Learning Time-Series Representations by Hierarchical Uniformity-Tolerance Latent Balancing
Authors: Amin Jalali
Milad Soltany
Michael Greenspan
Ali Etemad
Venue: Accepted by TMLR ()

Abstract: We propose TimeHUT, a novel method for learning time-series representations by hierarchical uniformity-tolerance balancing of contrastive representations. Our method uses two distinct losses to learn strong representations with the aim of striking an effective balance between uniformity and tolerance in the embedding space. First, TimeHUT uses a hierarchical setup to learn both instance-wise and temporal information from input time-series. Next, we integrate a temperature scheduler within the vanilla contrastive loss to balance the uniformity and tolerance characteristics of the embeddings. Additionally, a hierarchical angular margin loss enforces instance-wise and temporal contrast losses, creating geometric margins between positive and negative pairs of temporal sequences. This approach improves the coherence of positive pairs and their separation from the negatives, enhancing the capture of temporal dependencies within a time-series sample. We evaluate our approach on a wide range of tasks, namely 128 UCR and 30 UAE datasets for univariate and multivariate classification, as well as Yahoo and KPI datasets for anomaly detection. The results demonstrate that TimeHUT outperforms prior methods by considerable margins on classification, while obtaining competitive results for anomaly detection. Finally, detailed sensitivity and ablation studies are performed to evaluate different components and hyperparameters of our method.

Published in Transactions on Machine Learning Research (10/2025)
Learning Time-Series Representations by Hierarchical Uniformity-Toleraan Latent Balancing
Amin Jalali', Milad Soltany", Michael Greenspan, Ali Etemad
falin.jalali, solann,, michael.greenspee ali. Queen's University, Canada
Reviewed on OpenReview: https: openreview. net/ farun?? id= NTTVEA
Abstract
We propose TimeHUT, novel method for learning time-series representations by hierar- chical mnifrrmity-tolcrance balancing of contrastive representations. Our method uses two distinct losses to learn strong representations with the aim of striking effective balance between uniformity and lolerance in the embedding space. First, TimeHUT uses hierar- chical setup to learn both instance-wis wise and temporal information from input time-series. Next, we integrate a temperature scheduler within the vanilla contrastive loss to balance the uniformity and lolerance characteristics of the embeddings. Additionally, a hierarchical angular margin loss enforces instance-wise and temporal contrast losses, creating geometric margins between positive and negative pairs of temporal sequences. This approach improves the coherence of positive pairs and their separation from the negatives, enhancing the cap- ture of temporal dependencies within time-series sample. We evaluate our approach on wide range of tasks, namely 128 UCR and 30 UAE datasets for univariate and multivariate classification, as well as Yahoo and KPI datasets for anomaly detection. The results demon- strate that TimeHUT outperforms prior methods by considerable margins on classification, while obtaining competitive results for anomaly detection. Finally, detailed sensitivity and ablation studies are performed to evaluate different components and hyperparameters of our method.
1 Introduction
Time-scrics data are prevalent across diverse fields such as healtheare, metcorology. finance, smart homes. and energy applications (Yang & Hong 2022 Hajimoradlou et al. 2022 Liu & Chen 2024 Zheng et al.
2024). The advent of self-supervised deep learning has resulted in remarkable success in handling diverse forms of time-series due to its ability to leverage data without requiring annotations (Yang & Hong 2022 Luo et al., 2023 Zhang al.) 2024). Contrastive methods, which enforce augmentations from the same sample to be close to each other as positive pairs while pushing augmentations from other samples apart negative pairs,
popular approach to self-supervised learning (Lee et al., 2024 Zerveas et al. 2021 These methods have shown strong performances in various areas including vision, language, and time-series
Dosovitskiy et al. 2020 Gao et al. 2021 Zhang et al. 2022b).
