape tensor.\nTVNet implements consistent state-of-the-art performance time series analysis tasks across multiple mainstreams, demonstrating excellent task generalization.", "weaknesses": "1. 3D-EMBEDDING\nThis is your innovation, but you did not tell it  clearly. For example: \n\"stride S to divide into N patches($X_{emb} ∈ R^{N×P ×C_m}$)\" \nIt is hard for me to know how do you achieve this. Almost the whole process in this part is confused. You should give explanations.", "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)