Learning Soft Sparse Shapes for Efficient Time-Series Classification
Authors: Zhen Liu
Yicheng Luo
Boyuan Li
Emadeldeen Eldele
Min Wu
Qianli Ma
Venue: ICML 2025 spotlightposter (2025)
Keywords: deep learning
time series classification
shapelets
interpretability
Primary area: deep_learning->sequential_models_time_series
TL;DR: We propose a soft sparse shapes model for efficient time series classification, using soft shapes as inputs to facilitate shapelet learning.

Abstract: Shapelets are discriminative subsequences (or shapes) with high interpretability in time series classification. Due to the time-intensive nature of shapelet discovery, existing shapelet-based methods mainly focus on selecting discriminative shapes while discarding others to achieve candidate subsequence sparsification. However, this approach may exclude beneficial shapes and overlook the varying contributions of shapelets to classification performance. To this end, we propose a Soft sparse Shapes (SoftShape) model for efficient time series classification. Our approach mainly introduces soft shape sparsification and soft shape learning blocks. The former transforms shapes into soft representations based on classification contribution scores, merging lower-scored ones into a single shape to retain and differentiate all subsequence information. The latter facilitates intra- and inter-shape temporal pattern learning, improving model efficiency by using sparsified soft shapes as inputs. Specifically, we employ a learnable router to activate a subset of class-specific expert networks for intra-shape pattern learning. Meanwhile, a shared expert network learns inter-shape patterns by converting sparsified shapes into sequences. Extensive experiments show that SoftShape outperforms state-of-the-art methods and produces interpretable results.

Learning Soft Sparse Shapes for Efficient Time-Series Classification
Zhen Liu Yicheng Luo'
Boyuan Li'
Emadeldeen Eldele? Min Wu? Qianli Ma
Abstract
volue
Shapelets are discriminative subsequences (or shapes) with high interpretability in time series classification. Due to the time-intensive nature of shapelet discovery, existing shapelet-based methods mainly focus selecting discrimina- tive shapes while discarding others to achieve candidate subsequence sparsification. However, this approach may exclude beneficial shapes and overlook the varying contributions of shapelets to classification performance. To this end, we pro- pose a Soft sparse Shapes (SoftShape) model for efficient time series classification. Our approach mainly introduces soft shape sparsification and soft shape learning blocks. The former transforms shapes into soft representations based on classifi- cation contribution scores, merging lower-scored ones into a single shape to retain and differentiate all subsequence information. The latter facilitates intra- and inter-shape temporal pattern learning, improving model efficiency by using sparsified soft shapes as inputs. Specifically, we employ a learnable router to activate subset of class- specific expert networks for intra-shape pattern learning. Mcanwhile, a shared expert network learns inter-shape patterns by converting sparsi- fied shapes into sequences. Extensive experiments show that SoftShape outperforms state-of-the-art methods and produces interpretable results. Our source code is available at https: ///pt/gttt////////// com/ q anl 1 imm- - lab/ ft
40 (e) Walking Carpet
20
Leigh
63
Lengt 40
6
Shopelats (Red subsequences)
20
40
63
Longth
Length
Walking
(d) Discriminatory regions (Rec)
Figure 1: (a) Yellow and (c) Blue lines represent two time se- ries class samples from the SonyAlBORRbooSurfucce UCR dataset. (b) Red subsequences denote shapelets for the "Walking on Carpet" class. (d) Red regions show discrimi- native parts of the "Walking on Carpet" class, with darker red indicating greater discriminative power.
nition (Lara & Labrador, 2012) and medical diagnostics (Wang et al., 2024). Unlike traditional data types, time series data consists of ordered numerical observations with tempo- ral dependencies, which is often difficult for human intuition to understand. Recent studies (Mohammadi Foumani et al., 2024; Middlehurst et al., 2024; Jin et al., 2024; Ma et al., 2024) indicate that deep neural networks showed remark- able success in TSC, even without specialized knowledge. However, their black-box nature is barrier adopting effeective models in critical applications such healthcare, where insights about model decisions are important. There- fore, enhancing the interpretability of these models for TSC is a crucial ongoing issue.
Shapelets, which are discriminative subsequences that char- acterize target classes, offer promising approach towards interpretable TSC models (Ye & Keogh, 2009). For in- stance, Figures ((a) and I(c) show time series classes of robotic dog walking on carpet and cement ( (Vail & Veloso, 2004). The red subsequences shown in Figure 1(b) illus- trate shapelets, as selected by Hou et al. (2016). However, identifying these shapelets usually computationally inten- sive (Rakthanmanon & Keogh, 2013), as it requires evaluat- ing subsequences across varying positions and lengths.
1. Introduction
Time series classification (TSC) is a critical task with vari- ous real-world applications, such as human activity recog-
School of Computer Science and Engineering, South China University of Technology, Guangzhou, China "Institute for In- focomm Research, Agency for Science, Technology and Re- search, Singapore. Correspondence to: Qianli Ma <qian- wean@@ssut.uuuu...... Min Wu <wumin @ i2ra star....gg.
Existing methods (Grabocka et al., 2014; Li et al., 2020) address this issue via shapelet transformation strategy for candidate subsequence sparsification. Specifically, they con- vert each subsequence into a feature that quantifies the dis- tance between a time series sample and the subsequence (Ma
Proceedings of the 4nnd International Conference Machine Learning. Vancouver, Canada. PMLR 267, 2025. Copyright 2025 by the author(s).

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Learning Soft Sparse Shapes for Efficient Time-Series Classification
al., 2020). Subsequently, this strategy was followed by
We conduct extensive experiments on 128 UCR time se- ries datasets, demonstrating the superior performance of our proposed method against state-of-the-ar ap- proaches while showcasing interpretable results.
many methods (Li al., 2021; Le al., 2024) to learn shapelet representations, thereby enhancing the model's in- terpretabilityy. While efficient, this approach discards many subsequences from the entire time series in a hard manner, those that could be beneficial for the classification tasks. In addition, this approach fails to account for the varying importance of shapelets to classification. As shown in Fig- ure I(b), this leads to poor capture of class patterns in the third and fourth subsequences due to minimal class differ- ences, while omitting many informative regions.
2. Related Work
2.1. Deep Learning for Time-Series Classification
Recently, deep learning has received significant attention from scholars in time series classification tasks due to its powerful feature extraction capabilities (Ismail Fawaz et al., 2020; Zhang et al., 2024). For example, Ismail Fawaz et al. (2019) and Mohammadi Foumani et al. (2024) have system- atically reviewed deep learning approaches for time series classification, focusing on different types of deep neural networks and deep learning paradigms, respectively. In ad- dition, Middlehurst et al. (2024) and Ma et al. (2024) have conducted extensive experiments to evaluate recent time series classification methods. Their findings demonstrate that deep learning models can be effectively applied to time series classification tasks. Despite their strong performance, these deep learning- basedd time series classification methods often struggle to improve the interpretability of classifica- tion results.
Recent advances in time series patch tokenization (Nie et al., 2023; Bian et al., 2024), i.e., converting time series into subsequence- tokens, and in the mixture of experts (MoE) architectures (Riquelme et al., 2021; Fedus et al., 2022) inspired new direction. In computer vision, MoE routers dynamically assign input patches to specialized ex- perts, which can improve both efficiency and class-specific feature learning (Chen et al., 2022; Chowdhury et al., 2023). By analogy, time series shapelets, which can exhibit intra- class similarity and inter-class distribution, can act as patch tokens, with MoE enabling adaptive focus on the most discriminative subsequences. Yet, existing shapelet-based methods overlooked such approach.
In this paper, we propose the Soft sparse Shapes (SoftShape) model for TSC, which replaces hard shapelet sparsification with soft shapelets. Specifically, we introduce a soft shape sparsification mechanism to reduce the num- ber of learning shapes. thereby enhancing the efficiency of model training. To clarify our motivation, Figure (d) shows the classification results of InceptionTime (Ismail Fawaz et al., 2020) using multiple-instane, learning (Early et al., 2024). Unlike the hard way depicted in Figure 1 ((b), our soft shapelet sparsification assigns weights to shapes based on their classification contribution scores, effectively pre- serving and differentiating all subsequence information enhance the dis-
2.2. Time-Series Classification with Shapelets
Ye & Keogh (2009) first introduced shapelets, provid- ing good interpretability for time series classification re- sults. Early methods (Mueen et al., 2011; Rakthanmanon & Keogh, 2013) selected the most discriminative subse- quences as shapelets using an evaluation function, but the sparsification process was computationally intensive due to the numerous candidate subsequences. To tackle this prob- lem, Hills et al. (2014) introduced the shapelet transform, converting all candidate subsequences into distance- based features for shapelet discovery. Recent studies (Qu et al., 2024; Le et al., 2024; Wen et al., 2025) have applied the shapelet transform strategy in deep learning models for time series classification, thereby improving model interoper- ability. However, these methods often handle candidate subsequences in a hard way, which easily Ieads to the loss of helpful temporal patterns from the time series sample.
from the time series. Furthermore, criminability of the learned soft shapes by combining: (1) Intra-shape patterns via MoF, where experts specialize in class-specific shapelet types; and (2) Inter-shape dependen- cies via a shared expert that models temporal relationships among sparsified shapes.
In summary, the major contributions are as follows:
More recently, Nie et al. (2023); Wu et al. (2025) showed that using patches of time series as input data enhances forecasting performance and reduces training time. Build- ing on this, Luo & Wang (2024), Wang et al. (2024), and Wen et al. (2024) validated the effectiveness of patch tech- niques for time series classification. Eldele et al. (2024) further demonstrated that using time series patches as CNN inputs outperformed Transformer- these methods typically use all patches inputs, leading to computational inefficiency in TSC for long sequences.
We propose SoftShape, a soft shapelet sparsification approach for TSC. This weighted aggregation of subse- quences is based on classification contribution scores, avoiding information loss from hard filtering.
We introduce a dual-pattern shapelet learning approach based on an MoE-driven intra-shape specialization and sequence-awe aware inter-shape modeling, improving the discriminative power of learned shape embeddings.
methods. However,
2

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Learning Soft Sparse Shapes for Efficient Time-Series Classification
2.3. Mixture-oo-Exxpets in Time Series
Shapelets are defined subset of discriminative subse- quences within A that maximally represent the class of each time series Xr (Ye & Keogh, 2009). Given that every shape in A could potentially serve as shapelet, a brute-force search to evaluate all subsequences of each X₂ using an eval- uation function becomes computationally prohibitive as the number of samples N and the sequence length increase. Thus, the design of appropriate sparsification techniques for the set A is crucial for enhancing the computational efficiency of shapelet-based TSC methods.
Mixture of experts (MoE) typically consist of multiple sub- networks (experts) and learnable router (Shazeer et al., 2017; Zhou et al., 2022). MoE has been utilized in time series forecasting for decades (Zeevi et al., 1996; Ni et al., 2024) and recently applied to improve the efficiency of time series forecasting foundation models (Liu ct al., 2024a; Shi et al., 2025). In addition, Huang et al. (2025) extended MoE to graph-based models for time series anomaly detec- tion. Wen et al. (2025) introduced a gated router within MoE to integrate DNNs for learning time series representa- tions, combining them with shapelet transform features to address the performance limitations of using shapelet trans- form alone in TSC. Unlike the above methods, we utilize the MoE router to activate class-specific experts for learn- ing intra- sarra-shapeeTae local temporal patterns. Furthermore, we employ shared expert capture global temporal patterns across sparsified shapes from the same time series, thereby enhancing the discriminative power of shape embeddings.
4. Methodology
4.1. Model Overview
The overall architecture of the SoftShape model is illus- trated Figure 2. SoftShape begins with a shape embed- ding layer that transforms the input time series into shape embeddings corresponding to multiple equal-length subse- quences. These embeddings are normalized with a norm layer and then processed using soft shape sparsification (see Section 4.2). Specifically, an attention head assigns weight scores to each shape embedding based on its classification contribution. High-weight embeddings are scaled by their scores to form soft shapes, while low-weight embeddings are merged into a single shape for sparsification. The nor- malized sparsified shape embeddings are then input into the soft shape learning block to learn temporal patterns (see Section 4.3). Within this block, a MoΣ router activates few class-specific experts to capture intra-shape temporal pat- terns (see Section 4.3.1). Meanwhile, these sparsified soft shapes are transformed into sequences, with a shared expert learning inter-shape temporal patterns (see Section 4.3.2). Finally, the sparsified soft shape embeddings, along with the intra-shape and inter-shape embeddings learned by the soft shape learning block, are combined in a residual way. After stacking T, layers, the output is passed to a linear layer for classification training (see Section 4.4).
3. Preliminaries
3.1. Problem Definition
In this study, we focus on the use of deep learning models for univariate time series classification. Let the time series dataset be represented as D {(K,, Dr,,,,))) )r) ) where N denotes the total number of time series samples. Each uni- variate time series X, = (,1, ................................ J is an ordered sequence of T" real-valued observations. The corresponding label Vn E RC is a one-hot encoded vector, where each value ye. E (0, }} indicates whether Xr belongs to class e, with C representing the total number of classes. Given a deep learning model parameterized by 0, the objective of the TSC task is to optimize the function fe IRTT - RC such that it can accurately predict the label Vn corresponding to any input time series Xx,.
3.2. Time Series Shapelets
4.2. Soft Shape Sparsification
Given a time series Xn, subsequence of length m, where
For each input time series Xx, we use a ID convolutional neural network (CNN) as the shape embedding layer to obtain M T-m + (q < m) overlapping subsequence
m < T, is denoted as St,p = {xp, Tpt1...., Ip+m-1}- Here, p denotes the starting index of Sth, where 0 < p << T - m. All subsequences of length m from the time series Xr can be extracted using a sliding window of size m with a fixed step size q (commonly q = =)) traversing from f to T. Thus, the set of all subsequences of length from Xr can be defined as St = (SW; 0 < p < T - m).
embeddings, denoted STm = (S |0 S p < T T-m).. Each shape embedding Sm is computed using the following convolution operation:
Due to the length of the subsequences varying within the range S m - T - 1, the candidate set A of all possible subsequences for the time series dataset D is expressed as:
St
W.Sm 1=
p = 0, 29. ..... T m (2)
where We denotes the weights of the i-th filter within the kernel of the CNN, and Sm m.p E Rd, with d representing the dimension of the shape embedding. Like patch-based meth- ods (Nie et al., 2023; Eldele et al., 2024), we incorporate
N T-1
A = U = SSH <<p<<== < m]. Fm 2
(1)
3

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Learning Soft Sparse Shapes for Efficient Time-Series Classification
Soft Shape L Learning Block
Classifier
Expert
Expert 2
Router
Expert 3
Combine
Soft Shape L earning Block
[48.1.0
[50
[8.1.0]
Expert
Reshape
Norm Layer
Intra-Shape Temporal Patterns
8. 0.0.5)
X L
[.D.5
D..
Soft Shape Sparsification
Shared Expert
Inter-Shape Teemporl Patterns
Norm Layer
Soft Shape Sparsification
Sparse Shape Embeddings
Wi eighted Fusion
0,9
0.3
A Attention Scores
Shape Embedding Layer
A ttention Head
Shape Embeddings
Original Time-Series
The general architecture of SoftShape model. SoftShape mainly involves: a) Soft Shape Sparsification converts shapes into soft forms and fuses those with lower scores into single shape. b) Soft Shape Learning Block employs MoE router to activate class-specifie experts to learn intra-shape patterns and utilizes shared expert to learn inter-shape patterns.
Figure 2:
learablee positional embeddings into shape embeddings to capture temporal dependencies within the time series.
can perform soft shape sparsification using scores from the attention head based on their ranking. For each attention score of Sm ranked within the top 1) proportion among the total J = T-m + shape embeddings in STm we convert them into soft shape embeddings as follows:
To identify the most discriminative shape embeddings in Smh, we employ a parameter-shared attention head across soft shape learning blocks at different depths. Unlike the self-attention mechanism Transformers, we employ a gated attention mechanism (Ilse et al., 2018) that assumes independence among shape embeddings. This design facili- tates label-guided identification of key shapes while main- taining linear computational complexity with respect to the number of shapes (Farly et al., 2024). The attention head evaluates the contribution score of each n. for classifica- tion training, defined as follows:
np = a a
St n.p S
(4)
For those with scores below the top n proportion, we fuse them into single shape embedding as follows:
n, fused
Σ PEE
Ea(Sm (a
(5)
where & denotes the index of scores that are below the top 1) proportion. Finally, the soft shape embeddings are sorted according to their original order in S with the fused embedding 5m fused appended at the end to form the sparsified soft shape embeddings S.m.
(sSm o (We tanh SW + b1) + bz).
(3)
where o(.) (.) the sigmoid function outputting (0, Lanh( :) is the hyperbolic tangent function, Wi Bddm xd
Through this sparsification process, we transform the time series X, into sparsified soft shape embeddings S Com- pared to directly using all shape embeddings in S.T input, the number shape embeddings in Stz" reduced, thereby decreasing the cost of the model's 's computation.
and W2 E I xld are the weights of linear layer, and b, E dd and b2 E IR are the bias terms.
The value a (() h closer to indicates a greater contri- bution enhancing classification performance. Hence, we

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Learning Soft Sparse Shapes for Efficient Time-Series Classification
4.3. Soft Shape Learning Block
where W Wimp is the learning weight parameters and CV(:)
denotes the coefficient of variation, thus ensuring all experts contribute equally.
4.3.1. INTRA-SHAPE LEARNING
Intuitively, shapelets from different classes show distinct temporal patterns, whereas those from the same class are more similar. Recently, Chen et al. (2022); Chowdhury et al. (2023) theoretically indicated that the MoE router can direct input embeddings with similar class patterns to the same expert while filtering out class-irrelevant features. This allows the router to selectively activate a subset of ex- perts ssub-networks for each shape embedding, enabling class-specific feature learning while reducing computational overhead compared to activating all experts simultancously. Therefore, we introduce a module that employs the MoE router to activate class-specific experts for learning intra- shape temporal patterns, thereby enhancing the discrimina- tive capability of each soft shape embedding. The function of the MoE router defined as:
Lroud (S = W Wond (V
(11)
where W is the learning weight parameters for load balancing and Load(S..p) n.p) is the number of soft shape em- beddings assigned to each expert, thereby reducing the risk of underutilization. By jointly optimizing Limp and Lload in the overall loss function, we can alleviate the likelihood of underfitting in some experts. In addition, following Zoph et al. (2022), we apply residual connection between the input shape embedding Sp.p and the output (0, Sw;p) to enhance training stability.
4.3.2. SYEER-SHAPE LEARNING
While the MoE router activates a few experts to learn class- specific temporal patterns within each soft shape, it treats the multiple shapes extracted from each time series sample inde- pendently, thereby overlooking the temporal dependencies among shapes. In general, learning intra-shape temporal pat- terns is beneficial for capturing local discriminative features, but it can be difficult to learn the global temporal patterns from the time series that are vital for classification. To this end, we introduce a shared expert to learn the temporal patterns among sparsified shapes within the time series.
G(S p.p
TOPx (softmax W (SSp)))
(6)
U/ if 2 is in the top i values of v,
TOPx(0)
0, otherwise.
where W, E RCCd are the learning weights of the router that convert the sparsified shape embedding Sth, into a vec- tor of corresponding to the total number of experts Ć. The (v) is applied after the softmax function to prevent the values of G(Stpp) being zero almost everywhere during training (Riquelme et al., 2021), particularly when Ie- = 1.
The sparsified soft shape embeddings are first transformed into sequence where each shape is treated as individual unit. This transformation is defined as:
In the paper, each MoF expert employs lightweight MLP network to learn class-specific patterns using each soft shape embedding as input. The e-th expert function is defined as:
mh = (5TH)T where
STh E BBBxNamxd (12)
where 2Th E IR BRBxxxNum, and B denotes the batch size, N um = J x 17 + is the number of sparsified soft shapes of each time series, and d is the dimension of one soft shape embedding. Recent studies (Middlehurst et al., 2024) have shown that CNN-based models perform remarkably in TSC tasks. In this work, we employ a CNN-based Inception module (Ismail Fawaz et al., 2020) as the shared expert. The shared expert comprises three 1D convolutional layers with different kernel sizes, sliding along the third dimension of Qm from 0 to N wm. This allows it to learn multi-resolution temporal patterns across soft shapes effectively. For raw input time series samples, the input dimension containing B univariate time series can be represented as (B, 1, T),, where T is the length of each time series. Traditional CNN-based methods (Ismail Fawaz et al., 2020) typically transform each point in the time series into d-dimensional embeddings, resulting in an input dimension of (B, d, T). Unlike the above, we treat each shape as a sequence point and convert it into d-dimensional embeddings for training.
(0,, 5m
(.m, n.p) GeLLU(W. 5m n.
+ be), (8)
(o(STT)))
EiETOP,(M) Ci(Sm,)))
where We and be represent the weight and bias terms of the MLP network, and GeLU(.) denotes the gaussian error linear unit activation function. The MoE experts' parameters shared across soft shape learning blocks different depths, ensuring the efficiency of parameter optimization.
However, the MoE router often tends to converge to state where it assigns higher weights to a few favored experts. This imbalance can cause the favored experts to train faster and dominate the expert selection process, resulting in un- derutilization and potential underfitting of less frequently chosen experts. To address this issue, following (Shazeer et al., 2017), we employ two loss functions as follows:
2
Camp
(Smp (Smpp) W "imp
Σ S5m
G(Smp)
(10)
As shown in Equations (1) and (5), with a higher sparsity rate (1 - 17), the actual sequence length Num of Q fed
mip
5