Prior works have defined two concepts that play key roles in contrastive self-supervised representation learn- ing: uniformity and tolerance (Wang Liu 2021 Wang Isola 2020). Uniformity refers to the maximization of information and spread of representations in the latent space, while tolerance is the ability of the model to allow small variations in the input (e-g., augmentations, noise, or natural variations between semantically similar samples) without significantly altering the learned representation. While uniformity and tolerance are both desired characteristics there exists a trade-off between the two that hinders self-supervised con- trastive learning /Wang & Liu 2021 Xiao & Lyu 2024). An excessive focus on uniformity can result in
*These authors contributed equally.

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representations that are overly spread out, complicating the formation of meaningful clusters. Conversely, placing too much emphasis on tolerance can lead to an inefficient distributed representational space, with clusters potentially becoming too close or overlapping with one another. Therefore, careful consideration and balancing of these two objectives during the learning process is essential for each time-serics instance and for the temporal segments within it. Accordingly, we pose the question: How can we strike an effeclive balance between uniformitt and tolerance to optimize the effectiveness of self-superoiee contrastive learning for time-series data?
In this paper, to address the challenge above and achieve strong balance between uniformity and toler- ance in the representation space, we propose novel method for hicrarchical instance-wise and temporal Time-series contrastive representation learning with Hierarchical Uniformity-Tolere (TimeHUT). Our method uses a hierarchical approach inspired by TS2Vec (uue et al.) 2022) and consid- ers both instance-wise and temporal segments to learn comprchensive representations. Second, TimcHUT applics temperature scheduling function (Kuklova et al., 2023) to the vanilla contrastive loss to balance the uniformity and lolerance characteristios of the embeddings. For small temperature, the contrastiive objective maximizes the average distance to the nearest neighbors of each sample, leading to a uniform distri- bution over the hypersphere. On the other hand, a large temperature maximizes the average distance over a wider range of neighbors considering more distant samples to result in tighter clusters. Our method includes a temperature scheduler that systematically explores a range of temperatures to consider different ranges of contrastive neighbors, optimizing the trade-off between achieving a uniform distribution of embeddings in the feature space and clustering of similar samples. Additionally, our method leverages a hicrarchical angular margin loss to enforce instance-wise and temporal contrastive learning between positive and negative pairs of temporal sequences. The angular margin loss is inspired by face recognition literature (Boutros et al.) 2022; Zhang et al. 2022a), which we adapt for lime-series. This approach increases the coherence of positive pair segments and their separation from negatives within single time-series sample to capture better temporal dependencies. We evaluate the efficacy of our model by conducting extensive experiments on univariate/ univariate/mul- muul- tivariate time-series classification and anomaly detection, using 128 UCR and 30 UEA classification datasets along with Yahoo and KPT anomaly detection datasets. These experiments demonstrate that our met outperforms the competitive results versus the stato-of-tho-art on anomaly detection. Detailed ablation and scnsitivity studies demonstrate the impact of different components of our method.
latent balancing
on both univariate and multivariate classification, while achieving the best
Our contributions are summarized below:
We present TimeHUT, a framework for learning effective time-series representations, which uses a periodic temperature scheduling function in its hierarchical contrastive loss to facilitate changing the emphasis between uniformity and tolerance of instances and their temporal segments within an instance. The temperature scheduler balances this trade-off dynamically during training, addressing the limitation of contrastive loss where a fixed temperature cannot adapt the cvolving represen- lation space. This mechanism results in more effective learning of temporal patterns across classes while capturing distinctions between different segments within the time-series.
TimeHUT additionally employs an instance-wise and temporal hierarchical contrastive angular mar- gin loss. Although angular margin is well established in other areas such as face recognition, we adapt it for both temporal and instanco-wise contrastive losses in timc-series, enforcing better coher- ence among segments with close proximity, while distinctly separating them from non-neighboring ones within the same time-series sample. This adaptation enforces geometric margins between tem- poral segments within sequences for both temporal and instance-wise contrast losses, which remains unexplored in prior time-serics work.
Extensive experiments demonstrate that TimeHUT achieves state-of-the-art performance on classi- fication and competitive results on anomaly delection. Our ablation study shows the combination achieves 86.4% accuracy vs. 83.0% with only hierarchical loss, demonstrating improvements beyond the sum of individual components. Our contribution lics in the novel adaptation and synergistic integration of temperature scheduling and angular margins to address the miformity-ttlorann problem in time-series representation learning. We have released our code implementation
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http:://ghhao.ooo//////aaaarrar2 to contribute to the area and enable fast and accurate reproducibility.
2 Related Work
In recent years self-supervised represcntation learning has become an influential strategy for time-scries representation learning, primarily due to its capacity to alleviate the substantial cost associaled with labeling. In the following, we summarize key recent papers in this area.
Non-contrastive methods. A number of studies have applied non-contrastive methods such as employing encoer-deccoder structures to minimize reconstruction errors for time-series representation learning (Zereass et al. 2021 Li et al. 2023). Some have developed generative- based architectures to minimize the recon- struction error between raw data and the generated counterparts (Vaid et al., 2023). Others have utilized adversarial- based approaches with generators and discriminators for adversarial learning of time-series data (Seyfi et al. 2022 Jeon et al. 2022 Floss (Yang et al. 2023) introduces regularizer to learn represen- tations in the frequency domain by utilizing the periodic shift and spectral density similarity measures to learn the features with periodic consistency.
Contrastive methods. The fundamental concept behind contrastive learning is to maximize the similarity among different contexts of the same sample while minimizing the similarity among different samples (Luo je al. 2023 Lee et al. 2024: Nonnenmacher al. 2022). T-Loss (Franceschi el al., 2019). for instance, uses sub-segmentt of an input time-series as a positive sample with its random sub-segment while contrasting the same sub-segment with another time-scries to obtain the representations. TS-TCC (Eldele et al. 2021 uses temporal contrasting to capture temporal dependencies by cross-view prediction task. This module takes the past features of one augmentation to predict the future of another augmentation by utilizing different timestamp variations and augmentations. VS2Vec (Zerveas et al. 2021) employs instance-wise and temporal contrastive losses on two augmented sub-segments of time-scries to capture both multi-resolution and multi- scale contextual details. adopts a hierarchical approach to contrast augmented views, ensuring a robust representation for each timestamp.
TNC (Tonekaboni et al. 2021 defines temporal neighborhood boundaries in which the distribution of samples within the neighborhood vicinity is dissimilar from signals outside that neighborhood in the latent space using de-biased contrastive loss. TimeCLR (Yang et al. 2022 obtains the invariant features through the maximization of similarity between the positive pairs and minimization of similarity between negative pairs of time-series. TF-C (Yang & Hong. 2022) focuses on capturing dime-frequency consistency, where the representations derived from the time and frequency domains of a given time-series should exhibit proximity the latent space. Another study (Hajimoradlou et al. 2022) presents a sulf-supe contrastive framework that incorporates similarity distiillaiion across both instance and temporal dimensions pre-train the universal representations model. FEAT (Kim et al. 2023 integrates hierarchical temporal contrasting loss, feature contrasting loss, and reconstruction loss to concurrently learn fcature and temporal consistency. SoftCLT (Lee et al. 2024) introduces soft assignments to sample pairs for instance-wise and temporal contrastive losses to capture the inter- and intra-temporal relationships in the data space. TimesURL, (Liu & Chen 2024) proposes frequency-temppral augmentations to preserve the temporal properties. It then constructs hard negative pairs guide better contrastive learning along with the time reconstruction module to jointly optimize the model.