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Learning Soft Sparse Shapes for Efficient Time-Series Classification
into the shared expert is significantly smaller than T. thus reducing the model's computational load. The shared expert ensures efficient learning of temporal patterns across sparsi- fied soft shapes, better capturing global features of the time series for classification training.
CNN-based (DL-CNN): FCN (Wang et al., 2017).
T-Loss (Franceschi et al., 2019), SelfTime (Fan et al., 2020), TS-TCC (Eldele et al., 2021),
TS2Vec (Yue et al., 2022), TimesNet (Wu et al., 2023b), InceptionTime (Ismail Fawaz et al., 2020), LightTS (Campos et al., 2023), ShapeConv (Qu et al., 2024), ModemnTN (Luo Wang. 2024), and TSLANet (Eldele et al., 2024). Transformer-based (DL-Trans); TST (Zerveas et al., 2021), ) PatchTST (Nie et al., 2023), Shape- former (Le et al., 2024), and Medformer (Wang et al., 2024).
4.4. The Training of SoftShape
The SoftShape model stacks L layers of the soft shape learn- ing block for classification training. Each layer's output is processed using a G.LU(.) activation function. The final layer outputs three types of embeddings: the sparsified soft shape embeddings, the intra-shape embeddings, which are combined through residual way denoted O To accu- rately represent the learned attention scores for each shape embedding associated with the target class, we employ con- junctive pooling (Early et al., 2024) for training:
Foundation models (DL-FM): GPT4TS (Zhou et al., 2023) and UniTS (Gao et al., 2024).
Non-Deep Learning Methods (Non-DL): RDST (Guil- laume et al., 2022) and MultiRocket- (MR- H) (Dempster et al., 2023).
Num
Num Σ ((OT))(OT,))
(13)
For information on datasets, baselines, and implementation details, please refer to Appendix A.
where á denotes a linear layer as the classifier. For all time series samples, we use the cross-entropy loss for classifica- tion training, defined as:
5.1. Main Results
B (X,))) B
Table 1:
Test classification accuracy comparisons on 128 UCR time series datasets. The best results are in bold, and the second best results are underlined.
1y = log(O,)))
(14)
where Di, is the predicted class probability the j-th class for the sample X₁ Therefore, the overall training objective for SoftShape is given by:
Methods
Avg. Acc
Avg. Rank
Win
P-value
FCN
0.8296
9.53
13
1443-12 12
T-LLoss
0,8325
11.12
9
2.95F-14
SeifTime
0,8017
13.80
4.53E-25 0
Liotal fre + X(iimp + Liond).
(15)
DL.CNN
TS-TCC
0.7807
13.96
1.60E-15 0
TS2Vec
0.8691
8.43
1.69E-15
where A is a hyperparameter to adjust the training loss ratio.
TimesNet
0.8367
10.13
4.22E-15
Additionally, the pseudo-code for SoftShape can be found in Algorithm located in the Appendix.
InceptionTime
0,9181
4.05
29
7.39E-06
ShapeConv
0,7688
13.91
5
3.58E-24
ModernTCN
0.7938
11.37
1.78F-18
TSLANet
0,9205
3.68
1.06E-03 31
5. Experiments
DL Truns
TST
0.7755
13.54
2.00E-19
PatchTST
0.8265
9.56
1.27E-15 12
To evaluate the performance of various methods for TSC, we conduct experiments using the UCR time series archive (Dau et al., 2019), widely recognized benchmark in TSC (Ismail Fawaz et al., 2019). Many datasets in the UCR archive contain a significantly higher number of test samples compared the training samples. Also, the original UCR time series datasets lack specific validation set, increasing the risk of overfitting in deep learning methods. Following (Dau et al., 2019; Ma et al., 2024), we merge the original training and test sets of each UCR dataset. These merged datasets are then divided into train-validation-tes sets at a ratio of 60%-20%.-0%% This paper compares SoftShape against 19 baseline methods, categorized as follows:
Medformer
0,8541
9.26
7.15E-16 7
DL
FM
GPT4TS
0,8593
9.34
6
7.89E-16
UniTS
0,8502
9.66
5
1.41E-13
Non
DL
RDST
0,8897
6.41
23
7.54F-10
MR-H
0.8972
5.51
29
3.80E-07
SoftShape (Ours)
0.9334
2.72
53
The classification accuracies on the test sets of the 128 UCR datasets are presented in Table with detailed re- sults provided in Appendix B. The average ranking (Avg. Rank) reflects the method's 's relative position based on test accuracy, where lower values signify higher accuracy. Win indicates the number of datasets where the baseline achieves the highest test accuracy. The P-value from the Wilcoxon signed-rank test (Demšar, 2006) assesses the significance of
Deep Learning Methods (DL):
6

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Learning Soft Sparse Shapes for Efficient Time-Series Classification
differences in test accuracy between pairwise methods. A P- value 0.05 suggests SoftShape outperforms the baseline.
firms the superiority of the CNN architecture for learning shape embeddings. These results confirm the importance of each component in the SoftShape model.
Due to the high computational cost of LightTS (Campos et al., 2023) and Shapeformer (Le et al.. 2024), their results are reported only on 18 selected UCR time series datasets in Table 10 of Appendix B. Detailed reasons for 18 UCR dataset selection are in Appendix B.3. The experimental re- sults in Table 1 and Table 10 highlight SoftShape's 's superior classification performance, demonstrating its effectiveness in TSC. Also, the P-value results confirm the statistical significance of SoftShape's ' performance compared to base- lines, highlighting its capacity to capture the discriminative patterns of time series data. The critical diagram (Figure 6) in the Appendix further supports the statistical significance of SoftShape's performance improvement.
5.3. Shape Sparsification and Learning Analysis
Table 3: Test accuracy of different sparse ratios on 18 UCR datasets. The best results are in bold, and the second best results are underlined.
Sparse Ratio
Avg. Acc
Avg. Rank
Win
P-value
0%
0.9461
2.44
4
10%
0.9469
2.39
7
2.97E-01
30%
0.9448
2.78
5
2.66E-01
50%
0.9453
2.61
6
3.46F-01
70%
0,9323
3.89
5
9.37E-03
5.2. Ablation Study
90%
0.9261
4.50
2
4.02E-04
Table 2:
Test accuracy of ablation study on 128 UCR datasets. The best results are in bold, and the second best results are underlined.
Evaluating all 128 UCR time series datasets takes consid- erable time, so we selected 18 datasets from the UCR time series archive for analysis and subsequent experiments. Ta- ble 3 presents the test results when combining shape embed- dings with weighted fusion at varying sparse ratio (1 - n) proportions during sparsification, with detailed results pro- vided in Appendix B.3. When (1- n) S 50%, test accu- racy showed no significant decline compared to the non- sparsified case (0%), with all p-values > 0.05. Conversely, when (1 - > 50% particularly at 90%, performance declined significantly compared to 0%, indicating that ex- cessive spursification can remove some shape embeddings beneficial for capturing inter-shape global temporal pat- terns. Furthermore, the performance degradation under high sparsity ratios suggests that hard shapelet- -ased methods discard numerous informative subsequences, which may result in the loss of critical patterns useful for classification. As performance at 50% is statistically comparable to 0%, we set 1) to 50% in the main experiments to optimize the computational efficiency of the soft shape learning block.
Methods
Avg. Ace
Avg. Rank
Win
P-value
w/o Soft Sparse
0.9123
3.04
29
4.69F-06
w/o Intra
0.9245
2.75
31
5.39E-04
w/o Inter
0,9022
3.74
19
1.81E-09
w/o Intra& & Inter
0.8696
5.02
11
4,35E-16
with Linear Shape
0.9164
3.23
22
1.80E-09
SoftShape (Ours)
0.9334
2.04
60
The ablation studies include: 1) w/o Soft Sparse removes the soft sparse process, using only the selected top 7) shape embeddings for training: 2) w/o Intra eliminates the intra- shape learning process via the class-specific experts; 3) w/o Inter removes the inter-shape learning process via the shared expert: 4) w/o Intra & Inter excludes both the intra- shape learning and inter-shape learning processes; 5) with Linear Shape employs a linear layer commonly used in (Nie et al., 2023; Wang et al., 2024) to replace the 1D CNN in Equation (2) as the shape embedding layer.
Table 4 illustrates the effect of the number of activated experts (k) selected by the MoE router during intra-shape learning, with detailed results provided in Appendix B.3, The results show that when & = 3 or k 4, the average rank is worse than when k: = 1 or k = 2. This suggests that activating greater number of class-specific experts for each soft shape increases computational cost while diminishing the class discriminability of the intra-shape embeddings.
Table 2 presents the statistical ablation results, with detailed results provided in Appendix B.2. w/o Soft Sparse reduces accuracy and lowers the Avg. Rank, indicating the impor- tance of this process in capturing the most helpful shape em- beddings for classification. Similarly, w/o Intra highlights the significant role of the intra-shape module in SoftShape. Moreover, w/o Inter leads to a large drop in performance, underscoring the critical contribution of inter-shape rela- tionships in learning global patterns of time series. When both the intra- and inter-shape learning processes are ex- cluded (w/ Intra & Inter), performance further degrades, demonstrating that these two processes are foundational to SoftShape's 's effectiveness. Finally, with Linear Shape con-
Also, select one non-deep learning method (MR-H) and three deep learning baselines for runtime analysis. MR-H uses randomly initialized convolutional kernels for feature extraction, with training times measured on a CPU. The deep learning methods are evaluated on a GPU. Inception- Time is an advanced deep learning method described in
7

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Learning Soft Sparse Shapes for Efficient Time-Series Classification
Table 4: Test accuracy comparison of the number of acti-
Support for the predictod class
Retuie the prodicted class
vated experts on 18 UCR datasets. The best result is in bold.
Ulase Clas
2.5
Vopa propottie
0.75
-0.0
0.50
0.25
Activated Experts
k=1
k=2
k=3
h=4
20
40
60
20
20
60
(a) Shape Regions
(b) Losrming Score Shopes
Avg. Rank
1.89
1.94
2.78
2.39
22.5
Vspa suppetion
0.75
Clee 2
.0.0
0.25
120000
0
100
200
100 (4) Learning Soore Time Points
200
time Deccoees
100000
B Softthape B ISLANN
# MR-11
SoftShape
MR-il
ASSLNCT
(c) Saries Begions
2900
mospttor Time
00000
B Midiarmer-S 550
# oomo
2000
Medioomer-S
Figure 4: The MIL visualization on the Trace dataset.
1500
40000
1000
500
Muthods
Muthods
ries that improve classification performance. This study applies MIL highlight significant shapes. Figure 4 shows the discriminative regions and attention scores learned by SoftShape on Class / of the Trace dataset. Deeper red in- dicates beneficial regions for classification, while deeper blue shows less relevant ones. Figures 4(a) and 4(b) treat each shape (length m = 64) as one sequence point, while Figures 4(C) and 4(d) map these results to the entire time series. SoftShape assigns higher attention scores subse- quences with significant differences between Class / and Class 2, while sparsifying less discriminative regions. These findings indicate that SoftShape learns highly discriminative shapes as shapelets, enhancing interpretability through at- tention scores. Further MII. visualisations on the Lightning? dataset in the Appendix of Figure support this finding.
Ciboodoooooommmreeaa (Lergtt, 10000)
Ubi WouseTWaatty (Lengh), 20000)
16000
1000
MR-H
Time (Secondo
14000
SoftShape
TRUANet
lime Decordb
1200
1000
Softshape
TSEPWer
10000
Medionmer
InceptianTimm mo
000
Micfommer
Bincopt onti
600
2000
Methods
Methods
66 Cooneoooonnn (1 enggh, 16R)
(() HosseiTwarty (lagg 2003)
Figure 3: Running time analysis on the ChlorineConcentra- tion and House Twenty datasets.
(Middlehurst et al., 2024). TSLANet and Medformer are recent patch-based models utilizing CNNs and Transform- ers, respectively. To evaluate SoftShape's sparsification efficiency, we select two datasets: ChlorineCCnncentration (4,307 samples, length 166) and HouseTTwenty (159 samples, length 2,000). In Figures 3(a) and 3(b), sequence lengths are extended to 16,600 and 20,000 by sample concatenation to simulate long-sequence scenarios. Given Medformer's s high computational cost for long sequences, we report only its runtime at 50 epochs (out of a maximum of 500), de- noted as Medformer-50. As shown in Figures 3(a) and 3(b), SoftShape outperforms all deep learning baselines and is slightly slower than MR-H. Specifically, Medformer's 's self- attention leads to higher training time with long sequences, while SoftShape's linear-comllextty gated attention ensures greater efficiency. In short-sequence [Figure 3(c) and small- sample [Figure 3(d)) scenarios, SoftShape exhibits slightly higher runtime than TSLANet and substantially higher than MR-H. In these settings, sparsification offers limited effi- ciency gains, as the number of sparsified shapes does not decrease significantly compared to greater number of train- ing samples with long sequences. Additionally, Table 14 in Appendix B.3 presents the inference times and parameter counts for the settings in Figures 3(c) and 3(d).
The t-distributed Stochastic Neighbor Embedding (t-SNE) (Van der Maaten & Hinton, 2008) is used to visualize shape embeddings learned by SoftShape. Figure 5(a) shows in- put shape embeddings from ID CNN (Eq. (2)) on the CBF dataset. Figures 5(b) and 5(c) present sparsified intra-shape and inter-shape embeddings from the soft shape learning block, while Figure 5(d) displays final output sparsified shape embeddings for classification. Compared to Fig- ure 5(a), the intra-shape embeddings [Figure 5(b)) learned by activating class-specific experts form clusters for sam- ples of the same class but still mix some samples from different classes. The inter-shape embeddings [Figure 5(c) learned by a shared expert effectively separate different classes while dispersing same-class samples into multiple clusters. Combining intra- and inter-shape embeddings, Figure 5(d) balances class distinction and clusters samples of the same class closely together. These results indicate that SoftShape leverages intra- and inter-shape patterns to improve shape embedding discriminability. Further t-SNE visualization on the TwoPutterns, Fiflywords, and ECG200 datasets with different classification difficulty can be seen in the Appendix of Figures 8, 9, and 10, respectively.
5.4. Visualization Analysis
5.5. Hyperparameter Analysis
To evaluate SoftShape's effectiveness and interpretability, we use Multiple Instance Learning (MIL) (Early et al., 2024) for visualization. MII. identifies key time points in time se-
Table presents the classification results of SoftShape for various sliding fixed step sizes g. We observed worse Avg.
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Learning Soft Sparse Shapes for Efficient Time-Series Classification
Val-Select and Multi-Seq (p-value < 0.05). The Val-Select model also has fewer parameters and lower runtime. In addition, Tables 22 and 23 in Appendix B.5 present analyses of SoftShape's s time series forecasting performance.
Table 7: Test accuracy comparison of shape length m on 18 UCR datasets. The best result is in bold.
(a) Input Shape Embeddings
(b) Intra- Shape Embeddings
Methods
Val-Select
Fixed-8
Multi-Seq
Avg. Rank
1.72
2.28
1.44
P-value
2.88F-01
4.68F-02
(c) Inter- Shape Embeddings
(d) Output Shage Embesldinss
6. Conclusion
Figure 5: The t-SNE visualization on the CBF dataset.
In this paper, we propose a soft sparse shapes model for efficient time series classification. Specifically, we intro- duce a soft shape sparsification mechanism that merges low-diseriminative subsequences into single shape based learned attention scores, reducing the number of shapes for shapelet learning. Moreover, we propose soft shape learning block for learning intra-shape and inter-shape tem- poral patterns, enhancing shape embedding discriminability. Extensive experiments demonstrate that SoftShape achieves state-of-the-ar classification performance while providing interpretable results. However, this study does not consider the modelling of relationships among multiple variables of the time series. In the future, we will investigate deep learning methods for multivariate TSC.
Table 5: Test accuracy comparison of different sliding win- dow sizes on 18 UCR datasets. The best result is in bold.
Sliding Step Size
q=1
q=2
q=3
q=4
g=m
Avg. Rank
3.83
2.78
2.44
1.78
2.94
Table 6: Test accuracy comparison of model depth on 18
UCR datasets. The best result is in bold.
Depth
L=1
L=2
L=3
L=4
L=5
L=6
Avg. Rank
3.72
2.61
3.06
3.33
3.44
3.06
A Acknowledgements
Rank values when q = or q = m (non-overlapping). With q the maximum subsequences result in redundancy and irrelevant information. Conversely, 9 generates the fewest subsequences, possibly missing important dis- criminative subsequences. Table 6 examines the influence of model depth L,, revealing that SoftShape achieves the lowest Avg. Rank at = 2, demonstrating shape embeddings cap- ture discriminative features effectively, even at low depths. Detailed results of Tables 5 and provided in Appendix B.4. Also, Tables 18, 19, 20, and 21 in Appendix B.4 present sta- tistical test results on the impact of the maximum number of class-specific experts, class-specing expert networks, shared expert networks, and the hyperparameter X.
We thank the anonymous reviewers for their helpful feed- backs. We thank Professor Eamonn Keogh and all the people who have contributed to the UCR time series clas- sification archive. Zhen Liu and Yicheng Luo equally contributed to this work. The work described in this pa- per was partially funded by the National Natural Science Foundation of China (Grant No. 62272173). the Natural Science Foundation of Guangdong Province (Grant Nos. 2024A 15141151500008) 1522211155011170 the Science and Technology Planning Project of Guangdong Province (Grant No. 2023A0505050106) the National Key R&D Program of China (Grant No. 2023YFA 101 1601), and the China Scholarship Council program (Grant No. 202406150081),
To evaluate the impact of the hyperparameter shape length m on classification performance, we conducted three exper- iments: (1) Val-Select: Choose a fixed m for one SoftShape model using the validation set. (2) Fixed-8: Set m 8 for one SoftShape model. (3) Multi-Seq: Use fixed lengths (8, 16. 32) in parallel three SoftShape models, with cross- scale residual fusion (Liu et al., 2023) for classification. As shown in Table 7 (detailed results in Appendix B.4), there was no significant difference performance between
Impact Statement
Our proposed work Soft aims to advance the field of Machine Learning by providing a more efficient and interpretable model for time series classification across vari- ous applications. There are many potential societal conse- quences of our work, none which we feel must be specifi- cally highlighted here.