3 Method
3.1
Problem definition
be a time-series dalaset, where x; E RR TxN is sample recorded al cerlain time intervals with T' denoting the length of the time-series, and signifying the number of variables. The full dataset X contains a total number of n time-scrics samples. Here, N = indicates a univariate time-scries dataset, while N indicates a multivariate time-series dataset which retttioclasosssiiss across variables may exist. Time-series representation learning aims to develop a nonlinear embedding function fo x
Ti, Let X = f2,,,,
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Hierarchical Contrasting
Positive Pairs
Hierarchical Scheduler
Hierarchical Margin
Nagativa Pains
Temporal Contrast
Instance wise Contrast
Pre
MASE
ing
Crop
batchh
Letherch Le Liturnnn
Enooder
lime
X
Figure Overview of TimeHUT architecture. (a) Input time-series X (with samples i, j, and & shown in different colors) are randomly cropped into two overlapping subseries. (b) The encoder processes these subseries, followed by hierarchical contrasting both temporal and instance-wise levels through max pool- ing, computing both temporal contrastive (within-sample across time) and instance-wise contrastive losses (across samples). (c) The temperature scheduler r(a) dynamically balances unformitty-tolerance trade-offs (Liiiescch) while angular margin loss enforces geometric separation between positive and negative pairs (LHierAng). The final loss combines both components.
where are the learnable model parameters, and 2, e IR TxM are the encoded representations with M denoting the dimension of the encoded features.
3.2 Modeling insight and theoretical foundation
Our method builds upon the hierarchical contrasting framework from TS2Vec (uue et al. 2022) incorporat- ing temperature scheduling inspired by Kukleva et al. (023 and angular margin losses adapted from face recognition literature (Boutros al. 2022; Zhang al. 2022a Our contribution lies in the novel adaptation
and integration of these techniques for time-scries representation learning to address the unforrmity-tolcrane problem. While TS2Vec uses fixed temperature in hierarchical contrasting, we introduce periodic schedul- ing (Kukleva et al. 2023 within the hierarchical framework that balances uniformity- trade-offs dynamically during training. This addresses the limitation contrastive learning where fixed temperature parameters cannot adapt the evolving representation space during training. The temperature parameter controls the boundaries between negative and positive pairs based theoretical studies in Kukleva et al. (2023) and Wang & Isola (2020). When is small, the gradients are sharper and promote uniformity by maximizing average distances to the ncarest neighbors. When 7 is large, the gradients become smoother and promote tolerance by allowing tighter clustering, TimeHUT additionally employs instance wise and temporal hierarchical contrastive angular margin losses to enforce coherence among proximate segments, while dis- tinctly separating them from noi-neighboring ones within the same time-series sample. This adaptation of angular margins for both temporal and instance-wiss wise contrast losses is unexplored in prior time-series work. The combination of hierarchical temperature scheduling with the angular margins allows to navigate the unforrmity-tolcracce trado-off more effectively than fixed-temperature approaches.
3.3 Proposed approach
The overall architecture of TimcHUT is shown in Figure 1 To learn position-agnostic representations
Kayhan & Gemerl. 2020 Liu & Chen 2024), our model processes input raw time-series X by randomly cropping two overlapping subseries from the input time-series to obtain X. This is done by randomly sampling two overlapping subscries b, and b2] such that 0 < aj S 02 b, & by s T. Subsequently, these subseries are fed into the encoder. The encoder optimized using hierarchical contrastive loss in the temporal dimension well as the individual instance level by summing over multiple scales (Yue et. al.
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2022). The hicrarchical structure captures multi-level features through maximum pooling. Next, our model applies two unique losses, which we describe in the following.
Preliminary. To capture the temporal characteristics of time-series, we apply a temporal contrastive loss given as:
exp(Sat.ve)
(1,t,t L Temp = -- -log( (ex((su, 1 [uee exp (xp(su.e)]
(1)
Σ def
where St = sim(2i,,,42) denotes the similarity between the representations of positive pains at the same timestamp t from the two subseries of the imput time-series. Moreover, Si,, = sim(( (i,((i,,,((,)) denotes the similarity between the representations of negative pairs at different timestamps t' from the two subseries and Sit, = sim( 25,v) represents the similarity between the represcntations of negative pairs at different timestamps 1' from the same subseries. 1 and i represent the timestamp and the index of the input time- series samples, respectively. sim(:.- calculates the similarity function between the embeddings of the two segments. Ω is the set of timestamps within the overlap of the two subseries, and the indicator function [(we)) is one when t# t' and zero otherwise. In addition to Lremp: to learn discriminate representation between different instances, the instance-wise contrastive (Inst. loss is defined by:
exp($se,Pt)
L (bdit) -log(
(2)
B Σ
(xp($aa.))) + ||w exp($st.31)
where B denotes the batch size, sarrt = sim(2,, 24,,, 2,,e), Sa,jt (2, 2/,e), and satft = sim sim(2,,, 24, and Zj.z denote the representations of two different time-series at timestamp t in the same batch, and [(4s]] is an indicator function that is one when i and zero otherwise.
This formulation for learning both instance-wise and temporal representations from time-series has been widely adopted in recent statc-of-thc-art solutions such as (Yue et al.] 2022 Lee et al., 2024 Liu & Chen 2024). This approach, however, does not consider the compactness and uniformity of the learned represen- tations, and can therefore result in disrupting the semantic ructure of embedding space. We address this problem by proposing the modified hierarchical learning scheme follows.
Unformitty-tolerance hierarchical latent balancing. In order to allow for a gradual shift from unifor- mity in the embedding space to more distinct clusters, we propose a temperature parameter in the loss. A simple temperature parameter can be added to the standard LTmmp + Linst formulation by dividing all the similarity measures St,,t', Sit,'e' Stt,i'', Stt''t: and St by т. We note that this new formulation, higher temperature values will lead to tighter clusters in which the data points within a cluster are more closely packed. However, this tighter clustering comes at the cost of reduced uniformity across the entire dataset, as the data points tend to cluster more densely rather than being spread out evenly. Instead, we aim for the model to have the flexibility to move between forming well-defined clusters and ensuring there is sufficient separation between them. More specifically, we aim for the model to effectively balance the identification of discriminative and subtle instance-wiet wise and temporal patterns through uniformity while enhancing the tolerance by bringing the features of semantically similar items close to each other (Wang & Liu. 2021 Kukleva et al. 2023 Manna et al., 2023).
To this end, we introduce a temperature scheduler r(o) to the hierarchical instance-wise and temporal contrastive losses in the context of time-series representation learning for the first time. This scheduler will enable the model to consistently shift from uniformity to tolerance without incurring extra computa- tional expenses. Accordingly, we generate the dynamic values for the temperature scheduling mechanism by sinusoidal periodic variations through the cosine function with an amplitude and offset adjustment as (()) = AT x cos? (wr) Tmin- The linear transformation (Ar Tmaa - Tmin) adjusts the amplitude of varia- tions and Tmin shifts the entire function vertically (offset). The angular frequency is represented by w 2r in which T(O) oscillates with a period T and varies between Tmin and Tian + Ar. The cosine term introduces periodic oscillations with a frequency determined by period T. a represents the time variable, Tmaz and Tmin are maximum and minimum values for temperature hyperparameter. The use of cos" suggests that the parameter changes in smooth, periodic manner, with its rate of change being slowest at the extremes and
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fastest in the middle of each cycle. The time-varying temperature parameter inffuenced by wave function in contrastive loss reflects how the similarity between embeddings is scaled over time, potentially adapting the
learning focus from coarse to fine features. The reason for choosing the sinusoidal function is theoretically
detailed in literature Kukleva et al. 2023 Manna et al. 2023 Hence Eqs. and 2 can be re-written as:
exp(sn,.s/7(o))
TTempSch = - log(
(3)
exp exp($in,v//(oo)) |[se) exp(sx,
t'es?