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Learning Soft Sparse Shapes for Efficient Time-Series Classification
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Learning Soft Sparse Shapes for Efficient Time-Series Classification
A. Experimental Setup
A.1. Datasets
In this study, we employ the UCR time series archive (Dau et al., 2019), a widely recognized benchmark for time series classification tasks (Ismail Fawaz et al., 2019; Middlehurst et al., 2024), to systematically evaluate the effectiveness of the proposed method. This archive encompasses datasets from diverse real-world domains, including human activity recognition, medical diagnostics, and intelligent transportation systems. The UCR archive consists of 128 distinct time series datasets.
As shown in Table 8, many datasets in the UCR archive have notably greater number of test samples than training samples, such as the CBF, DiatomSizeReduction ECGFiveDays, MoteStrain, and TwoLeadECG time series datasets, Moreover, the original UCR time series datasets lack a specific validation set. The limited amount of training samples and the lack of a validation set present challenges in fairly comparing various deep learning- time series classification methods.
Following the experimental settings outlined (Ma al.. 2024) and the recommendations of (Dau et al., 2019), we integrate the raw training and test sets and employ five-fold cross-validation strategy partition the dataset into training, validation, and test sets in a 3:1:1 ratio. Consistent with the approach in (Ma et al., 2024), each fold is sequentially designated as the test set, while the remaining four folds are randomly divided into training and validation sets in a 3:1 ratio. This coss-validation procedure ensures that each time series sample in the dataset is utilized as a test sample at once, thereby providing a comprehensive evaluation of classifier performance. Consequently, the specific indexing of samples during coss-validation does not substantially influence the final classification results, as each sample contributes to assessing the model's performance.
A.2. Baselines
We conduct a comparative analysis of SoftShape against 19 baseline methods. Notably, nine of these baseline deep learning methods are derived from the experimental setting presented in (Ma al., 2024), including FCN, T-Loss, SelfTime, TS-TCC, TST, VS2Vec, TimesNet, PStchTST, and GPT4TS. While Ma et al. (2024) review a broad range of techniques for time series pre-training, its experimental design for the UCR 128 time series datasets specifically structured to evaluate the strengths and limitations of these nine deep learning models in the context of supervised time series classification. Therefore, we adopt these nine deep learning methods as baseline models for our experimental analysis, as described below:
FCN' (Wang et al., 2017) employs three-layer one-dimensional fully convolutional network along with one-layer global average pooling layer for time series classification.
T-Loss² (Franceschi al., 2019) utilizes temporal convolutional networks as its foundation and presents an innovative triplet loss for learning representations of time series in the time series classification task.
SelfTime (Fan et al., 2020) a framework for time series representation learning that explores both inter-sample and intra-temporal relationships for time series classification tasks.
TS-TCC' (Eldele et al., 2021) is framework for learning time series representations through temporal and contextual contrasting for classification tasks.
TST$ (Zerveas et al., 2021) is framework for multivariate time series representation learning based on the Transformer architecture for classification tasks.
TS2Vec (Yue et al., 2022) is general framework for time series representation learning across various semantic levels, aimed at tasks such as time series classification, forecasting, and anomaly detection. In the context of the time series classification task, the authors utilized temporal convolutional networks (TCN) as the foundational framework, leveraging the low-dimensional feature representation derived from TCN as input for support vector machine classifier utilizing a radial basis function kernel for the classification process.
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Learning Soft Sparse Shapes for Efficient Time-Series Classification
Table 8: Details of the UCR 128 time series datasets, "Train" represents the count of samples within the raw training set. "Test" represents the count of samples within the raw test set. "Total" represents the overall count of samples within the time series dataset. "Class" indicates the number of classes present within each time series dataset. "Length" refers to the sequence length of the univariate time series within the corresponding dataset. The presence of "Vary" signifies that the dataset includes instances with missing values.
Name
Train
Class
Length
Name
+Trin
Total
Class
Length
1
ACSFI
100
1001
2001
10
1460
61
IowlyPowerreemadd
67
1029
1096
2
24
2
Adiac
390
391
781
37
176
LangeKiehcaAgplinnes
375
375
750
720
3
AllGeestneWimmeee
300
7001
1000
10
Vary
67
Lightning2
60
61
121
637
"GGesttreWiineee"
300
700
1000
10
Vary
68
Lightning?
70
73
143
319
5
BilGesturWiimokee
300
700
1000
10
Vary
Mallat
55
2345
2400
1024
6
ArroWHead
36
175
211
3
251
70
Meat
60
60
120
448
7
Beef
30
470
71
Medicalimages
381
760
1141
99
8
BeetleFly
20
40
2
512
72
Melboumeeedesttiunn
1194
2439
3633
10
24
RiriChicken
20
MickleePhalans OutillaPeaaanntttinnnneeeee Omtep
400
154
554
80
10
BME
30
150
180
3
128
74
HhedleePahammOttiieCCCo
600
291
891
80
Car 11
60
527
MicdlePPalanxXTV
399
154
553
12
CBF
30
900
930
3
128
76
SisedSttaps&Rgglaar Train
500
2425
2925
1024
Chinatown
MiscdStage
100
2425
2525
1024
14
ChiorincComeenntattio
467
3840
4.007
3
166
78
MoteStrain
20
1252
1272
84
15
CisCECGTorso
1800
1965
3765
750
16
Coffee
28
28
56
2
286
8D
NoninoaiieeeellECGTT
1800
1965
3765
42
750
17
Computers
250
OliveOil
18
CricketX
390
390
780
12
300
82
OSULeaf
200
242
442
427
19
CricketY
390
12
PhalangesOutineSCorree
1800
858
2658
20
CricketZ
390
390
780
12
300
84
Phoneme
214
1896
2110
39
1024
21
Crop
7200
16800
24000
24
PickupGGettrre WiimoteZ.
50
100
Vary
22
DimoonSizeRecchciinn
16
306
322
4
345
86
MgAirwayPressum
104
208
312
52
2000
23
SmallPaalasSOtlinnAggGG
400
139
539
3
87
PigAriPressuic
104
208
312
S2
2000
24
DistaPhaaaan Outil CntrineCorreet
600
276
876
2
80
88
PV/UVP
104
208
312
52
2000
25
DisalPMalanxTW
400
139
539
6
PLAID
537
537
1074
11
Vary
26
DodgerLoopDay
78
158
7
288
Plane
105
105
210
144
27
DoodgerLaopGaane
20
138
158
2
288
91
PowerCons
180
180
360
144
28
CodggrrLoopWeekent
20
138
158
2
288
ProsimuPPalanssOullnneeeee
400
205
605
80
29
Earthquakes
322
139
461
2
512
93
600
291
891
80
BCG200
100
ProximulPhalanxt IW
41K1
605
31
ECG5000
500
4500
5000
5
140
95
RefrigerationDevices
375
375
750
720
BCGHHveDays
23
Rock
50
70
2844
33
ElsctrieDevioes
8926
7711
16637
7
96
97
SeroenTyppe
375
375
750
720
34
EoGHorizontaaignall
362
SemgHHandGemdeChh2
600
900
1500
35
BOGVerticaSiguall
362
362
724
12
1250
99
SongHHeedMoweannihhhhh
450
450
900
1500
36
EevanelLvvel
504
SemgtEasdSahjerthh2
900
1500
37
FaceAll
560
1690
22,00
14
131
101
ShakeGesture Wiimotelz
50
50
100
10
Vary
38
FaceFour
ShapeletSin
180
200
500
39
FCC
200
2050
2250
14
131
103
ShapesAll
600
600
1200
60
512
40
HiftyWords
450
455
50
Small Aphhenpppens
375
375
750
7201
41 Fish
175
175
350
7
463
105
Smooth
150
150
300
15
42 FordA
3601
1320
4921
2
500
20
601
621
70
43
FordB
3636
810
4446
2
500
107
SonyAIBOR Suuuo
27
953
980
65
44
FroozerRegularTrai
150
2850
3000
2
301
108
StarLiigtturress
1000
8236
9236
1024
45
28
2850
2878
2
301
109
Strawberry
613
370
983
235
46
Fungi
18
186
204
18
201
110
SwedishLeaf
500
625
1125
15
128
47
GesturMidAAidI
208
130
338
26
111
Symhols
25
995
1020
398
48
GesureMidAAiD2
208
130
338
26
Vary
112
SymiheticControl
300
300
600
60
49
GestrrMidAAitD
208
130
338
26
Vary
113
TeeSegmentatiinn
40
228
268
277
50
GesturPeehil111
132
172
304
6
Vary
114
ToeSegrnentttion2
36
130
166
343
51
GestucPebblz22
146
Vary
Trace
100
200
52
GamPoint
50
150
2000
2
150
116
Twol enFFOG
23
11.39
1162
82
53
GunPoiintAgeppan
TwoPatterns
1000
4000
5000
128
51
135
316
451
2
150
118
UMD
36
144
180
150
3582
44778
56
Ham
109
105
214
2
431
120
UWaaCGestureLitraryy
896
3582
4478
31.5
57
HandOulines
1370
UWaveGesturel
896
3582
4478
315
58
Haptics
155
308
463
S
1092
122
WWWaveGeestueell abrury?
896
3582
4478
31.5
59
Herring
Wafer
1000
6164
7164
152
60
House Twenyy
40
119
159
2
2000
124
Wine
$7
54
111
234
61
InlineSkate
100
550
650
7
1882
125
WordSynonyms
267
638
905
25
270
62
InsectEPGReguarrTaai
62
249
311
3
601
126
Worms
181
77
258
9001
63
17
249
266
3
601
127
WormsTwoClass
181
77
258
900
61
InsoeeingbesSoond
220
1980
2200
11
256
128
Yoga
300
3000
3300
426
T (Wu et al., 2023b) employs TimesBlock to identify multiple periods and capture temporal 2D variations from transformed 2D tensors using parameter-efficient inception block for time series modeling.
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14

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Learning Soft Sparse Shapes for Efficient Time-Series Classification
PatchTST (Nie al., 2023) segment time series into patches while assuming that channels independent for multivariate time series forecasting. Considering that GPT4TS (Zhou al., 2023) has utilised similar patch and channel-independent strategies for time series modeling, we employ only the patch strategy and the channel-independent approach by integrating a transformer for time series classification.
GPT4TS' (Zhou al., 2023) a unified framework for time-series modeling that utilises pre-trained large language models. Specifically, GPT4TS adopts the same patch and channel- channel-independent strategies used in PatchTST (Nie et al., 2023) for time series classification tasks.
Furthermore, Middlehurst et al. (2024) conduct comprehensive analysis of the advantages and limitations of eight categories of time series classification methods: distance-based feature-based, interval-based, shapelet- dictionary- based, convolution-base deep baaning-baaed. and hybrid-based approaches. However, in their experimental evaluation, Middlehurst et al. (2024) utilize only a training set and test set, without incorporating validation set for deep learning-based methods performance assessment.
Specifically, for the selected deep learning- based time series classification methods, Middlehurst et al. (2024) employ the training epoch with the lowest training loss to generate test results. This approach increases the risk of overfitting, as the deep learning model is optimized solely on training data, potentially compromising its generalization capability. Nonetheless, the findings of (Middlehurst et al., 2024) indicate that the deep learning- bearning-based InceptionTima (Ismail Fawaz et al., 2020) model achieves superior classification performance. Additionally, experimental results (Middlehurst al., 2024) demonstrate that HIVE-COTE version 2 (HC2) (Middlehurst et al., 2021), which a hybrid-based method, MultiROCKET-Hyle (MR-H) (Dempster et al., 2023), a convolution-based method, and RDST, shapelet-based approach, exhibit strong classification performance.
Given that HC2 is computationally intensive, we select the deep learning-base based InceptionTime model along with two non-deep learning methods, MR-H and RDST, as baseline models for our study. The details of these baseline methods are outlined as follows:
Random Dilated Shapelet Transform (RDST) 10 (Guillaume et al., 2022) is a shapelet- based algorithm that adopts many of the techniques of randomly parameterised convolutional kernels to obtain shapelet features for time series classification.
MuliROCKET--yddra (MR-H)" (Dempster et al., 2023) is model that combines dictionary- and convolution- based models, using competing convolutional kernels and combining key aspects of both Rocket and conventional dictionary methods for time series classification.
InceptionTime" 12 (Ismail Fawaz et al., 2020) is a deep convolutional neural network-based model for time series classification, drawing inspiration from the Inception-v4 architecture.
In recent years, scholars have introduced deep learning models based on convolutional neural networks, transformer architectures, and foundation models for time series classification tasks. For experimental analysis, we have selected seven recently published methods as baseline models, which are detailed as follows:
LightTS (Campos et al., 2023) employs model distillation to reduce runtime by ensembling multiple classifiers. It consists of two stages: a teacher phase, where at least ten models (c.g.. Inception'Time) are trained, and student phase that distills their knowledge. Due to the time-intensive nature of the teacher phase, evaluation is limited to 18 selected UCR datasets. Moreover, since LightTS (student) underperforms compared to LightTS (teacher), only the latter's results are reported.
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15

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Learning Soft Sparse Shapes for Efficient Time-Series Classification
ShapeCony (Qu et al., 2024) introduces an interpretable convolutional layer for time series analysis, where the convolutional kernels are designed to act as shapelets. This convolutional design is inspired by the Shapelet distance, widely adopted approach in time series classification.
Shapeformer (Le et al., 2024) is a Shapelet Transformer that combines class-specific and generic transformer modules to effectively capture both types of features. Due the conemminnn shapelet discovery process in Shapeformer, we evaluate its performance on 18 selected UCR datasets
1Cd (Luo & Wang, 2024) is a pure convolution architecture for time series modeling, which utilizes depthwise convolution and grouped pointwise convolution to learn cross-variable and cross-fcature information in a decoupled way.
TSLANer !? (Eldele et al., 2024) is time series lightweight adaptive metwork, as a universal convolutional model by combining an adaptive spectral block and interactive convolution block using patch- patch-based technologies for time series modeling.
U (Gao et al., 2024) is unified pre-trained foundation model for time series, designed to handle various forecasting and classification tasks across diverse datasets. Following the experiments in Table 14 of UniTS, we use the UNITS- SUPTS model as the baseline.
Medformer 19 (Wang et al., 2024) is a transformer model designed for medical time series classification that utilizes cross-channel multi-granularity patching, and intra-inter granularity self-attention within and among granularities.
A.3. Implementation Details
We employ the Adam optimizer with learning rate of 0.001 and a maximum training epoch of 500. Also, for all baseline method training, we implement a consistent early stopping strategy based on validation set loss values (Ma et al., 2024). For all UCR datasets, we apply a uniform normalization strategy to standardize each time series within the dataset (Ismail Fawaz et al., 2019). For datasets containing missing values, we use the mean of observed values at each specific timestamp across all samples in the training set to impute missing values at corresponding timestamps within the time series samples (Ma et al., 2024). Following (Wang et al., 2017), we set the batch size for model training as min (rrain Shapee [0] 10, 16). where Train Shapee[ represents the number of time series samples in the training set, and min(-) denotes the function that selects the minimum value.
From Equation (1) in the main text, the length of time series shapelets, m, satisfies 2 S m TT 1. Directly using subsequences of varying lengths as model inputs significantly increases computational complexity and requires additional preprocessing to standardize imput dimensions. To address this, Grabocka et al. (2014); Qu et al. (2024) employ a validation set to select fixed-length m of subsequence for shapelet learning, where m is defined as 7T, with possible values {0.12, 0.27, ..., 0.8T). This approach reduces the total number of candidate subsequences in Equation (I), thereby lowering computational costs. For patch-based time series classification (Nie et al., 2023; Wang et al., 2024), patch lengths are typically chosen from (4, 16, 24, 32, 48, 64). Our preliminary experiments indicate that setting shape length mn within this range yields better classification performance. However, due to variations in sequence lengths across UCR 128 datasets, a fixed-length setting may be problematic. For datasets with long sequences, setting m = 4 results in excessive candidate subsequences, while for short sequences, setting m = 64 may eliminate viable subsequences. To balance these issues, we select m from {4,8, 8, 16, 24, 32, 48, 64, 0. 0.8T) using the validation set.
Additionally, we set the model depth L to 2. The number of activated experts k used for the Mixture of Experts (MoB) router in Equation (6) is set to 1, while the total number of experts Ö in MoE is defined as the total number of classes in each dataset. The parameter X, which regulates the learning progression of the loss term in Equation (15), is set to 0.001. The sliding window size for extracting subsequences is set to 4. The dattn in Equation (3) is set to 8 (Early et al., 2024). The rate y in Equation (5) is set to 50%. To mitigate the issue of inaccurate attention score evaluations for most shapes
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16

---

Learning Soft Sparse Shapes for Efficient Time-Series Classification
during the initial training phase, the model is warm-up trained for 150 epochs before initiating the soft shape sparsification process. For each UCR time series, we calculate the average test accuracy using five-fold test sets from single seed. To ensure a fair comparison, we maintain consistent random seed, as well as standardized dataset preprocessing and partitioning for all baseline methods. For SoftShape and deep bearning-based baselines, the same optimizer and learning rate are applied during training, selecting the model with the lowest validation loss for test evaluation. Non-deep learning methods are trained on the training set and evaluated on the test set. Furthermore, for deep learning baselines, except LighTTS (Campos et al., 2023), a single model instance is employed without ensembling multiple models initialized differently during both training and evaluation. Like (Ismail Fawaz al., 2019; Ma et al., 2024), we evaluate performance based the classification accuracy of the test set. Each experiment is conducted five times with five different random seeds, utilizing the PyTorch 1.12.1 platform and four NVIDIA GeForce RTX 3090 GPUs. The source code for SoftShape is available at https: / /i thub. com/qt /qi an i ma - lab/ Soft S.aapp..
Algorithm 1 The proposed SoftShape model.
Input: shape embedding layer Wshapes attention head Wattns soft shape learning block Wblock a classifier wer sparse ratio 7)
Output: Wahapes Wattn; Whlckk, and W.-
1: Step one: Obtain all shape embeddings STz through Wshope via Eq. (2);
Using a norm layer to process 5Th denoted as norm((S;))) (Str))
2: Step two: Soft shape sparsification using norm(S.)) as inputs;
Calculate the attention score for all shapes via the Wattn:
Convert scores in the top 1) proportion of all shapes into soft shape embeddings via Eq. (4); Fuse those with scores below the top 1) proportion into single shape embedding via Eq. (5); Combine soft shape embeddings and the fused single shape embedding, denoted S.;;
3: Step three: Shape and Inter-Shape Learning through Wilock using Stm as inputs: Using a norm layer to process S denoted as nor"(S;)) Obtain
Embedings via Wbtock using Eq. (8), denoted as Sintrai Obtain Inter-Shape Embedings via Wbock using a shared expert, denoted as Sinteri Combine STD SIntra and Sinter in a residul way, denoted as Sout = STD + SIntra + SInter:
4: Step four: Set model depth to L for training by rerunning Step two and Step three L times using Sant as inputs, denoted the end outputs as 0%,
5: Step five:
Classification training using OT as inputs:
Update Wshape: Wattn, Whlook; We via training objective Lrotal using Eq. (15);
B. Details of Experimental Results
B.1. Main Results
The test classification accuracy results of SoftShape and 17 baseline methods on the UCR 128 time series dataset are presented in Table 9. Specifically, the test classification accuracy results of nine methods, including FCN, T-Loss, SelfTime, TS-TCC, TST, TS2Vec, TemesNet, PatchTST, and GPT4TS, are obtained from (Ma et al., 2024). Figure illustrates the critical difference diagram and significance analysis results for SoftShape and the 17 baseline methods on the UCR 128 time series dataset. Additionally, Table 10 presents the detailed test classification accuracies of LightTS, Shapeformer, and SoftShape on the selected 18 UCR datasets.
Table 9: The detailed test classification accuracy comparisons 128 UCR time series datasets. Among these, Incep refers to the InceptionTine method, and MoTCN refers to the ModernTCN method. The best results are in bold.
Thstaset
FCN
asl Selttime
TS-TCC
TST
TS:Vo
TimesNet
PaisTTT GPT4TS
RDST
MR-H
Incep
StupeCon MoTCN TSI.ANer
UniTS
Medioeeer
Sah
ACSFI
0.6250 0.5050
0.7050
0,8800
0.6000
0,7600
0.9050
0.8350
Adiac
0.6492
0.7811
0.7322
04003
0.7363
0.8066
0.8082
0.8358
0.8069
0.7848
0.8527
0.9354
0.5635
0.8550
0.8837
0.6596
0.8364
0.9374
A.IGessareW.
0,7110 0.3170
0.6461
0.7201
0.5280
0.7820
0.5120
0,5730
0.7220
0.7930
0.8050
0.85-00
0,3170
0.7250
0.8970
0.5530
0.6130
0.8950
A.lGesureeW.
0.6740 0.110
0.7170
0.7615
0.3850
0,8400
0.5820
0.6730
0.7800
0.8360
0.8770
0.9110
0.2990
0.7470
0.9180
0.5690
0.8250
0.9110
AlIGestrreWZ
0,7200
0,4780
0.7730
0.6620
0.5890
0.7550
0.3920
0.3070
0.7250
0,5850
ArrowHeead
0.8958 0.8770
0.8155
0.8200
0.5722
0.898
0.7821
0.7078
0.8348
0.9382
0.9:30
0.92888
0.6638
0.8152
0.9672
0.943
0.9434
0.9135
Beef
0.8250 0.5750
0,5167
0.633
0.8667
0,6833
0.8000
0.4167
0.9333
0.8133
0.8500
0.7833
0.6833
0.8500
0.7500
0.7167
0.8333
0.5667
BeeileFly
0.9250 0.9750
0,8000
0,6350
0,6750
0.9250
0.7000
0.8500
0.7250
0.0000
0.9250
0.5500
0.9250
0.7500
0.9750
0.8750
0.9000
0.9750
BirdChicken
0.9000
0,8000
0.8250
0.8500
0.7500
0,9000
0.9500
0,9500
0.8250
0.5250
10 BME
0.8000
0.5333
0,9722
0.9899
0.9722
0.9944
0.9788
0,9500
0.961]
1,0000
1,0000
1.0000
0.6722
0,9833
1.0000
0.9889
1,0000
0.9914
17