and
exp(st,:1)/T(o))
L (GJ.t) InstSch - -log(
(4)
B Σ
[exp(su.t/7(O))) [ins]
The hierarchical instance-wise and temporal loss with temperature scheduling is calculated by contrasting all samples in the batch and their temporal segments as:
LHierSch NT E (htt) (6J.1) TempScch Instsch)
(5)
To further elaborate, when the temperature is small, the contrastive loss maximizes separation among embeddings to enhance uniformity. Conversely, with a large temperature, the loss encourages embeddings of similar samples to cluster tightly, promoting tolerance. By scheduling the temperature, our method explores and balances uniformity and tolerance over the training period, optimizing representational quality. The sinusoidal scheduling introduces periodic exploration of the representation space by adjusting in a smooth and non-monotonic manner. Furthermore, the temperature scheduler periodically modulates uniformity and tolerance. The dependence on T ensures that the scheduler cycles over temporal horizon aligned with the time-series sample. This cyclic modulation has theoretical grounding in literature (Kukleva et al. 2023 Manna et al. 2023 3, and empirically improves learning stability.
Given that the formulation of hierarchical contrastive learning pushes the representations of the same in- stances together while pushing those of different ones apart without explicitly considering semantic relation- ships, our model is likely to achieve higher uniformity at the cost of less tolerance. To remedy this, we take inspiration from margin separation of negative pairs (Boutros et al., 2022 Alirezazadeh & Dornaika 2023 Terhörst et al.] 2023 Zhang et al.) 2022a Choi et al. 2020), which has not been explored in this context before. Accordingly, we define a hicrarchical angular margin loss to encourage the model to maintain min- imum angular distance between negative pairs of hierarchical representations, ensuring better separability in the latent space. The hierarchical angular margin loss is composed of two specific terms: the temporal an- gular margin loss TTmmpAng and the eetance-wise angular margin loss L InstAng: These losses hierarchically calculate the cosine similarity between segment. embeddings based on the positive or negative instances to apply the marginal distance. We define (G,,,")) TempAng as:
(6.j.)
( max m2 cos () )²
if I(
L
(b,t,t) AemmpAng
if ((""",t') = 1,
(6)
ma m. cos- (8 if [tt)
where the indicator function I takes condition and returns 1 if the condition is true and 0 otherwise. T(ii, (t) denotes an indicator for positive pair segments at the same timestamp from the two subseries it'. 1(ii',tt) denotes the negative pairs at different timestamps t' from the two subseries ii, highlighting those segments that are temporally distant. Moreover, I(ii, ((') represents the negative pairs at different timestamps t' from the same subseries ti. The arccosine function, denoted by cos-1, computes the angle corresponding to the cosine similarity. The smaller the angle, the more similar the vectors are. m, the angular margin that enforces minimum angular separation for negative pairs.
In this formulation, if the similarity measure St,Ft between positive pairs increases, the loss term (b,t,e) will decrease as the term cos (su. decreases when the embeddings become more aligned, with the angle
LempAng

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approaching 0 degrees. Conversely, (sa,r)) increases the similarity between the positive pairs deviates from perfect alignment, with the angle between the two embeddings approaching 90 degrees. This encourages the model to adjust the embeddings such that the positive pairs are pulled closer together in the feature space. Morcover, for negative pairs I(i', "il',tt) tt') and [(ti, tt'), when the cosine the angle between them is less than the margin, mh - (84,,v) > O, the model penalized, and the gradient directs the optimization to increase the angle between them. This pushes the negative pairs further apart in the feature space, increasing cos (sa,, within the angular constraints imposed by ma- The margin ma acts as threshold, beyond which the loss for negative pairs does not increase. This ensures that the model enforces minimum angular distance between the negative pairs, resulting in structured separation in the feature space based on the temporal relationships of segments.