---

Learning Soft Sparse Shapes for Efficient Time-Series Classification
ID
Daiase
FCN
T-Loss
Selftime
TS-TCC
TST
VSIVec
TimesNet
PatcTTT
GPT-TS
RDST
MR-II
Ineep
ShapeCom
MoTCN
TSLANa
UniTS
Medioeeerr
SuliShape
11 Car
L0000
1,0000
0,6883
0.7167
0,7583
0,8833
0.8417
0.9083
0.9000
0.9500
0,9583
0.9583
0,7750
0.8250
0.9500
0.9083
0.8417
0.9583
CBF
0.9417 0,8251
0.99%
0.9967
0.934
1,0000
1,0000
1,0000
0.9978
1,0000
1,0000
1,0000
0.9989
1,0000
1,0000
0.9978
1,0000
1,0000
Chinatowa
0.9753 0.8877
0.9669
0.9507
0,9029
0,9726
0.9833
0.98%
0.9863
0,909
0.9808
0,9836
0.9123
0,923
0.9663
09781
0.563
0,9890
14 ChlorinoCon
0.9984
0.988
0.6116
0.8424
0.9074
0.9998
0.9993
0.9995
0,99%
0.9636
0.9054
0.9093
0.6973
0.9991
0.9988
0.998%
0.6427
0.9968
15 CioCECGTeso
0.99% 0.5944
0.887
0.992
0.999
0.9972
0.9500
1,0000
0.9930
1,0000
1,0000
0.992
0.9789
0.999
1,0000
0.9958
0.9986
1,0000
16 Coffee
1,0000 0.9818
0.9275
0:5455
0,8758
1,0000
1,0000
1,0000
1.0000
1,0000
1.0000
1,0000
0:9667
1.0000
1.0000
1.0000
0:9818
1,0000
17. Computers
0.8900 0.7140
0.7920
0.6000
0.680
0,040
08120
0.830
0.8000
0.100
0.840
0.5470
0.6660
0.6540
0.890
08120
0.220
08810
18 CrickeXX
0.9064 0.7755
0.7316
0.7327
0.7006
018211
0.7974
0.7821
0.7910
0.8628
0.8628
0.9013
0.8179
1
0,9205
0.8925
0.8397
0.9321
19. CricketY
0,9000 0,7487
0.6904
0.7161
0,6963
0.7808
0.762
08026
0
0.446
0,8487
0.8923
0.7692
0.7513
0.8987
088877000
0.880K
0.8500
0.9154
Cricket7
0.8831 0.7835
0.7411
0.7584
0.50%
0.8467
0.7923
0.8026
88602
0.85%
0.5679
0.7744
0.7385
0.9064
0090640000
0.8859
0.856
0.9372
21 Crop
0:1312 0.7065
0.6634
0.7501
0,7700
0,7448
08503
0:119
08764
0,7675
0.7805
0.5757
0.1853
0.0222
0.5781
0.417
0,5043
0.8765
22 DistumSizeRe.
0,9960 0.9999
0,9723
0.9783
1,0000
0.9060
09938
1.0000
0000000000000000000000000000000
0.9907
1,0000
1.0000
0.9069
0.9531
0.9677
0.9969
0.9719
0.9978
1,0000
25 DisalPPhlannOOt
0.9091 0.8274
0,7950
0.8300
0.5464
0.8125
0.850
0.8890
0.831]
0,829
0.5850
0.7662
0.8088
0.9333
0.8070
0.8312
0.9518
DisalPtolanxOaa
0.8917 0.5471
0,7895
0.7646
0,825
0,8185
0.8860
0.9009
0.8929
0,8323
0.8448
0,5802
0.7960
0. 1
0.9018
0.7365
0.6529
0.9854
25. DisalPhalmmTTW
0.8423 0.7421
0.7514
0.7755
0.7511
0.7792
0.499
088233
0,7866
0.7700 0.8500
0.7421
0. 0.7979
0.8796
0.771K
0.8349
0.9037
26 Dedga
0.74%6 0.4819
0.4742
0.5885
0.5337
0.6391
07107
0.6994
0.7408
0.6366
0.5315
0.7688
0.7671
0.5538
0.8244
0,8750
0.8621
0.8623
27
Dodgeel/opCamee
0.8167 0.8921
0.822200
0.8857
0
0.8988
0,9563
0.8184
0.882
0.9001
0.9175
0.9631
0.9573
0.7966
0.9563
009563000
0.8144
0,9342
0.9433
DolgeeLLopWec
0.9612 0.9677
0,9681
0.9743
1.967900000
09688
0,9492
0.9165
0,9746
0.9873
0.9006
0.9937
0:9917
0,9873
0 0.9806
1,0000
1.0000
29 Fantqqukes
0.7576 0.7417
0.7983
0.7505
0.7061
0,7963
09136
09115
0.7809
0.7939 0.7239
0.8536
0.7533
0.9222
0022200000
01813
0.8967
0.8917
30 ECG200
0.8482 0.7983
0,7900
007000000000
0.7930
0.8000
0.8800
09100
0.8763
0.8951
0.9200
0.9250
0.9250
000250000000
0.
0.8600
0.9050
0.9450
0.8850
0.9100
0.9475
31 FOG5000
0,9350 0,5000
0.9317:0
0.9525
0.95020000
0.9578
0.9564
0.9746
0.552
0.9566
0.9750
0.3455
0.5510
0.9760
0.9622
0.9460
0.97%
BOOiFwaDays
0.9258 0,9478
0,9873
0.9972
0.997
1,0000
10000
0000000000
1,0000
000000000000000000000000
0.2978
1,0000
1.0000
1.0000
1,0000
1.0000
1.00000
1,0000
1,0000
33 ElccrriDevices
0.8519 0.6577
0.7173
0.8639
0.8758
0.8848
0,8610
116600000000
0
086100000
0,902
0.9094 0,949
0.7259
0.3500
0.8991
0.7921
0.7665
0.9208
34 BOCHorivnmiis
10000 1.0000
0,7579
0.6295
0.6781
0.7279
0.692
0.8010
0.7581
0.7842
0.8453
0.8910
115010:0000
0.7056
0.7281
1
0.8993
0.8469
0.8344
0.9007
35 FOGVarieal..
0.6731 0.736
0.6774
04190
0,4806
0.65119
06369
0.8013
0.7804
0,7335
0.7984
0.5709
0.4764
0
0.896
0.6620
0.8220
0.8814
DisnnlLevel
0.8307 0.5627
0.4864
0.2965
0.7919000
0.5897700
0,7690
0,7248
0.337
0,7480
0.726]
09144
0.9184
0.1771
0.577
0,8019
0.9201
37 FaozAll
0.9462 0.9720
0.9552
0.9914
0,9720
09733
0.8057
0.9877
0.9911
0.9951 0,9673
0. 0.9530
0.9534
0.997
0,9880
09778
0.9978
38 FaceFvur
0,9557 0.9281
0,8830
0288300000
0.9179
0.9375
0,9610
0,557
0,9968
0.9826
1,0000
0.9909 1,0000
1,0000
0.9626
0.9913
0.913390
0.9735
0.9626
0.9909
39 FacesUCR
0,9959 0.9729
0.9564
0.9899
0,9702
0,9900
09600
0.9824
0.9796
0.9938
0.9938
0.9938(000
0.9973
0.9653
0.9540
0.9960
0.9889
0.9631
0.9956
Finly Words
0.5072 0,8088
0.6705
0.7678
0,7381
0,9002
08376
0.8417
0.770
0.7709
0 0.8619
00869908000 0.8718 0
0.8718
0.9249
0.8807
0
0.8665
0.9359
41 Fish
0,9636 0.5743
0.8514
0.8114
0,8628
0.9343
08000
0.933
0.1133
0,8557
0.9829 0,9943
0.837]
0.8800
096629
0,9:00
0.9086
0.9771
42 FonlA
0,9734 0.9114
0,878710
0.9343
0,8900000
0,9303
00000000000000000000000000000000
09344
0,9500
08484
0.9537
0,9728
0.8935
0,9500
0.9740
0974000000
0.9718
0.8450
0.9772
43 FinlR
0,9312 0,9035
0.871
0.9087
0
0.8650
0,9132
000112000000
0.9445
0.937
0.9287
0.927
0.9345
0.9708
0.8954
0.9476
0.9658
096588000
0.9338
0.8498
0.9744
FreezerRegolar.
0,9790 0.9980
0.9974
0.9969
0,9987
0.9977
0.9990
00000000000
0.9393
0.9967
0,999
0.9997
09993
0,7590
0.9993
0,8100
0.6950
0.999
45 Small
0.8359 0.9965
0,9975
0.9966
0,9979
0,9969
0.9969
0.8492
0.9983
0.9993
0.9997
0,9986
0.7575
1
0.997700
0.9396
0.8311
0.9990
Funga 46
0,9118 1.0000
0.9316100
0.9557
0.9902
1.0000
01000000000
0.8337
0.7296
0.9029
1,0000
1.0000
1.0000
0.9951
0.9415
1.0000
1,0000000
0.9902
L,0000
47
GestumMsdAAiD
GeaunoMidAitD2
0,5860 0.4973
0.6951 0.5919
0,7067
0.5504
0.6120
0,4853
0.5475
0.6181
0,5270
0.6479
0,5449
0.609
0.600
0,5692
0.540
0.5410
0.6119
0.541000000000
0,5559
0.7452
0274520.77
0.5858
0,7632
0.7786
176666
0.6810
0.548]
0.630
0.7074
0
0.7600000
0.3051
0.7287
0,7813
0,7079
0.8610
0.7962
49
GesturMadAinDD
0,3819 0.3108
0,3664
0.3137
0.3462
0.3315
0,4559
0,4962
0.5282
0,4141
0.129] 06104
00104:000
0.5399
1
0.6572
0.6343
0.6091
0,7613
50
Gestureebbllli
0,9541 0.6120
0,9043
0.90430000
0.8977
0.776]100
0.9507
0.8316
0.9158
0.9769
0.9703 01963n
0.6289
0.9177
0,9967
0.9573
0.9572
0.9967
51
GonPoint
GostumPebble22
1,000 0.9850
0,9543 0,6614
0.9550
0,8817
0,9500
0.8914
0,9700
0.81590000
0.9473
0,9950
09850
0,8850
0.700
0.9800
078000000000
00000000000000000000000000000000
09332
0.9800
1,0000
0,9666
0,9540
1,0000
0.95000000
0.9836
1,000
0.8127
0.9475
0
0,990
0.9738
0.9606
0.9:00
0,9800
0.9409
0,9900
0.9836
53
CunPrrintAgeSpunn
0.9956 0.9756
0,9800
0.9578
0.9788
0,9889
09823
0.9589
00088900000
0.98000000
0,9956
1.0000 0.9689
0,9157
0
0.9890
0089000000
0.9179
0.9911
0.9668
54
GunPointMMal.
0,9978 0.9911
0,9845
0.9823
0.9867
0.9116
099366
1,0000
000000000
0.9956
1,0000
1.0000 0:9933
0.9712
0.
039934
0.9845
0.9924
0.9926
55
CunPaintOOd.
0,9934 0.9168
0,9:90
0.9512
0,9667
0,9956
09800
0.9912
0.964]
0.9956
0399560.300
0.9978
0.99780000 0,911
0,7653
0.9150
09923
0.9625
0.9712
0.9779
Iamm
0.6632 0,8080
0.7193
0.8275
0,8450
0.8711
08023
0,5420
015420000000
03349
0,806
0.9061..00 0.8760 0.3161
1
0.8922
0.8788
0,8007
0.9161
57
HandOullinss
0.8456 0.9075
0.8425
0.8657
0.7170110
0,9100
0.9168
09029
0.930
0.8956
0,9482
0.9682
0396820000 0.9006
0.8934
0,9700
09960
0.9336
0,9131
0.9533
Hlptics 58
0.6155 0.1879
0.4730
0.4950
0.69940000
0,5554
0,5591
06122
0
0.6812
0.5211
1.59630000 0.0960
0,5033
0.5962
0
0.1899
0.6255
0.7522
59
Herring
HouseTwaaty
0,9575 0.8935
0.6405 0.5929
0.9746
0.6086
0.8244
0,5452
0,8400
0,7673
0,8006
0:4426
0,8066
01010
06560
07801
B8617
03083
0.8003
08005000
030830000
08868
0,9750
0.6551 0,7185
0,9475
002200
0.8649
0.9623
0.579
0,5500
0,8212
0
0,9466
0,7046
0.9658
0.7671
61
InlineSkale
0.7016 0.6351
0,1922
0.4172
0.5754
0.6415
0.5369
0
0008500000
0.6399
0.5508
0.5080000
0,7384 0.7551
0.5446
1
0
0,7769
0
0.7662
0
62
63
InsectEPGS.
InsectEPGR.
InsectWing.
0,7309 0.6673
0,8761 0.9850
0,9935 019839
0,9774
0.609200
0.8308
0.8554
0.7119
0,8235
0,8962
11527710 019807
0,7077
03999
0
0.7355
01010
7
199117
08600
09511
0.851
0.11
03307
0
0,728
1,0000
1,6000
1.00001.000
07728607770
0.730
0.7309 03305
1,0000 1.0000
09963
0.0662
0.79445
0.2073
0
0
0
0.7535
0
0.8780
039914
0,5005
03779
0
0.5918
0.883
0:993
0,9983
65
InlyPowerDemand
0 0.9671
0.9674
1586001000
0.5726
018745
05966
0
0.800
0226000.300
0397350000 05772
0
0.9644
0,9891
0.9681
0.9891
66
67
Lighuning?
LargeKiichenA
0,7910
0.9507 0.8907
0.5090
0,7860
0.9403
00040300000
0.7187
0.7401
0.5692
0,8787
0,0010
0,0010
(19147
07520
09219
0
0.8956
0.6747
0.8916
0.7200
0.9240
0.7603 054130
0396900000 019613
0,0155
0.5700
0
09100
055533
03267
08240
0.885)
0,8857
0.9627
65 Lighning?
0.8405 0355
0,7419
0.7411
0,009
08339
03278
0,7023
03825 00024
0
03882
06133
0.8866
69
Mallat
0.9975 0.9875
0,9901
00900100000
0.9857
119557100
0.9954
0,9960
0,9462
0000220000
05955
0
0.9983
1,000
1,000
1,0000
1,0000
0.9983
0.9683
0.98S
1,0000
000000100
1
1.0000
000000000000
0.9821
0,9588
0.9988
70 Mear
Medicalinages
0.8397
0.9667
0.8211
1.0000
0,7530
0.8917
0
0.5417
0.53%5
0.0000
018333
(1343)
1.0000
118431
00000
139750
1,0000
0
03361
05533
0.3750
0.553
09200
019917
014667
0.7892
0.7852
1.0000
1,0010
09211
055500
0
72 MelboumePsdesstiaa
0.8145
0.8489
0.8885
0088500000
0
0,588
0,8266
09567
08573
0.9820
0,000
0.920
0.9203 09611
0.8271
0
0,5522
0,8611
73
Mostle-geffomm
08117
0.7544
0,7527
8.7563
0,7600
1776001130
0.7:44
001400
09140
B8092
0.7699
0.7365
0.7530
035200
0.7454
0.7698
0.9170
0,7490
75
74
Mi
Maretet
0.2074
0.8854
0.6202
03894
0,7936
0.71338
0.8356
0,8456
18507
0.4455
(1850)
69339
0
0.7027
0.3924
0
0,0000
0.8455
0.5931
0.8608
03310
09911
05310
0.6330
0.7105
0.6766
0.7645
0.6766
0.8377
039259
0.7372
0.708
08383
102200
0.9224
76
MixedRegula:
0.7463 0.9586
0,0500000
095500
0,22%6
B77318
0.9601
08880
0.9887
029005
038600
0
0
09874
0
77 MixedSmall.
0.7339 0.9541
0.9530
8.9235
0,8215
0.8110
02030
0.6234
0.9543
005551100
0
0.8577000
0.9885
0.9885000
05636
0,8600
0,929
0.9229
0
09537
78 MoxeStrain
Nonlavaivet.
0.8542 0,9384
0,9819
0.9670
0,8199
0.9505
0030050000
0.9435
0.9253
019119
0.972
0.9717
09349
09623
035544
09757
0
0.9694
03630
099694
05341
0.9966
0.9610
0.9698
09772
019866
09972
0.5550
0.8995
0.35000
0.9473
0:5575
0.9474
0.9022
0:9843
0.9623
095580
1
Nontawasive..
0.8022 09461
0,9012
00901220000000000
0.800
0,2286
02520
09573
09451
0.9007
0.449
00346900000
0.967]
0.8944
0
0.679
19440
099783
OlveOil 81
0.9887 0,304
0,5335
0.4000
0.5334
118500
08500
1.6967
0.9000
00000000000000 0,0000
0.9167 0,5333
0.4167
0.600
07333
0
04167
0
82
OSULLaa
PhalangesOattines.
0,3019 0.3664
0,7000 03833
0,7466
08370
00837000000
0.730
0.7300
0.6493
0,8423
05111
039537
03449
03127
09316
03619
08799
03619
0.8558
030085
0.5163
0.9774
0.6638
0.9751 000254
1.86880000
(5097
0.725
0.7000
0.225
0.737%
0.737%
02267
0,7995
07550
0
0.5004
84 Phaneme
0.7800 0.2200
03557
0,120
0,204
18610
07781
0.5569
0,600
1.0000.000
0.5044
0:5044 077116
D 0:3052
0.5400
09260
16911
0
0-7844
85 Pioluupeesture
0.1091 0.1700
0.8000
0.0000100000
0,6200
1.8400
072000
0.6000
0.7000
022000000000000
0.8000
0.0000000000
(0020000x300
00:300
0,5400
0,6500
000000000000
038200
0
037300
0.9009
86 PigAawayPressure
0.4822
0,5164 0.6436
0.6731
0,945
0.2182
0,0929
0,0575
0.1312
030353
100353110
015354
120008
02446
03500
0
03500
0
0.428
0
04429
0.5149
0,5744
0.9648
0,8878
1,000
0:5000
0.4415
0
0.9658
0.5595
0.4980
12074
155448
0
PigUVP
0.4348
0,121
0.7085
00521
08753
18180
05529
0.222
0.9166
0
0-
0
077942
0
89 PLAID
0.8691 0,8424
0.3912-
04832
0.7421
0.5503
0050000000
055551
0
0
0.8305
0.9115
07478
0.3818
0
0
0487
0.4055
0.6192
90 Plate
L10000 1.0000
0.9722
0.9714
0.5381
119508
098000
029922
09810
1,0000
L.0000
1.0000
1,0000
(13857
059552
0.9619
1,0000
PowerCons
0.9139 0.9194
0,8889
0.5444
0.97722
0.9861
09722
09333
0.9833
0.7122
0.9667
(19894
0.7722
0
0.9944
0,9944
015833
0.9944
92 ProdimalAgeeCrmpp
0.8727
0.846
0.8446
0.831
0
1.84966000
18845
08860
08727
08793
0.834
08364
0.0058
0. 0:8000
0
0.9190
000000000000
0:441
0.8678
8:900
93 Prodimal Coreet.
0.9214
0,8899
0,838
0.5303
0,8739
(18833
01833380000
0.9406
19170
0.8945
018687
0.9168
0.9122
0.7990
0
09238
0.7531
0.70037
8.9234
94 ProtimolPhalaantWw
0.8083
03215
0.000
0.7633
0.834
0.8281
0
0.8645
0.8116
0.8033
0.8777
11.0033
0..79
0.9774
0.824
0.8198
0.9273
RefiegenntinnDeviisss
0:5747
0.3775
0.7193
0.5170
0,5146
0.5693
0.7267
0.7500
0.7773
0.7677
0.5547
0.8333
0,4600
0
96 Rock
0.6429
0.7145
0.6857
0.7857
0,7714
08266
09143
B6040
00004000000
0.9143
0,9143
0.9144
0.7429
0.9144
0.9000
0.8286
0.7288
0,9143
0.8236
97
ScreetTyype
ScreenTyre
0.6001
0.5480
0.6852
0.4003
0
06347
0.5001
0.6700
0,7613
0.4250
0.5573
0.8267
0.3907
0.3907
0.6480
0.680
0. 0.7027
95
0.9578
O,7456
0.875
0.9516
011111100
0,9944
0.937
0.9378
0.0389
0.9200
0.9511
0.044
0.7044
0.8144
0.9744
0.9444
155444
0.9211
0.9778
0.71%
0.4056
0,5769
0,690
0,466
0.7767
0.7800
0.6311
0.7989
0.5933
0,2011
0.6744
0.3111
0.6611
0.8578
0.8422
0.7933
0.8256
100 StmpHiddsahjsschh
0.6922
0.636
0.8286
0.9310
0.8467
0.9544
0.941
0.8278
0.9089
0 0.844
0.9267
0:9433
0.71.6
0.9044
0.9556
0.9400
0.9389
0.9633
18

---

Learning Soft Sparse Shapes for Efficient Time-Series Classification
ID
Duiase
FCN
T-Loss
Sellime
TS-TCC
TST
VS2
TimesNet
PatcTTT
GPT-TS
RDST
MR-II
Insep
ShapeCome
MoTCN
TSLANet
UniTS
Medioeeer
SuliShape
101
ShikeWimoce..
0,9200
0.9100
0,8900
0,8500
0.6800
0,9300
0.5900
0.6900
0.7200
0.9330
0,5300
0.9600
0.8700
0.7400
0.9500
0.5400
0.8300
0.9800
ShapeletSim
0,9700
0.9200
0.560
0,9450
0.5500
0.9150
0.6300
1,0000
1,0000
1.0000
0.8500
0.6450
1,0000
0.9800
0.5850
0:9950
ShapesAll
0.7267 039955
0.8835
0.777
0.7292
0,9133
03325
08833
03500
0.9417
0,533
0.553
0.8225
0.895
0.9883
09192
0.8617
0.9575
104 SmallApplinnee
0.7957
0.7227
0.8256
0.7005
0.5747
0.7347
0.7840
0.6367
0,7215
0.8131
0.833
0.0088
0.5413
0.6573
0.9040
0.7840
0.8173
0,9053
105
SmoothSuhqquee
0.9467 0.2235
0.9367
0.3433
0,9800
0,9633
09767
0.9633
0.9133
0.990
0.9833
0.5800
0.9433
0,8567
0.9567
0.5400
0.9733
0.9867
0.9954
0,9823
0,9552
09952
0.983
0.984
1,0000
0.9984
0.9646
0.9904
107 Sony AlSurfooe2.
0,9000 0,8878
0.9376
0.8899
0,9847
0,949
09939
09999
0.9949
0,980
0.9900
1,0000
0.8990
0.9847
0.969
0.9867
0.9837
0,0080
108 Stel Cuhhaie
0.9903 0,7785
0.9795
0.9738
0.5734
119901
09611
0
0.9818
0.9627
0.9838
0.9903
0.9686
0.9892
0.9110
0.9675
0,9094
0.9005
109
Strawberry
0,9756 0.9614
0,9426
0.9414
0,9735
0,9685
0.766
0.9624
0.9766
0.9786
0.9797
0.9797
0,5790
0.9542
0.9817
0.9532
0.9054
0,986
110 Swndichl anf
0,9999
0.9253
0,9500
0.9671
0.0640
0.9250
0.9760
0.9680
Symbhol
0.961 0.9244
0.9798
0.733
0.9765
0,963
09618
09922
0.9667
0,951
0.995
0.9961
0.9685
0.9765
09833
09977
0.7455
0.941
112 SynfbetisCumine
0,9700 0.883
0,9683
0.9030
0.9767
0,0063
099767
0,9700
0.9717
0.9011
0.9033
1,0000
0.9783
0,9400
0.9967
0.9935
0.9000
0.9967
113 TesSepmenntrionl
0 0.9664 0.951
0,9143
0.9181
0.6001
0,9388
08814
0.9219
0.8846
0.9776
0.977
0,9812
0.9291
0.6761
0.9778
0.7500
0.8771
0.9852
TeeSegnentarion2
0.9252
0.8455
0,9517
08315
0
0.143
0,638
05517
09700
0:9706
0.856
0,9522
0.9045
0.8554
0
115 Trace
L0000 1.0000
0,9930
0.9130
0
1,0000
09400
1,0000
0.800
1,0000
1,0000
1,000
1,0000
0,9800
1.0000
0.8000
1,0000
1.0000
116 20dFF
L0000 0,9983
0,0932
0.9065
0.9914
0.0991
0.983
0.9991
0.9948
0.9991
1,0000
1.0000
0.8615
0.90K3
0.9991
0.9991
0.9974
1,0000
117 TwoPuilers
0.9451 1.0000
0.9513
0,990
0.9991
1,0000
0,9980
0,990
0.9962
1,0000
1,0000
1,000
0.9944
1,0000
0.9996
0.9994
0.9986
1,0000
0.8778
0,9944
0,983
1,0000
0.978
1,0000
1,0000
0.9056
0.9944
1,0000
119 I.WaeeCesrrerAll.
0.9245 0,9118
0.8995
0.9750
0,3607
0,8652
09504
0,9913
0.700
0,9822
0.9877
0,8112
0.9253
0.9588
0.9913
0.7795
0,9757
8,9900
120 UWWaeeGettree..
0.8665 0.5457
0.6680
0.8385
0.8091
0.8513
0.8924
0,9214
0.9002
0.8503
0.9015
0.9196
0.7977
0.9216
0.9413
0.945K
0.9119
0.9406
121 L'VaneGesareYY
0,7906
0,7887
0,5342
0.7573
0,7500
0,7874
0.8455
0.8955
0.8399
0.8109
0.848]
0.5850
0.69%
0.8828
0.9194
0.9100
0.8777
0:9109
0.8454
0,8021
0,4790
0.8074
0.9006
0.8314
0.5812
0.7603
0.8781
0.9219
123 Wafer
10000 0.9989
0,9587
0.9882
0,9992
0,9950
0.9985
0.9992
0.9992
1,0000
1,0000
0.9999
0.9785
0.9991
0.9999
0.9994
0.9971
1,0000
124 Wine
0.5411
0.9353
0.6743
0.5221
0.5854
0.9648
0.8289
0.5135
0.856]
0.9551
0.9644
0.7993
0,5490
0,5043
0.7494
0.4953
0.5130
0.8842
125 WixdSynonyms
0.5967
0,8022
0,5718
0,7444
0,7053
0,7989
0.8442
0.8600
0.7823
0.8575
0,8740
0.93155
0.8254
0,8441
0.8928
0,8762
0.8446
0:9175
Worms
0,7906
0.6821
0,4148
0.7210
0.7446
0,8072
0.7097
0.7357
0.8181
0.5236
127 WormsTwooCass
0.8025
0.7634
0.7557
0,6808
0.6340
0.7716
0,7833
0,9037
0.8221
0.7715
0.7753
0,7983
0.6710
0,6906
0.8692
0.8414
0.8376
128 Yoga
0
0.966]
0,7699
0.9207
0,9497
0,9709
0,9539
0,9739
0.9476
0,9642
0,9905
0,9933
0,7661
0.9815
0.9694
0.8970
0,9718
0,9K30
Aug. Ace
0.8256
0.3225
0,80117
0.7755
018091
0.8367
0.N236
0.8591
0,5997
0,8972
09181
0.7688
0.7928
0.9205
0,85012
0.8541
0.9334
Avg. Rank
9,53
11.12
13,80
13996
13.54
8.43
10:13
9,56
9.34
6.41
5.51
4.05
13.91
11,37
3.68
9.66
9.26
Win
13
9
0
9
7
12
23
29
29
9
31
3
7
53
Table 10: The detailed test classification accuracy of LighTTS, Shapeformer, and SoftShape on 18 UCR datasets.
Dataset
LighTTS Shapeformer SoftShape (Ours)
ArrowHead
0.9480
0.8439
0.9435
CBF
1.0000
0.9978
1.0000
CricketX
0.9282
0.6564
0.9321
DistaPPallaxxOOttinAAggGooo
0.8664
0.7921
0.9518
DisalPPllancCuutineCorret
0.8460
0.8151
0.9054
ECG5000
0.9630
0.9166
0.9796
EOGVerticalSignal
0.7737
0.5635
0.9007
EthanolLevel
0.9044
0.7261
0.9204
Fish
0,9800
0.9114
0.9771
GunPoint
0.9850
0.9900
0.9900
InseetWingbeutSound
0,8300
0.6586
0.8882
IaaypoowerDemandd
0.9708
0.9690
0.9891
MelboureePcdestrran
0.9879
0.7134
0.9573
MiddlePhalanx TW
0.7673
0.6293
0.8376
MixedShapesRegularTTe
0.9795
0.8055
0.9757
OSULeaf
0.9523
0.7649
0.9504
Trace
1.0000
1.0000
1.0000
WordSynonyms
0.8892
0.6773
0.9161
Avg. Ace
0.9207
0.8017
0.9453
Avg. Rank
1.67
2.78
1.28
Win
7
2
13
P-value
8.91E-03
9.80F-06
B.2. Ablation Study
Table 11 presents the detailed test classification accuracy results for various ablation components of SoftShape across 128 UCR time series datasets.
19

---

Learning Soft Sparse Shapes for Efficient Time-Series Classification
18 17 16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
ShapeConv 14_0547
3.0039
SoftShape
TS-TCC 13,9219
4.6250
TSLANet
Selftime 13,7891
4.9102
InceptionTime MR-H
TST TST13_5977 13,5977
5.8867
ModernTCN 11,5664
6.8633
RDST
T-Loss 11_3242
8.7266
TS2Vec
TimesNet 10.3906
9.4336
GPT4TS
PatchTST 9.8242
9.5586
Medformer
UniTS 9,7695
9.7539
FCN
Figure 6: The critical diagram (CD) (Demšar, 2006) illustrates statistical testing comparisons between SoftShape and baseline methods the 128 UCR time series datasets. A smaller CD value indicates better method performance. The absence of connecting line between the two methods signifies statistically significant performance difference.
Support for the predicted class
Refute the predicted class
Class
Top y pmportion
0.60
Class
5.0
0.50
0.0
50
100
150
50
100
150
(a) Soft Shape Regions
(b) Learning Score of Shapes
Class Class
20
Top proportion
0.60
0.50
0.0
200
400
600
0
200
400
600
(c) Time Series Regions
(d) Leamiing Score of Time Points
Figure 7: The MIL visualization on the Lightning2 dataset.
(a) Input Shape Embeddings
(b) Intra-Shape Embeddings
(c) Inter-Shape Embeddings
(d) Output Shape Embeddings
Figure The t-SNE visualization on the TwoPatlerns dataset.
20

---

Learning Soft Sparse Shapes for Efficient Time-Series Classification
(a) Input Shape Embeddings
(b) Intra- Shrre Embeddings
(c) Inter- Shape Embeddings
(d) Output Shape Embeddings
Figure 9: The t-SNE visualization on the Fiftywords dataset.
(a) Input Shape Embeddings
(b) Intra- Shape Embeddings
(c) Inter Shape Embeddings
(d) Output Shape Embeddings
Figure 10: The t-SNE visualization the ECG200 dataset.
B.3. Shape Sparsification and Learning Analysis
Due to the considerable time requirements for conducting experimental evaluations on all 128 UCR time series datasets for some baselines and hyperparameter analysis, 18 datasets were chosen from the 128 UCR datasets based on four key criteria: the number of samples, the length of the sample sequences, the number of classes, and the relevance to various application scenarios. Specifically, these 18 datasets vary in sample size from 200 to 5000, in sequence length from 24 to 1751, and in classes from to 25, Besides, the selected datasets cover diverse application areas, including handwritten font sequence recognition (e.g., the WordSynonyms dataset), human activity recognition (e.g., the CricketX dataset), and medical diagnosis
21