Next, define L (1.j.) InstAng as:
if (tt'
L
(...t) InstAng
max(0, ma - cos (s)
if (fj( =1 if I(f"",tt))
(7)
max(0, mm cos (s))
where I(ij, It) denotes two different time-series i and j at timestamp t from the same batch. j' is a cropped subseries of time-series j in I(iij, tt) as indicated under the instance-wise contrast in Figure
Here, for positive instanco-wisc pairs where T(ii',tt) = the loss is calculated as the square of the angle (in radians) between the embeddings. This loss function penalizes large angles between embeddings of positive pairs, encouraging the model to learn embeddings that are closely positioned in the feature space. For negative instance-wise pairs 1(ij, tt) and (() the loss is defined as m, cos coim (sim z(,()) indicating that the model incurs a penalty if the angle between the embeddings is smaller than margin ma- For the loss to be zero, the m, - cos " (2,,,, =),)) s condition must. be satisfied. This encourages the embeddings of negative pairs to be positioned farther apart. Consequently, the loss function adjusts the embeddings such that positive pairs are separated by small angular distance while ensuring that negative pains are separated by an angular distance that is at least as large as the margin ma-
Obtaining hierarchical instance-wiee and temporal angular margin for all the time-series samples and tem- poral segments is defined as: Aiter = NT ; TempAng + +c (1..1)
ΣΣ(a (1t.t)
((5.)) InstAng)
(8)
where and e are the loss term coefficients.
Total loss. The total loss is calculated by the sum of the hierarchical temperature scheduling loss and hierarchical angular margin loss as follows:
LTotal LHierSch + LHierAng
(9)
The intuition of our work is that the hicrarchical temperature scheduler loss (LHierSeh)) promotes balancing between uniformity and tolerance in the feature space enhancing the representation quality. The angular margin loss (LHierAng) maintains distinct separations, or margins, between positive and negative pairs. This combination encourages representations that are both well-distributed and distinctive, enhancing per- formance. By adjusting the AnserAng term coefficients (c, and ct), we can fine-tune the margin separation instanco-wise and temporally to directly impact clustering. Angular margin loss this context enforces a minimum angular distance between negative pairs of embeddings, setting a margin (m,) to separate dis- similar instances time points. This loss is used to improve the model's ability to handle subtle temporal dependencies and to prevent overlapping clusters.
LHtterchh and Litiernng are combined with equal weighting, but each loss contains internal coefficients that can be tuned. Specifically, LafierSea incorporates Timin Tmen, and Tmar via its scheduler, while LitierAng uses coefficients & and et to balance instance wise and temporal angular losses. Hence, by combining the two losses cqually and relying on their internal tuning paramcters, no additional hyperparameters are roquired.
A Algorithm 1 provides Py Pore pseudo-code that describes the proposed TimeHUT model.
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4 Experiment setup
Datasets. We evaluate TimeHUT on both m classification and anomaly detection. For classification, use the standard UCR 128 univariate dataset (Dau et al. 2019) and UEA 30 multi- variate dataset (Bagnall et al. 2018). They consist of diverse lime-series datasets such as SCG/EEG/MBR /MEG classification, motion classification, human activity recognition, and audio spectra classification, among oth- crs. They are widely utilized due to their ability to offer a comprehensive evaluation, measuring the model's generalization capabilities. In addition, we utilize the commonly used Yahoo (Laptev et al.) 2015) and KPI (Ren et al,, (2119) datasets for anomaly detection. Yahoo contains 367 hourly sampled time-series with annotated anomaly points. The KPI dataset consists of 58 univariate time-series, each representing key performance indicator (KPT) collected from various internet companics. Each time-serics is sampled at one-minute intervals. Together, all the datasets used in this paper comprise total of 160 individual datasets.