---

Learning Soft Sparse Shapes for Efficient Time-Series Classification
Table II: The detailed test classification accuracy of the ablation study on 128 UCR datasets. Among these, w/o II refers to the w/o Intra & Inter method. The best results are in bold.
ID Dataset
SontStupe
w/o Soft
win Intra
wlo Inter
w/o II
with Linear
ID)
Dataset
SottShupe
w/o Soft
w/o Intra
w/o Inter
wlo II
with Lincar
ACSFI
0.9100
018770
0.8150
0,8000
0.8700
0.8850
67
Lighnning2
0.8857
0.9110
015819
0.9033
0.8450
0.9022
Adiac
0.9374
0.8810
0.9297
0.8274
0.8094
0.9259
68
Lighting?
0.8966
0.9308
0.9517
0.8997
0.9101
0.8894
WX.
0.8980
0,8680
0.8970
0.5040
0.5850
0,8620
69
0.9988
1.0000
1,0000
0.9996
0,9992
0.9996
AllGestureWY
0.9110
0.9030
0.9080
0,8360
0.6260
0.8930
70
Meal
0.9917
1,0000
0.9917
0.9917
0.9917
1,0000
A.lGesttreW2.
0
03330
0.8786
0,800
0.5960
0.750
71
Medicallmages
0.9213
0.9221
0.9204
0.9134
0.7785
0.9256
AmowHead
0.9435
019672
0.9765
0.9627
0.9248
0.9577
72
Pelloomeeaadesmiann
0.9573
0.9542
0.9570
0.9652
0.8466
0,9521
Beef 7
0.8667
0.8333
0,8500
0.7500
0.8000
0.8167
73
AiddleAgoGroup
0.8701
0.8430
0.9134
0.8179
0.7743
0.8304
BeeeleFly
0,9750
1,0000
0.9800
0.8750
0.8500
0,9250
MisiileCennct
0.9201
0,9260
0.9150
0.8598
0.8239
0,9070
BindChicken
0,9000
0.9250
0,8750
0,9250
0.9250
0
75
MistilePtalannTWW
0.8376
0.8179
0.8629
0.72U3
0.6746
0.8305
RME
0,9944
1,0000
0.9944
0.9044
1,0000
0.9944
76
MixedRagular.
0.9757
0.9750
0.9715
0.9627
0.9350
0.9682
Car 11
0,9533
0.9167
0.9483
0,9250
0,9333
0
77
MixedSmall.
0,9743
0.9695
0.9799
0.9671
0.9446
0.9695
CBF
1,0000
1,0000
0.9989
1,0000
0.9978
0.9989
78
MoseStrain
0.9843
0.9843
0,9714
0.9835
0.9764
0.9851
13
Chinatown
0,9890
0.9890
0.9808
0.989
0,9808
0
79
No
0,9724
0.9676
0.9787
0.9625
0.9554
0.9625
ChloninnCon.
0.9988
0.9988
0.9991
0:9991
0.9025
0.9998
80 Nonlivasive..
0,9782
0.9665
0.9694
0.9636
0.975
0.9604
15
CioCEOGTonO
1,0000
1.0000
0.9993
0,9993
1.0000
0.9993
81 OliveOil
0.8333
0.8167
0.8333
0.8167
0.7333
0.8667
Coffee 16
1,0000
1,0000
1,0000
00000000000000
1,0000
1,0000
1.0000
82
OSUI Len
0,4504
0.9257
0.9922
0.8626
08810
0
Computers
0.8160
0.8120
0,8040
0.8540
0.8640
0,8240
PhalangesCkutines.
0.9300
0.9312
0.9135
0.9022
0.7957
0.9105
18 CricketX
0.9321
0.9064
0.9223
0.903S
0.8538
0.9346
84 Phoneme
0.7844
0.6545
0.6455
0.6234
0,6051
0.6567
CticketY
0.9154
0,8808
0.9069
0.7974
0.9256
PickupGesture.
0.9000
0.8600
0.5900
0.9000
0,8100
0. 0,8200
20
CricketZ
0,9372
0.9013
0.9133
0.8933
0.8179
0.9467
86 Pressie
0.6432
0.2446
D. 0.5664
0.5625
0.5662
0.4963
Crop
0.8765
0.7342
0.7435
0.7236
0.5973
0,8856
PigAriPrescure
0.9937
0.8622
0.9994
0.8120
0.6972
0.9748
22
DintomSizeRe.
1,0000
1.0000
0.9938
0.9938
1.0000
0
88 PigCVP
0,9458
0.7926
0.9172
0.6783
0,6530
0.8344
23
DistalPhalanssen.
0,9518
0.9162
0.9107
0.8975
0.8961
0,9162
89 PLAID
0.6192
0.5922
0.6025
0.5157
0,4879
0.5383
24
DistulPiallnsSat.
0,9054
0.9477
0.8348
0,8937
0.8631
0.8871
90
Plane
1.0000
0.9952
0.9912
1.0000
0.9952
0.9952
25
DisuiPhalaaxTW
0.9057
0.9092
0.9203
0
0.8628
0.9242
91
PowerCons
0.9944
0.9917
0.9902
0.9972
0,9806
0.9750
26
Doply
0.8623
0.8625
0,8500
0.8698
0.8183
0.8433
92
0.9091
0.9107
0,9022
0.8810
0.8744
0,9074
27
Dadgert Game
0,9433
0.9388
0.9260
0
0.8556
0.9268
93
Proximal Comeet.
0.9294
0.9541
0.9473
0.8488
0.831
0.9294
Dodgerl.oopWeek
1.0000
1.0000
0.9917
0.9927
0.9310
0.9935
ProximulPhalaxxTWW
0.9273
0.8876
0.9207
0.8529
0.8612
0.8942
29 Earthquikes
0.8917
0.9135
0.8940
0,9331
0.9135
0.9070
95
RefrigeratioDDvvices
0.8027
0.7347
0.7910
0.7653
0.7480
0,7720
ECG200
0,9475
0.9400
0,9400
0,9600
0,9450
0.9050
Rock
0.8286
0.8571
0.8857
0,8714
0
038571
O 8286
31
BCG5000
B,9796
0.9810
0.9818
0,9720
0.9566
0.9796
97
ScreenType
0.7027
0,7693
0.7776
0.8253
07755
0.693
BCGFivelayss
1.0000
1,0000
1,0000
1.0000
1,0000
1.0000
98
SemgHannGeneechh2
0.9778
0.9211
0.9478
0,9811
0.9211
0.9456
33
ElectriDDevices
0.9208
0.8675
0.8756
0.8651
0.7428
0.3654
99
SemgMMvemeniCh2.
0.8256
0.7867
0.8489
0.6300
0.8022
0.8156
34
EOGHoriontalS.
0,9007
0.8386
0.8731
0.8109
0,7612
0,8275
100
0.9633
0,9667
0,9133
0.9611
0,919
0.9541
35
BOGVertieaS.
0.8814
018413
0.8565
0.7212
0.7861
0.7723
101
Shake WlimeelZ.
0.9800
0.9600
0.9700
0,9700
0.9100
0.9800
36
Ethanoll evel
0.9204
0.9243
0,8898
0.6993
0.7730
0.8456
102
ShapeletSim
0.9950
1,0000
1.0000
0:9350
0.8900
1.0000
FaceAll
0.9978
0.9982
0.9908
0.9911
0.9538
0.9973
103
ShapesAll
0.9575
0.9158
0.9508
0.9317
0.8700
0.9442
38 FaceFour
0,9909
1,0000
1.0000
0.9913
0.9913
0.9913
101
Small Applianess
0.9053
0.8973
0.9067
0.8813
0.7747
0.8773
FaceSUCR
0.9956
0,9969
0.9880
0,9507
0.9964
105
SulseuSu
0,9867
0.9633
0.9800
0.9867
0.9300
0,9000
40
FiftyWards
0,9359
0.8972
0,9414
0.9395
0
0,9359
106
SonyAlS AlSurfacel.
0.9936
0.9920
0.9936
0.9968
0.9852
0.9936
Fish
0.9771
0,9800
0,9800
0.9314
0,9371
0.9571
Sony AlSurfaee2.
0,9980
0,9839
0,990
0.9939
0.9847
0.9969
FordA 42
0,9772
0.9722
0.9811
0.9259
0,8417
0.9793
108
Strd ghiCCreees
0,9905
0.9675
0.9679
0.9563
0,9905
0.9656
43
FordB
0,9744
0.9683
0.9721
0.9240
0,8655
0.9696
109
Strawberry
0,9868
0.9718
0.9756
0.9746
0.9705
0.9827
44
FrpezerRegular.
0,9990
0.9990
0,9997
0,9973
0,9877
0,9990
110
SwedishLeaf
0,9867
0,9813
0.9904
0.9778
0,9484
0,9858
45
FrovoorSmall.
0,9990
0.9993
0.9997
0.9972
0,9920
0
111
Symbols
0,9941
0.9912
0.9922
0.9863
019863000
0,9022
0.9931
Pungi
1,0000
1.0000
1,0000
1,0000
0.9951
1.0000
112
SyntheticConrel
0.9967
0:9917
0,9915
0.9983
098667
0.917
47
GestuneMidAirDi
0,8640
0.7550
0.8553
0,8287
0.8169
0.82011
113
TreSegmenntttoon
0.9852
0.9739
0.9855
0.9000
099077
0:9741
GesuneMGAAiD22
0.7962
0.6693
0.7847
0.7520
0.6871
0.7584
114
ToeSegmnenraiin2
0.9882
0.9824
0.9884
0.9865
0.9283
0.9820
49
GostreMalAinDS
0,7613
0.5629
0.7226
0.6935
0.6135
0.6815
115
Trace
1,0000
0,9950
0.9950
0.9950
0,9600
1.0000
GesturPPbbee211
0.9667
0.9934
0.9967
0:9672
0
0.997
116
TwoLesdEC
1,0000
0.9991
0.9981
0.9991
0.9957
0.991
51
Gestureeehbee222
0.9836
0.9720
0.9836
0.9738
0.9205
0
117
TwoPattems
1,0000
1.0000
1.0000
0.9964
0.9864
1.0000
52
GunPoint
0,9900
0.9950
1.0000
0.9900
0,9950
0,9850
118
UMD
0.9941
1.0000
0.9833
0.9889
0.9889000
0.9444
0.9889
53
GumPointAgeSpun
0,9868
0.9867
0.9667
0,9823
0
0.9779
119
UWaeGGetturAll.
0,9900
0.9891
0.9931
0.9861
0.979
0,9933
54
GanPointMale.
0,9955
0.9934
0.9978
0.9956
0.9978
0,9956
120
UWaveGestureX.
0.9406
0.9270
0.9434
0.9087
0.8336
0:9241
55
GunPointOld.
0,9779
0.9778
0.9815
0,9712
0
0.9889
121
UWareGestrrY..
0,9109
0.9011
0.9013
0.8881
0.7224
0,9087
56
Hum
0.9161
0.9116
0,9395
0.9349
0.9301
0,8882
122
UWaneGesturez
0,9170
0.8706
0,8704
0.8591
0,7722
0 0.881
HandDurlines
0,9533
0.9365
0.9000
0.9343
0.9197
0.9248
123
Water
1,0000
0.9999
0.999%
0.9996
0.9990
1,0000
Hapeics 58
0,7522
0.6770
0.7652
0.7349
0.7327
0.6744
124
Wine
0,8842
0.7763
0.7225
0.6036
0.5047
0.8115
Hetting
0.7671
0.7351
0.7985
0.7828
0.8375
0.7991
125
WordSynoyyms
0.9175
0.8961
0.9093
0.8873
0.8331
0.9094
60
HouseTwenty
0.9688
0.9750
0.9550
0. 0.9695
0.9375
0.9688
126
Worms
0.8-153
0.8304
0.8305
0.8458
0.8533
0.7834
InlineSkate
0,8077
0.69918
0.7169
0.7346
0.7062
0.7431
127
WormsTwoClass
0.8802
0.8786
0186688
0.8307
03836
0.8726
62
InsecIEPGR.
0.9968
1.0000
0.9968
0.9329
0.9744
0.9936
128
Yoga
0.9830
0.9788
0.9773
0.9703
0.9230
0.9609
63
InsecIEPGS.
0
0.9925
0.9925
0.9548
0.9329
0,9550
Avg. Acc
03333
0.9123
0.9245
0.9022
0.3099
09964
61
InscetWing.
0.8882
0.8682
0.8786
0.8736
0.7455
0.8986
Avg. Rank
2.04
3.01
2.75
3.74
5.02
3.23
65
Itly PewerDandddd
0.9891
0.9900
0.9836
0,9900
0.9726
0.9888
Win
60
29
31
19
11
22
LatgeKitchesA.
0.9627
0.9560
0.9640
0.9400
0.9107
0.9520
(e.g., the ECG5000 dataset).
Table 12 presents the detailed test classification accuracy results across 18 UCR time series datasets for different values of the parameter 77 during SoftShape sparsification. Table 13 provides the test classification accuracy results of SoftShape on 18 UCR time series datasets when varying the number of class-specific experts k activated by the MoE router during intra-shape learning. Also, as baseline settings in Figure 3(c) and 3(d) of the main text, we report the parameter counts and inference times (in seconds) for SoftShape, MedFormer, TSLANet, InceptionTime, and MR-H on the ChlorineConcentrua (4.307
22

---

Learning Soft Sparse Shapes for Efficient Time-Series Classification
samples, length 166) and HouseTwenty (159 samples, length 2,000) datasets. It important to note that MR-H is executed CPU because its modules do not deep learning techniques, whereas other deep learning methods an NVIDIA GeForce RTX 3090 GPU. As shown in Table 14, the differences in inference time between the deep learning methods are negligible. However, we observed that SoftShape demonstrates slight advantage in inference time on the House Twenty dataset, which has a longer sequence length.
Table 12: The detailed test classification accuracy of sparse ratios 18 UCR datasets. The best results are in bold.
Dataset
1 0
17
0.1
77
0.3
1 = 0.5
1]
0.7
0.9
ArrowHead
0.9576
0.9576
0.9576
0.9435
0.9717
0.9435
CBF
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
CricketX
0.9365
0.9375
0.9331
0.9321
0.9211
0.9006
AissalPhalaxxuuttinnAgeeee
0.9529
0.9510
0.9288
0.9518
0.9530
0.8861
0.8951
0.8871
0.9055
0.9054
0.8780
0.8734
ECG5000
0.9772
0.9802
0.9810
0.9796
0.9810
0.9696
BOGVerticalSignal
0.9145
0.9321
0.9310
0.9007
0.8730
0.8690
Ethe
0.9214
0,9205
0.9205
0.9204
0.8985
0.8856
Fish
0.9742
0.9799
0.9656
0.9771
0.9628
0.9713
GunPoint
0.9850
0.9750
0.9850
0.9900
0.9850
0.9850
InsectWingbeutSound
0.8828
0.8760
0.8819
0.8882
0.8700
0.8860
IalyPowerDDemand
0.9891
0.9917
0.9846
0.9891
0.9837
0.9901
MelbournePcdestrian
0,9511
0.9603
0.9545
0.9573
0.9391
0.9319
MiddlePhalanxTW
0.8340
0,8322
0.8268
0.8376
0.7474
0.7781
MixedShapesRRggllarTTii
0,9784
0,9781
0.9801
0.9757
0.9644
0.9620
OSULeaf
0.9414
0,9491
0.9413
0.9504
0.9436
0.9256
Trace
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
WordSynonyms
0.9382
0.9360
0.9294
0.9161
0.9095
0.9128
Avg. Acc
0.9461
0.9469
0.9448
0.9453
0.9323
0.9261
Avg. Rank
2.44
2.39
2.78
2.61
3.89
4.50
Win
4
7
5
5
2
B.4. Hyperparameter Analysis
Table 15 provides the test classification accuracy results of SoftShape on UCR time series datasets when varying the sliding fixed step size (q). Table 16 presents the detailed test classification accuracy results of SoftShape across 18 UCR time series datasets for different model depth (T.) values. Table 17 presents the detailed test classification accuracies of SoftShape across 18 UCR datasets, evaluated with varying setting shape lengths m.
Tables 18, 19, 20, and 21 present the statistical test classification results of SoftShape on 18 selected UCR time series datasets. The evaluations are conducted under varying conditions, including different maximum numbers of experts for intra-shape learning, class-specific MoE expert networks, shared expert networks, and hyperparameter A. For clarity and ease of analysis, only the statistical results of accuracies are reported in Tables 18, 19, 20, and 21.
B.5. Time Series Forecasting Results
For the forecasting task, we evaluate SoftShape on the ETThI, ETTh2, ETTml, and ETTm2 datasets, using TS2Vec (Yue al., 2022), TimesNet (Wu et al., 2023a), PatchTST (Nie et al., 2023), GPT4TS (Zhou al., 2023), and iTransformer (Liu al., 2024b) baselines. Following the experimental setup of (Ma et al., 2024), report the Mean Squared Error (MSE) and Mean Absolute Error (MAE) for all methods in Tables 22 and 23. Notably, do not adjust hyperparameters for SoftShape across the four datasets, nor do modify its shape embedding layer done in (Nie et al., 2023). The results demonstrate that SoftShape outperforms TS2Vec and TimesNet, highlighting its potential for time series forecasting tasks.
23

---

Learning Soft Sparse Shapes for Efficient Time-Series Classification
Table 13: The detailed test accuracy of the number of activated experts on 18 UCR datasets. The best results are bold.
Dataset
k=1
k=
k=3
k=4
ArrowHead
0.9435
0.9324
0.9196
0.9147
CBF
1.0000
1.0000
1.0000
1.0000
CricketX
0.9321
0.9487
0.9334
0.9475
DisalPPallaxOOutiinAAggguuuuu
0.9518
0.9665
0,9221
0.9518
DistlPPhllaxxOOtiineCorett
0.9054
0.8517
0.8574
0.8517
ECG5000
0.9796
0.9840
0.9792
0.9640
EOGVerticalSignal
0.9007
0.9381
0.9490
0.9353
EthanolLevel
0.9204
0.9264
0.9054
0.9164
Fish
0.9771
0.9513
0.9571
0.9656
GunPoint
0.9900
0.9850
0.9850
0.9850
InsectWingbeatSound
0.8882
0.8782
0.8732
0.8659
ItalyPowerDemand
0.9891
0.9809
0.9809
0.9873
MellsuurnePedestrrinn
0.9573
0.9581
0.9568
0.9601
MiddlePhalanxTW
0.8376
0.8429
0.8231
0.8719
MixedShapesReggllrTTaiii
0.9757
0.9675
0.8629
0.9535
OSULeaf
0.9504
0.9302
0.9390
0.8963
Trace
1.0000
1.0000
1.0000
1.0000
WordSynonyms
0.9161
0.9580
0.9536
0.9625
Avg. Ace
0.9453
0.9444
0.9332
0.9405
Avg. Rank
1.89
1.94
2.78
2.39
Win
10
5
Table 14: Comparison of model parameter counts and inference times.
# Inference Time (Seconds)
Methods
# Parameters
ChlorineCooccentration
HouseTwenty
MR-H
6.60
2.97
InceptionTime
387.7 K
1.41
1.30
TSLANet
514.6 K
1.37
1.29
Medformer
1360.6 K
1.48
1.31
SoftShape (Ours)
472.5 K
1.39
1.26
24

---

Learning Soft Sparse Shapes for Efficient Time-Series Classification
Table 15: The detailed test classification accuracy sliding step size on 18 UCR datasets. The best results are in bold.
Dataset
9=1
q=2
q=3
q=4
q=m
ArrowHead
0.8913
0.9289
0.9431
0.9435
0.9451
CBF
1.0000
1.0000
1.0000
1.0000
1.0000
CricketX
0.8936
0.9231
0.9103
0.9321
0.9295
DistuPPallanOOOttineAeGgGooo
0.9147
0.9629
0.9610
0.9518
0.9184
DistaPPhalaaxxOutinnCCrreee
0.8688
0.8837
0.8540
0.9054
0.8632
ECG5000
0,9672
0.9734
0.9822
0.9796
0.9824
EOG Sigaeaa
0.8551
0,9104
0.9408
0.9007
0.9533
EthanolLevel
0.8656
0.8736
0.9294
0.9204
0.8786
Fish
0.9485
0.9513
0.9713
0.9771
0.9399
GunPoint
0.9800
0.9850
0.9650
0.9900
0.9800
InsectWingheatSound
0.7922
0.8563
0.8582
0.8882
0.8741
ItayPowerDeemand
0.9818
0.9873
0.9918
0.9891
0.9891
MelbournePedestrian
0.9538
0.9480
0.9518
0.9573
0.9431
MiddlePhalanxTTW
0.7451
0.8267
0.8629
0.8376
0.7724
MixedShapesRegularf Train
0.9477
0.9272
0.8783
0.9757
0.9157
OSULeaf
0.9300
0.9774
0.9525
0.9504
0.9204
Trace
1.0000
1.0000
1.0000
1.0000
1.0000
WordSynonyms
0.8310
0.9017
0.9172
0.9161
0.8261
Avg. Acc
0.9092
0.9343
0.9372
0.9453
0.9240
Avg. Rank
3.83
2.78
2.44
1.78
2.94
Win
2
5
5
Table 16: The detailed test classification accuracy model depth on 18 UCR datasets. The best results are in bold.
Dataset
L=1
L=2
L=3
L=4
L=5
L=6
ArrowHead
0.9437
0.9435
0.9390
0.9155
0.9155
0.9251
CBF
1.0000
1.0000
0.9989
0.9978
0.9989
0.9989
CricketX
0.8962
0.9321
0.9706
0.9783
0.9501
0.9539
DistalPhalanxOOttinnAggGGe
0.9629
0.9518
0.9740
0.9389
0.9741
0,9574
DisatPhalannOuutneCCrreetet
0.9054
0.9054
0.8917
0.8962
0.8811
0.9077
ECG5000
0,9830
0.9796
0.9770
0.9750
0.9810
0,9790
0.8038
0.9007
0.9187
0.9422
0.9083
0.8979
EthanolLevel
0.8189
0.9204
0.8905
0.8975
0.9005
0.8945
Fish
0.9428
0.9771
0.9914
0.9914
0.9685
0.9942
GunPoint
0.9800
0.9900
0.9900
0.9900
0.9900
0.9900
InseetWingbeatSound
0.9237
0.8882
0.8905
0.8968
0.8764
0.8777
IalyPowerDeemand
0.9854
0.9891
0.9982
0.9864
0.9937
0.9882
MelboumeePedestrian
0.9589
0.9573
0.9488
0.9567
0.9531
0,9578
MiddlcPhalanxTTW
0.8070
0.8376
0.7799
0.8052
0.7979
0.8124
MixedShapesRegular Train
0.9282
0.9757
0.9778
0.9781
0.9689
0.9747
OSULeaf
0.9368
0.9504
0.9503
0.9414
0.9571
0.9233
Trace
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
WordSynonyms
0.8344
0.9161
0.9062
0.8974
0.8951
0.9228
Avg. Acc
0.9228
0.9453
0.9441
0.9436
0.9395
0.9420
Avg. Rank
3.72
2.61
3.06
3.33
3,44
3.06
Win
5
3
4
25

---

Learning Soft Sparse Shapes for Efficient Time-Series Classification
Table 17: The detailed test classification accuracy of shape length 18 UCR datasets. The best results are in bold.
Dataset
Val-Select
Fixed-8
Multi-Seq
ArrowHead
0.9435
0.9435
0.9436
CBF
1.0000
1.0000
1.0000
CricketX
0.9321
0.9282
0,9320
DistaPhalannOOutieeAeGGrroo
0.9518
0.9611
0,9351
DisalPPhllnn&OuttnnCCrrett
0.9054
0.9065
0.9156
ECG5000
0.9796
0.9610
0.9810
EOGVerticalSignal
0.9007
0.8759
0.8952
EthanolLevel
0.9204
0.8785
0.9303
Fish
0.9771
0.9686
0.9697
GunPoint
0.9900
0.9900
0.9900
InsectWingbeatSound
0.8882
0.9010
0.9055
Iemmand
0.9891
0.9855
0.9867
MelstuunePddestraaa
0.9573
0.9641
0.9647
MiddlePhalanxITW
0.8376
0.8352
0.8414
MixedShapesRegullrTTee
0.9757
0.9808
0.9849
OSULeaf
0.9504
0.9392
0,9444
Trace
1.0000
1.0000
1.0000
WordSynonyms
0.9161
0.9028
0.9139
Avg. Acc
0.9453
0.9401
0.9463
Avg. Rank
1.72
2.28
1.44
Win
9
4
11
Table 18: The statistical test classification accuracy of the total number of experts Ó on 18 UCR datasets. And C' denotes the total number of classes within each time series dataset. The best results are bold.
Metric
C=C/2
Č=C
Č=2C'
Avg. Ace 0.9215
0.9453
0.9408
Avg. Rank
2.33
1.39
1.83
Win
12
Table 19: The statistical test classification accuracy across different networks used as MoE experts on 18 UCR datasets. TSLANet (ICB) indicates that the ICB block within TSLANet used the MoE expert. The best results in bold.
Metric
FCN
TSLANet (ICB)
Original MoE expert
Avg. Acc
0.8652
0.9049
0.9453
Avg. Rank
2.56
1.83
1.44
Win
4
10
Table 20: The statistical test classification accuracy and parameter counts across different networks used as the shared expert on 18 UCR datasets. The best results are in bold.
Metric
Transformer
MLP
Inception
Parameters
422.5 K
157.8
179.5
Avg. Acc
0.8239
0.8103
0.9453
Avg. Rank
2.22
2.44
1.11
Win
4
16
26

---

Learning Soft Sparse Shapes for Efficient Time-Series Classification
Table 21: The statistical test classification accuracy across different on 18 UCR datasets. The best results are in bold.
Metric
= 0..001
== 0.001
0.011
À 0.1
==
A= 10
== 100
Avg. Acc
0.9417
0.9453
0.9471
0.9374
0.9394
0.9438
0.9431
Avg. Rank
3.00
2.50
2.61
4.11
3.72
3.72
3.56
Win
6
6
4
4
5
7
Table 22: The detailed test forecasting performance (Mean Squared Error, MSE) of different methods. The best results are
bold.
Methods
VS2Vec
TimesNet
PatchTST
GPT4TS
iTransformer SoftShape (Ours)
Metric
MSE
MSE
MSE
MSE
MSE
MSE
24
0,5952
0.3485
0.3890
0.3102
0.3065
0.5239
48
0.6316
0.3991
0.4362
0.3529
0.3451
0.5160
168
0.7669
0.4846
0.5304
0.4600
0.4307
0.4564
ETTh1
336
0.9419
0.5583
0.5928
0.5167
0.4889
0.4992
720
1.0948
0.5886
0.6123
0.6878
0.5184
0.5099
Avg. Value
0.8061
0.4758
0.5121
0.4655
0.4179
0.5011
Avg. Rank
6
3.4
4.4
1.2
3
24
0.4478
0.2129
0.2176
0.2009
0.1831
0.2542
48
0,6460
0.2824
0.2722
0.2738
0.2413
0.2808
168
1.7771
0.4461
0.4092
0.4436
0.3725
0.3824
ETTh2
336
2.1157
0,4875
0.4670
0,5011
0.4368
0.4429
720
2.5823
0.5193
0.4721
0.5389
0.4479
0.4722
Avg. Value
1,5138
0.3896
0.3676
0.3917
0.3363
0.3665
Avg. Rank
4.2
2.8
3.8
3.2
24
0.1970
0.2416
0.2522
0.2004
0.2251
0.2980
48
0.2682
0.3194
0.3202
0.3006
0.3019
0.3197
96
0.3735
0.3558
0.3553
0.3008
0.3393
0.3389
ETTml
288
0.7566
0.4411
0.,2077
0.3712
0.4147
0.3953
672
1.8217
0.6567
0.4878
0.4570
0,4880
0.4706
Avg. Value
0.6834
0.4029
0.3672
0.3260
0.3538
0,3645
Avg. Rank
4.6
4.4
1.4
3.2
3.4
96
0.3502
0.1877
0.1876
0.1861
0.1830
0.1873
192
0.5684
0.2748
0.2544
0.2624
0.2507
0.2545
336
0.9589
0.3922
0.3173
0.3164
0.3179
0.3190
ETTm2
720
2.5705
0.4477
0.4179
0.4246
0.4161
0.4248
Avg. Value
1.1120
0.3256
0.2943
0.2974
0.2919
0.2964
Avg. Rank
5,6
4.92
2.88
2.28
1.84
3.48
27

---

Learning Soft Sparse Shapes for Efficient Time-Series Classification
Table 23: The detailed test forecasting performance (Mean Absolute Error, MAE) of different methods. The best results are
bold.
Methods
VS2Vec
TimesNet
PatchTST
GPT4TS
iTransformer
SoftShape (Ours)
Metric
MAE
MAE
MAE
MAE
MAE
MAE
24
0.5313
0.3873
0.4128
0.3626
0.3589
0.4817
48
0.5566
0.4169
0.4379
0.3904
0.3818
0.4794
168
0.6405
0.4670
0,4879
0.4661
0.4304
0.4481
ETThl
336
0.7334
0.5175
0.5193
0.4960
0.4602
0,4719
720
0.8098
0.5287
0.5442
0.5858
0.4982
0.4951
Avg. Value
0.6543
0,4635
0.4804
0,4602
0.4259
0.4752
Avg. Rank
6
3.4
4.4
1.2
3
24
0.5032
0.2929
0.3043
0.2917
0.2719
0.3344
48
0.6184
0.3429
0.3388
0.3443
0.3120
0.3475
168
1.0569
0.4361
0.4172
0.4476
0.3940
0,4042
ETTh2
336
1.1759
0.4687
0,4610
0.4876
0.4433
0.4484
720
1.3521
0.4893
0.4734
0.5146
0,4585
0,4721
Avg. Value
0,9413
0.4060
0.3989
0,4172
0.3759
0.4013
Avg. Rank
3.6
3
4.2
3.2
24
0.3179
0.3115
0.3186
0.2769
0.2967
0.3564
48
0.3784
0.3637
0.3593
0.3344
0.3474
0.3644
96
0,4496
0.3864
0.3793
0.3519
0.3740
0,3751
ETTml
288
0.6672
0.4304
0,4162
0.3989
0,4163
0,4072
672
1.0452
0.5324
0.4527
0.4483
0.4577
0,4512
Avg. Value
0.5717
0.4049
0.3852
0.3621
0.3784
0.3908
Avg. Rank
5.6
3.6
2.8
3.6
96
0.4381
0.2678
0.2728
0.2781
0.2652
0.2744
192
0.5732
0.3220
0.3140
0.3271
0.3101
0.3167
336
0.7532
0.3830
0.3527
0.3650
0.3524
0.3572
ETTm2
720
1.2483
0.4244
0.4075
0.4331
0.4090
0.4186
Avg. Value
0.7532
0.3493
0.3367
0.3508
0.3342
0.3418
Avg. Rank
5.92
3.88
2.32
1.56
3.32
28


Reviews:
[{"review_id": "CrYRTek8gB", "reviewer": "Reviewer_cgnW", "summary": "This paper focus on time-series classification using shapelets. It introduce an  attention based sparsification mechanism that merges the less discriminative subsequences into a single shape based their learned attention scores. A Mixture of Experts (MoE) architecture is used to learn intra-shape patterns   and a shared expert to learn inter-shape patterns (temporal relationships between shapes). The method is evaluated  on 128 UCR time series datasets and achieves state-of-the-art results.", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "**W1: MultiRocket-Hydra (MR-H) should be added to this comparison as a computationally efficient baseline.**\n\n**A**: MR-H is a combination of the Hydra [1] and MultiRocket [2] algorithm.\n\n- Hydra uses randomly initialized convolutional kernels, grouped into $g$ groups per dilation with  $k$ kernels per group. These kernels transform input time series and count the closest matches at each time point. The counts for each group are concatenated and used to train a linear classifier.\n\n- MultiRocket applies random initialized convolutional kernels to the time series, performs standard scaling, and fits a classifier using the transformed data (default: RidgeClassifierCV). \n\nHydra and MultiRocket utilize randomly initialized convolutional kernels to extract time series features, in contrast to deep learning methods that rely on a backpropagation algorithm. As a result, MR-H exhibits a fast runtime.\n\nThe core modules of MR-H do not employ deep learning techniques and operate efficiently. Thus, the official implementation code of MR-H provided by the authors is based on a CPU version.  Hence, the reported training and inference times for MR-H are measured using a CPU, which is consistent with other deep learning-based baselines.\n\nBased on training time analysis from Figure 3 in the main text, MR-H took $411$ seconds on ChlorineConcentration and $64$ seconds on HouseTwenty, significantly faster than SoftShape (2743 and 280 seconds) and MedFormer (14377 and 1296 seconds). We will include a runtime analysis of MR-H in the revised version of Figure 3.\n\n[1] Hydra: Competing convolutional kernels for fast and accurate time series classification. DMKD, 2023.\n\n[2] MultiRocket: multiple pooling operators and transformations for fast and effective time series classification. DMKD, 2022.\n\n---\n\n**W2: While training times are compared, a comparison of inference times and number of parameters is missing from the paper.**\n\n**A**: The sample length of a single time series may slightly influence the model parameter count for certain methods. The table below shows the average parameter count for the comparison methods across 128 UCR time series datasets, with $K$ denoting one thousand.\n\n| Method        | # Parameters  |\n|---------------|---------------|\n| FCN           | 266.9 K       |\n| T-Loss        | -             |\n| SelfTime      | -             |\n| TS-TCC        | 495.3 K       |\n| TST           | 25725.3 K     |\n| TS2Vec        | 1274.5 K      |\n| TimesNet      | 7428.3 K      |\n| PatchTST      | 1225.4 K      |\n| GPT4TS        | 11421.1 K     |\n| RDST          | -             |\n| MR-H          | -             |\n| InceptionTime | 387.7 K       |\n| ModernTCN     | 315.6 K       |\n| TSLANet       | 514.6 K       |\n| Medformer     | 1360.6 K      |\n| SoftShape     | 472.5 K       |\n\nT-loss and SelfTime are excluded from the parameter count due to difficulties in obtaining the parameter information from their official implementation code. Furthermore, RDST and MR-H are not deep learning algorithms, and thus, their parameter counts are not reported.\n\nAdditionally, as baseline settings in Figure 3 of the main text, we report the inference times (in seconds) for SoftShape, MedFormer, TSLANet, InceptionTime, and MR-H on the ChlorineConcentration (4,307 samples, length 166) and HouseTwenty (159 samples, length 2,000) datasets.\n\n| Method         | ChlorineConcentration | HouseTwenty |\n|----------------|-----------------------|-------------|\n| MR-H           | 6.60                  | 2.97        |\n| InceptionTime  | 1.41                  | 1.30        |\n| TSLANet        | 1.37                  | 1.29        |\n| Medformer      | 1.48                  | 1.31        |\n| SoftShape      | 1.39                  | 1.26        |\n\nIt is important to note that MR-H is executed on a CPU, whereas other deep learning methods are run on an NVIDIA GeForce RTX 3090 GPU. Overall, the differences in inference time between the deep learning methods are negligible. However, we observed that SoftShape demonstrates a slight advantage in inference time on the HouseTwenty dataset, which has a longer sequence length.\n\n---\n\n**W3: The paragraph listing the baselines used for comparisons (L#300 - L#316) need to be structured in a more informative way by indicated to which category each method belongs.**\n\n**A**: Thank you for your suggestions. We have classified the 15 baseline methods into two primary groups: Deep Learning-based and Non-Deep Learning-based methods. Among the Deep Learning-based methods, we have further subdivided them into two categories based on their network architecture: CNN-based and Transformer-based. This categorization will be updated in the revised version. The specific categories are as follows:\n\n- Deep Learning-based methods:\n\n    a) CNN-based: FCN, T-Loss, SelfTime, TS-TCC, TS2Vec, TimesNet, InceptionTime, ModernTCN, TSLANet.\n\n    b) Transformer-based: TST, PatchTST, GPT4TS, Medformer.\n\n- Non-Deep Learning-based methods: RDST, MR-H.", "claims_and_evidence": "- Interpretability: The interpretability of the method is evaluted using  Multiple Instance Learning (MIL) on the Trace and Lightning2 datasets. This evaluation shows that the method assigns higher attention scores to subsequences with significant differences between classes.\n- Performance: The paper claims superior performance   against state-of-the-art approaches. This is demonstrated through extensive experiments on 128 UCR time series datasets. \n- Efficiency : A training time comparison is conducted wrt  three baselines (Medformer,TSLANet,InceptionTime). It shows that the proposed method is faster compared to these baselines. However I think that MultiRocket-Hydra (MR-H)  should be added to this comparison as a computationally efficient baseline.", "methods_and_evaluation_criteria": "- The proposed method is well motivated and the main design choices are correctly ablated.\n- The method is extensively evaluated  on 128 UCR time series datasets a well recognized benchmark for TSC  (Ismail Fawaz et al., 2019).", "theoretical_claims": "There are no theoretical claims in the paper.", "experimental_designs_or_analyses": "The paper didn't propose any new experimental design. The method is evaluated on a classical time-series classification benchmark.", "relation_to_broader_scientific_literature": "The  contribution of the paper is two-fold: \n- The computationally intensive shapelets sparsification is addressed with  soft selection instead of  the hard selection approach adopted by recent approaches (Li et al., 2021; Le et al., 2024) . Instead of discarding the less discriminative subsequences, the proposed method merges them using their attention scores. It also weights the discriminative shapelets with their corresponding scores to account for their varying importance.  \n- A mixture of experts  router is used to activate **classe-specific** experts for intra-shape temporal patterns. Similar to how patch tokens (shapelets here)  are processed by  mixture of experts models in  computer vision  (Chowdhury et al., 2023).", "essential_references_not_discussed": "Essential References are cited and discussed in the paper.", "other_strengths_and_weaknesses": "**Strenghts**\n- The paper is well written and easy to follow. \n- The idea of using shapelets as token with a MoE model combined with soft shapelets selection seems novel and shows promising results. \n\n**Weaknesses:**\n-  While training times are compared, a comparison of inference times and number of parameters  is missing from the paper.", "other_comments_or_suggestions": "The  paragraph listing the baselines used for comparisons (L#300 - L#316) need to be structured in a more informative way by indicated to which categorie each method belongs.", "questions_for_authors": "See weaknesses.", "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": "xdEiWnewHL", "reviewer": "Reviewer_byt4", "summary": "This paper presents SoftShape, a learning-based soft sparse shapes model for time series classification, designed to enhance model interpretability. Specifically, SoftShape introduces the soft shape sparsification, replacing hard shapelets with soft shapelets to improve training efficiency. Moreover, SoftShape employs a dual-pattern learning approach, integrating Mixture-of-Experts (MoE)-driven and sequence-aware-driven mechanisms to capture both intra-shape and inter-shape temporal patterns, thereby improving the discriminability of learned soft shapes. Extensive experiments on 128 UCR time series datasets demonstrate that the proposed SoftShape model outperforms baseline methods, achieving state-of-the-art classification performance.", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "**W1: The authors do not provide an in-depth analysis of the networks used for class-specific experts and the shared expert.**\n\n**A**: Please refer to the answers in Q2 and Q3.\n\n---\n\n**W2 & Q4:  The authors do not discuss the rationale for using warm-up training.**\n\n**A**: During the early training phase, the model struggles to distinguish soft shapes, resulting in the fusion of many discriminative ones. Hence, we enable shape sparsification after warm-up training. Experiments on 18 selected UCR datasets showed average ranks of 1.27 and 1.56 with and without warm-up training, respectively, highlighting the strategy's effectiveness.\n\n---\n\n**W3 & Q1: The authors do not provide a detailed explanation of how the MoE combines the learned features from different experts to obtain the intra-shape representations.**\n\n**A**: For each expert's input, we use the top k indices from the MoE router to determine the activated experts for all input shapes. First, we store the shape indices in an array. After all experts output their intra-shape representations, we combine them in the original order using the stored indices.\n\n---\n\n**W4: It would be better to compare the proposed method with LightTS, a lightweight time series classification framework.**\n\n**A**: LightTS uses distillation to reduce runtime by ensembling multiple models. It consists of two stages: teacher and student. The teacher phase trains at least 10 classification models (e.g., InceptionTime), which are then used for distillation to create the student model. Since the teacher phase is time-consuming, we performed a comparison using the selected 18 UCR datasets.\n\n| Method             | Avg. Rank | P-value   |\n|--------------------|-----------|-----------|\n| LightTS (Student)  | 3.00      | 3.72E-14  |\n| LightTS (Teacher)  | 1.71      | 7.87E-03  |\n| SoftShape          | 1.18      | -         |\n\nThe results show that SoftShape outperforms both LightTS (Teacher) and LightTS (Student).\n\n---\n\n**W5: It is encouraged to compare the proposed method with existing time series foundation models, such as UniTS and OFA .**\n\n**A**: OFA corresponds to GPT4TS in the main text. We compared UniTS and OFA on the UCR 128 time series dataset: \n\n| Method     | Avg. Rank | P-value    |\n|------------|-----------|------------|\n| OFA        | 2.40      | 1.90E-12   |\n| UniTS      | 2.30      | 5.07E-12   |\n| SoftShape  | 1.21      | -          |\n\nSoftShape significantly outperforms both UniTS and OFA.\n\n---\n\n**Q2: . What impact would replacing the MoE expert as FCN or TSLANet have on the classification performance of the proposed SoftShape model?**\n\n**A**: Our experiments on the 18 selected UCR datasets show that replacing the original MoE expert network with FCN and TSLANet reduces SoftShape's performance. \n\n| Method              | Avg. Rank |\n|---------------------|-----------|\n| FCN                 | 2.56      |\n| TSLANet             | 1.83      |\n| Original MoE expert | 1.44      |\n\n\n---\n\n**Q3: How would substituting the shared expert other architectures, such as a Transformer, affect the performance of SoftShape?**\n\n**A**: We replaced the shared expert network with an MLP and Transformer, and the performance on the 18 selected UCR datasets is as follows:\n\n| Method      | Avg. Rank |\n|-------------|-----------|\n| Transformer | 2.22      |\n| MLP         | 2.44      |\n| Inception   | 1.11      |\n\nThe results show that Inception performs better.\n\n---\n\n**Q5: In Figure 5, panel (a) appears to contain a significantly larger number (or density) of samples compared to panels (b), (c), and (d). Could the authors clarify why this discrepancy exists?**\n\n**A**: Fig. 5 (a) shows the representations of all shapes, while Fig. 5 (b), (c), and (d) display the representations after soft shape sparsification. As a result, the shape density in (b), (c), and (d) is lower than in (a).\n\n---\n\n**Q6: Are there any specific modules of SoftShape for classification? Could you assess the performance of the proposed method on time series forecasting?**\n\n**A**: Shapelets, first introduced by Ye & Keogh (2009) for time series classification, enhance interpretability. Most existing shapelet-based methods focus on classification tasks. SoftShape, a shapelet-based method, aims to improve performance and interpretability in classification tasks.\nWe assessed SoftShape's forecasting performance on the following datasets using MSE-based average rank under TimesNet and TS2Vec's setting.\n\n| Method         | ETTh1 | ETTh2 | ETTm1 | ETTm2 |\n|----------------|-------|-------|-------|-------|\n| TS2Vec         | 6     | 6     | 4     | 5.6   |\n| TimesNet       | 3.4   | 4.2   | 4.6   | 4.92  |\n| PatchTST       | 4.4   | 2.8   | 4.4   | 2.88  |\n| GPT4TS         | 3     | 3.8   | 1.4   | 2.28  |\n| iTransformer   | 1.2   | 1     | 3.2   | 1.84  |\n| SoftShape | 3   | 3.2   | 3.4   | 3.48  |\n\nThe above results show that SoftShape outperforms TS2Vec and TimesNet, indicating its potential for time series forecasting tasks.", "claims_and_evidence": "The submission is clear and convincing, as the authors have made the source code of the proposed model available and provided detailed experimental procedures along with comprehensive results in the appendix, thereby enhancing the study’s reproducibility.", "methods_and_evaluation_criteria": "The benchmark datasets and evaluation criteria employed in this paper are appropriate. Additionally, the proposed method is well-suited for time series classification tasks, especially in real-world applications where interpretability is a key requirement.", "theoretical_claims": "I have thoroughly examined the equations supporting the theoretical claims presented in this paper and have found no issues.", "experimental_designs_or_analyses": "The overall experimental design and analysis presented in the paper are reasonable; however, there are several issues that need to be addressed:\n1. The authors use MoE router-activated class-specific expert networks with MLPs to learn intra-shape temporal patterns. Meanwhile, they employ a CNN-based Inception module as a shared expert for learning inter-shape temporal patterns. However, in the experimental section, the authors do not provide an in-depth analysis of the networks used for class-specific experts and the shared expert.\n2. The authors mention that the proposed SoftShape model requires 50 epochs for warm-up training in the experimental setup, but they do not discuss the rationale for using warm-up training in the experimental analysis. It is recommended that the authors include this aspect in the ablation study and provide further discussion.", "relation_to_broader_scientific_literature": "The use of soft shapelets for time series classification in this paper is novel and significantly improves interpretability, particularly in critical areas like medical time series classification. Building on prior shapelet-based methods, this approach introduces a more flexible and interpretable framework (i.e., MoE-driven and sequence-aware), offering substantial advancements in fields where understanding model decisions is crucial.", "essential_references_not_discussed": "[1]. LightTS: Lightweight Time Series Classification with Adaptive Ensemble Distillation, SIGMOD 2023.\n\n[2]. UniTS: A Unified Multi-Task Time Series Model, NeurIPS 2024.\n\n[3]. One Fits All: Power General Time Series Analysis by Pretrained LM, NeurIPS 2023.", "other_strengths_and_weaknesses": "Strengths:\n1. The writing and structure of the paper are clear, and the proposed soft shapelet sparsification approach effectively combines the interpretability advantages of shapelets for time series classification while significantly reducing the computational cost of model training.\n2. The use of a mixture of experts to learn intra-shape temporal patterns is innovative. By employing selected experts to learn class-specific features, it enhances the discriminability of the learned shapes.\nWeaknesses:\n1. The authors do not thoroughly discuss the impact of the chosen expert networks for intra-shape and inter-shape learning on the final classification performance of SoftShape in the experimental section.\n2. In Section 4.3.1 on intra-shape learning, the authors do not provide a detailed explanation of how the MoE combines the learned features from different experts to obtain the final intra-shape representations.\n3. It would be better to compare the proposed method with LightTS [1], a lightweight time series classification framework.\n4. It is encouraged to compare the proposed method with existing time series foundation models, such as UniTS [2] and OFA [3]. But this is not necessary.", "other_comments_or_suggestions": "The authors refer to the parameter q in Table 5 as the \"sliding window size,\" whereas in Section 3.2, the term \"fixed step size\" is used. It is recommended that the authors review this terminology and make corresponding adjustments to ensure consistency.", "questions_for_authors": "1. In Section 4.3.1, regarding the MoE approach for learning intra-shape temporal patterns, could the authors explain how the intra-shape features learned by each expert network (as described in Equation 8) are combined to form the final intra-shape representations?\n2. For intra-shape learning, the authors use an MLP network as the base network for each expert. What impact would replacing this with networks such as FCN or TSLANet have on the classification performance of the proposed SoftShape model?\n3. In the context of inter-shape learning, the authors use a CNN-based Inception module as the shared expert. How would substituting this with other architectures, such as a Transformer, affect the classification performance of SoftShape?\n4. The authors indicate that the proposed SoftShape model requires 50 epochs for warm-up training. What adverse effects might occur if the warm-up training were removed?\n5. In Figure 5, panel (a) appears to contain a significantly larger number (or density) of samples compared to panels (b), (c), and (d). Could the authors clarify why this discrepancy exists?\n6. The proposed framework seems general and can also be applied to time series forecasting. In addition, the baselines are most designed for time series forecasting. Are there any specific modules for classification? Could you assess the performance of the proposed method on time series forecasting (this is not necessary)?", "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": "4tE6eowNSu", "reviewer": "Reviewer_6rFK", "summary": "This paper presents Soft Sparse Shapes (SoftShape) for efficient time-series classification. It introduces soft shape sparsification to improve training efficiency by converting subsequences into soft representations. The model further enhances performance by employing a mixture of experts for intra-shape and inter-shape temporal pattern learning. Through extensive experiments on 128 UCR time series datasets, SoftShape outperforms existing methods with significantly better accuracy and training efficiency.", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "**W1 & Q2: The SoftShape model is reliance on fixed-length patch partitions for dividing the input time series, which may result in the loss of important discriminative information. Exploring the possibility of variable patch lengths might enhance the model’s flexibility and potentially improve its performance. It would be valuable to discuss this further.**\n\n**A**: Using shapes (or patches) of varying lengths as model inputs is intuitive but increases computational complexity and requires preprocessing for standardization. To address this, we follow [1,2] by selecting an optimal fixed-length shape via the validation set, balancing efficiency and performance. Also, SoftShape employs a shared expert with multi-scale convolutional kernels to capture dependencies across shapes, mitigating the limitations of fixed-length patches.\n\nFurther, we conducted further experiments on the 18 selected UCR datasets. The settings and results are as follows.\n\n1. **Val-Select**: Choose a fixed m for one SoftShape model using the validation set.  \n2. **Fixed-8**: Set m = 8  for one SoftShape model.  \n3. **Multi-Seq**: Use fixed lengths (8, 16, 32) in parallel three SoftShape models, with residual fusion for classification.\n\n| Model | Avg. Rank | P-value   |\n|-----------------|-----------|-----------|\n| Val-Select      | 1.72      | 2.88E-01  |\n| Fixed-8         | 2.28      | 4.68E-02  |\n| Multi-Seq       | 1.44      | -         |\n\nWe found no significant performance difference between Val-Select and Multi-Seq (p-value > 0.05). The Val-Select model also has fewer parameters and lower runtime.\n\n\n[1] Learning time-series shapelets. KDD, 2014.\n\n[2] CNN kernels can be the best shapelets. ICLR, 2024.\n\n---\n\n**Q1: A more detailed explanation of the shared expert mechanism could strengthen the understanding of how it contributes to the overall performance of the model.**\n\n**A**: For intra-shape learning, MoE treats each shape within a time series as an independent sample, making it difficult to capture dependencies between shapes. Additionally, while learning intra-shape temporal patterns helps extract local discriminative features, it struggles to capture global temporal patterns crucial for classification. To address this, we introduce a shared expert that converts soft shapes within a sample into a sequence and leverages Inception’s multi-scale convolutions to learn global temporal dependencies.\n\n---\n\n**Q3: The shared expert is currently not implemented with the same lightweight linear model as the class-specific expert. It might be worth considering whether using a lightweight linear model for the shared expert could simplify the architecture without negatively affecting performance.**\n\n**A**: We replaced the shared expert from Inception (hidden size 128) with MLP (hidden size 256) and Transformer (hidden size 512) and conducted experiments on 18 UCR datasets. \n\n| Model       | Avg. Rank | Parameters |\n|------------|-----------|------------|\n| Inception  | 1.11      | 179.5 K    |\n| MLP        | 2.44      | 157.8 K    |\n| Transformer | 2.22     | 422.5 K    |\n\nThe Parameters count represents the inter-shape module (shared expert). The results show that Inception and MLP have similar parameter sizes, both significantly smaller than Transformer. This suggests that using Inception as the shared expert provides a lightweight architecture while achieving better classification performance than MLP and Transformer.\n\n---\n\n**Q4: It would be useful to understand how λ affects the results and what range of values was tested during experimentation.**\n\n**A**: We analyzed the impact of different λ values on SoftShape's classification performance using 18 selected UCR datasets. \n\n| λ         | 0.0001 | 0.001 | 0.01 | 0.1  | 1    | 10   | 100  |\n|-----------|--------|-------|------|------|------|------|------|\n| Avg. Rank | 3.00   | 2.50  | 2.61 | 4.11 | 3.72 | 3.72 | 3.56 |\n\nThe results show that λ = 0.001 achieves the best performance, with minimal difference from λ = 0.01.\n\n---\n\n**Q5: It could be valuable to also include a comparison with other shapelet-based methods mentioned in Section 2.2.**\n\n**A**: We selected ShapeConv [2] and ShapeFormer [3] as baselines. The comparison between ShapeConv and SoftShape on 128 UCR time series datasets is shown below:\n\n| Method     | Avg. Rank | P-value  |\n|------------|----------|----------|\n| ShapeConv  | 1.95     | 1.28E-23 |\n| SoftShape  | 1.03     | -        |\n\nSince Shapeformer requires a time-consuming shapelet discovery process before training, we provide a comparison on the 18 UCR datasets selected in the main text for Shapeformer. \n\n| Method     | Avg. Rank      | P-value  |\n|------------|---------------|----------|\n| Shapeformer| 1.94   | 3.13E-06 |\n| SoftShape  | 1             | -        |\n\nThe results demonstrate that SoftShape outperforms both ShapeConv and ShapeFormer on the UCR time series datasets.\n\n[3] Shapeformer: Shapelet transformer for multivariate time series classification. KDD, 2024.", "claims_and_evidence": "Yes. The claims made in this paper are supported by extensive experiments on the UCR time series dataset, demonstrating SoftShape's superiority over 15 baseline methods. The P-values from the Wilcoxon signed-rank test confirm the statistical significance of SoftShape's performance improvements.", "methods_and_evaluation_criteria": "Yes. The proposed method, SoftShape, makes sense for time series classification as it addresses the issue of sparse shape learning by using a soft sparsification process that preserves important subsequences. The evaluation criteria, mainly test accuracy, are suitable for demonstrating the method’s effectiveness on the benchmark UCR datasets.", "theoretical_claims": "No theoretical claims or proofs in this paper.", "experimental_designs_or_analyses": "Yes. The paper employs a comprehensive experimental setup, comparing SoftShape with 15 baseline methods on 128 UCR datasets. The experimental design, including five-fold cross-validation, is sound and valid for evaluating the effectiveness of SoftShape. The use of test accuracy and P-values as evaluation metrics adds rigor to the analysis.", "relation_to_broader_scientific_literature": "The key contributions of SoftShape relate to previous work in time-series classification, particularly shapelet-based methods and mixture-of-experts (MoE) architectures. The paper builds on these techniques by introducing a soft shape sparsification mechanism and leveraging MoE to enhance performance, distinguishing it from prior work in time-series classification.", "essential_references_not_discussed": "The paper thoroughly cites relevant works in time-series classification, particularly those on shapelet methods and MoE architectures.", "other_strengths_and_weaknesses": "**Strengths**:\nSoftShape presents a novel approach to time-series classification, offering both interpretability and efficiency. A key strength of SoftShape is its ability to handle shape sparsification in a \"soft\" manner, which allows it to retain valuable discriminative features while improving computational efficiency.\n\n**Weaknesses**:\nOne potential weakness of the SoftShape model is its reliance on fixed-length patch partitions for dividing the input time series. While this approach can be efficient, it may result in the loss of important discriminative information. Specifically, longer discriminative subsequences may be split across multiple fixed-length patches, potentially disrupting important temporal patterns that are crucial for classification. Additionally, shorter discriminative subsequences could be mixed with non-discriminative segments, which may reduce the model's ability to accurately capture distinguishing features. This could potentially degrade the overall classification performance, particularly when working with time series data that contains both long and short discriminative patterns.", "other_comments_or_suggestions": "The paper is well-written, and the proposed approach is highly innovative. It would be interesting to see how SoftShape scales to datasets of varying sizes and how its performance may change as the complexity of the dataset increases.", "questions_for_authors": "1.\tIt would be helpful to further explain the statement in Section 2.3 regarding how the shared expert enhances the discriminative power of shape embeddings. A more detailed explanation of this mechanism could strengthen the understanding of how it contributes to the overall performance of the model.\n2.\tGiven that shapelets can vary in length, the use of fixed patch lengths in SoftShape may limit the ability to capture discriminative features that span different lengths. Exploring the possibility of variable patch lengths might enhance the model’s flexibility and potentially improve its performance. It would be valuable to discuss this further.\n3.\tThe shared expert is currently not implemented with the same lightweight linear model as the class-specific expert. It might be worth considering whether using a lightweight linear model for the shared expert could simplify the architecture without negatively affecting performance.\n4.\tIt would be useful to understand how λ affects the results and what range of values was tested during experimentation. This could provide valuable insight into the model’s sensitivity to this hyperparameter.\n5.\tWhile the paper compares SoftShape against various non-shapelet-based methods, it could be valuable to also include a comparison with other shapelet-based methods mentioned in Section 2.2.", "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": "By1227n2wJ", "reviewer": "Reviewer_XKP7", "summary": "The paper focuses on the univariate time series classification problem. It proposes a method called Soft Sparse Shapes (SoftShape) model. The model has two major components: 1) a soft shape sparsification module, and 2) a soft shape learning block. The soft shape sparsification module categorizes the input tokens into two groups based on their attention scores. The tokens with higher attention scores are passed to the next layer, while those with lower attention scores are added together. In the second module, the tokens are processed in two different paths. The first path utilizes a mixture of experts to process the location information, while the second path uses a time series model to capture the global information. The authors have conducted experiments to evaluate the performance of the proposed method.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "**W1: The claim is mostly supported by the ablation study. It would be better if the authors provided examples through theoretical analysis or demonstrated it with simple toy data.**\n\n**A**: SoftShape include:\n\n1)\tSoft Shape Sparsification\n\n- To justify its design, we provide toy real-world data (Figure 1 in the main text) with two classes: a robotic dog walking on carpet vs. cement. Existing methods discard shapes of data in a hard way, losing valuable information, whereas SoftShape uses attention-based soft weighting to preserve key shapes.\n\n2)\tSoft Shape Learning Block\n\n- Intra-shape learning: We use the MoE router to learn local class-discriminative shape features. Theoretical support: Theorem 4.2 in [1] states that the MoE router learns cluster-center features, simplifying complex issues into classification problems. Lemma 4.1 in [2] shows that MoE routers group class-discriminative patterns while filtering irrelevant patches.\n\n- Inter-shape learning: We use a shared expert to capture global temporal patterns via multi-scale kernels.  t-SNE visualizations of toy data (Figures 5 & 8 in the main text) show improved separation of mixed-class clusters over intra-shape learning.\n\n[1] Towards understanding the mixture-of-experts layer in deep learning. NIPS, 2022.\n\n[2] Patch-level routing in mixture-of-experts is provably sample-efficient for convolutional neural networks. ICML, 2023.\n\n---\n\n**W2: The ablation study is only conducted on a subset of datasets.**\n\n**A**: We performed ablation on 128 UCR datasets, with findings consistent with the subset of datasets.  Statistical results:\n\n| Method  | Avg. Rank | P-value|\n|----------------------|-----------|------------|\n| w/o Soft Sparse| 3.04| 4.06E-03   |\n| w/o Intra  | 2.75| 4.69E-03|\n| w/o Inter | 3.74| 3.90E-07|\n| w/o Intra & Inter   | 5.02  | 8.95E-16   |\n| with Linear Shape   | 3.23| 4.69E-03   |\n| SoftShape| 2.04| -  |\n\n---\n\n**W3 & Q1: The subsequence length $m$ is not included in the hyper-parameter analysis. While all shapelets include varying lengths, SoftShape uses only one. Can you explain the trade-off of this design?**\n\n**A**: Using variable-length subsequences as input data raises computational complexity.  Also, due to varying sequence lengths in UCR sub-datasets, larger $m$ may suit longer sequences, while smaller $m$ may be better in other cases. Following [3,4], we determine a fixed $m$ via a validation set with fewer training epochs. Experiments with a chosen $m$ reduce computation time and ensure good results, as seen in the answer to Q5.\n\n[3] Learning time-series shapelets. KDD, 2014.\n\n[4] CNN kernels can be the best shapelets. ICLR, 2024.\n\n---\n\n**Q2: Can you detail how the attention mechanism used in the paper differs from self-attention and compare their pros and cons?**\n\n**A**: As noted in [5], the key difference is that gated attention (used in our method) assumes instance independence, enabling key instance identification via labels, whereas self-attention captures dependencies across all instances without using labels.\n\n| | Pros| Cons |\n|------------|--------------------------|------------------------------|\n| Gated Attnention | Linear complexity with instance counts. | Weak in capturing instance relationships|\n| Self-Attention |  Captures dependencies across instances.  |Higher complexity with instance counts|\n\nHowever, gated attention implicitly captures shape relationships via labels. Also, we use a shared expert to learn temporal patterns among shapes.\n\n[5] Attention-based deep multiple instance learning. ICML, 2018.\n\n---\n\n**Q3: What is the definition of $\\eta$, and what is its relationship with $Num$?**\n\n**A**: For a time series of length $T$, the number of subsequences of length $m$ is $J = \\frac{T-m}{q}+1$, where $q$ is the sliding window step.  $\\eta$ represents the ratio of top subsequences based on attention scores. The number of sparsified subsequences $\\text{Num} = J \\times \\eta+1$.\n\n---\n\n**Q4: Can you explain the implementation of the linear shape in the ablation study?**\n\n**A**: Replace the 1D CNN in Eq. (2) with a linear layer to convert each subsequence of length $m$ into an embedding of dimension $d$.\n\n---\n\n**Q5: What is the effect of the hyper-parameter $m$ on the classification performance?**\n\n**A**: We conducted three experiments for $m$:  \n\n1. **Val-Select**: Choose a fixed m for one SoftShape model using the validation set.  \n2. **Fixed-8**: Set m = 8  for one SoftShape model.  \n3. **Multi-Seq**: Use fixed lengths (8, 16, 32) in parallel three SoftShape models, with residual fusion for classification.\n\n| Model | Avg. Rank | P-value   |\n|-----------------|-----------|-----------|\n| Val-Select      | 1.72      | 2.88E-01  |\n| Fixed-8         | 2.28      | 4.68E-02  |\n| Multi-Seq       | 1.44      | -         |\n\nWe found no significant performance difference between Val-Select and Multi-Seq (p-value > 0.05). The Val-Select model also has fewer parameters and lower runtime.", "claims_and_evidence": "1. The proposed method provides excellent performance for time series classification. This claim is mostly supported by the experimental results.\n2. The design of both modules is important for the resulting performance. This claim is mostly supported by the ablation study. It would be better if the authors provided examples of how each design resolves problems that other models failed to address through theoretical analysis or demonstrated it with simple toy data.", "methods_and_evaluation_criteria": "The proposed methods and evaluation criteria make sense for the problem at hand.", "theoretical_claims": "This paper does not present any proofs or theoretical analyses.", "experimental_designs_or_analyses": "One minor drawback is that the ablation study is only conducted on a subset of datasets. Another drawback is that the subsequence length $m$ is not included in the hyper-parameter analysis.", "relation_to_broader_scientific_literature": "The paper proposes a novel time series classification model for univariate time series data.", "essential_references_not_discussed": "To the best of my knowledge, there are no essential references missing from the paper's discussion.", "other_strengths_and_weaknesses": "- Strengths: The proposed method is novel and outperforms prior methods. \n- Weaknesses: The paper heavily relies on performance to motivate the proposed method. It would be better if some kind of theoretical analysis or demonstration with toy data could help the reader understand the merit of the proposed modules.", "other_comments_or_suggestions": "The definition of sparsity rate $\\eta$ is not clear. It would be better to properly define it, so readers understand the role of this hyper-parameter. How does the setting of $\\eta$ affect another variable $Num$?", "questions_for_authors": "1. In Equation 1, the set of all possible shapelets consists of subsequences of different lengths. However, I think the proposed method only uses one subsequence length. Can you explain the trade-off associated with this design discrepancy?\n2. For the soft shape sparsification module, can you provide more details about how the proposed method differs from the standard self-attention mechanism, and the pros and cons of these designs (proposed versus standard)?\n3. What is the definition of $\\eta$, and what is its relationship with $Num$?\n4. In the \"with linear shape\" setting in the ablation study, can you explain more about how the linear shape mechanism is implemented?\n5. What is the effect of the hyper-parameter $m$ on the classification performance?", "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:

Meta-review: This paper proposed a Soft sparse Shapes (SoftShapes) model for efficient time series classification. In order to do so the authors introduce soft shape sparsification and soft learning blocks. All reviews are very positive, recognize the novelty of the findings, and appreciate the presentation of the paper. The discussion between the reviewers and the authors was productive, and the paper's scores improved after the rebuttal. Therefore, the AC suggests acceptance and encourages the authors to include the rebuttal discussion in the final version of the paper.
Decision: Accept (spotlight poster)