Implementation details. We use Adam optimizer with a learning rate of 1e-3. The batch size is set to 8, with the number of epochs determined by the dataset size: 200 epochs for datasets smaller than 100,000, and 600 epochs for larger datasets. The representation dimension is fixed 320. During training, we segment large time-series sequences into 3,000 timestamps, following (Yue al.] 2022; Lee et al.) 2024). For the details of all the hyperparameters for all the datasets used in our study, please see Appendix C. We train our method using PyTorch 1.10 on 4 NVIDIA GeForce RTX 3090 GPUs. We used the PyHopper library [echner et al. 2022) to find the optimal values for each hyperparameter. It uses the Markov Chain Monte Carlo optimization ion algorithm to search for a range of values of [0.2, 0.8] for m, and [0. 10] for Q and q. It
selects the values resulting in the best performance as reported in Appendix Tables A5
A6 and A8
We use a standard encoder backbone in our method following (Yue et al.) 2022). This encoder consists of three components: a projection layer, a masking module, and convolution layers. The projection layer serves as fully connected layer that transforms the input segments into high-dimensional vectors, which represent the data in a more complex space. Following this, the masking module applics masks to these vectors at randomly chosen timestamps, creating a modified version of the data. This process helps in generating an augmented view of the input time-series by selectively hiding parts of the data, encouraging the model to learn more robust features. The convolution layers incorporate 10 residual blocks. The architecture of each residual block comprises two one-dimensional convolutional layers, each defined by a dilation block that increases the perceptual field across diverse channels. The exact hyperparameters of the backbone encoder follow prior works such as Yue et al. 2022 and (Lec et al. 2024
Baselines and comparisons. To assess the performance of our proposed TimeHUT, we use accuracy and rank following the experimental setup of [Pieper et al. (2023), Lee et al.) (2024), and Liu & Chen (2024). For comparison, we use commonly used prior works, namely TF-C (Liu ct al. 2023), MCL (Wickstrom et al. ),22), DTW (Franceschi et al.] (2019), T-Loss (Franceschi et al. 2019), TST (Zerveas el al. 2021
TS-TCC (Eldele et al.) 2021). TNC (Tonekaboni et al.) 2021), TS2Vec (uue et al. 2022], InfoT' Luo et al. 2023). InfoTS., SMDE (Zhang et al.
2024 FEAT (Kim et al.] 2023), SelfDis Pieper et al. 2023
Ti-MAE (Li et al., 2023 Floss (Yang et al. 2023 SoftCLT (Lee et al 2024). TimesURL (Liu & Chen 2024), and AutoTCL. (Zheng et al.] 2024). The InfoTS, model uses ground-truth labels only to train a meta-learner for selecting suitable augmentations, while InfoTS is entirely unsupervised. Note that among the individual datasets of UCR and UEA, some datasets cannot be handled by T-Loss, TS-TCC, TNC, and DTW due to missing observations, such as BodgerL.oopDay
and IinbeeWingbeat. Therefore, we considerod only 125 UCR and 29 UEA datascts to obtain the rank values
following prior works (Yue et al., 2022: Lee et al., 2024 Luo et al. 2023 Zheng et al.] 2024 Liu & Chen 2024). TimeHUT works on all UCR and UEA datasets, and full results of TimeHUT on all datasets are provided in Appendix A.
In addition, following the experimental setup of TS2Vec (Yue el al. 2022), ; Cof (Lee el al. 2024). and TimeURL (Liu & Chen 2024) on anomaly detection, we evaluate our method using Fl score, precision, and recall motrics. We compare TimeHUT for anomaly detection with SPOT Siffer et al. 2017 DSPOT
(Siffer et al. 2017). DONUT (Xu et al.) 20188) SR (Ren et al. 2019), TS2Vec (Yue et al. 2022). Times URL
[Liu & Chen 2024), and SoftCL. (Lee et. al. 2024) for the normal setting, and FFT (Rasheed et al. 2009
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Twitter-AD Vallis al.
2014
Luminol LinkedIn, 2018). SR (Ren et al., 2019 TS2Vec Yue et al. 2022
2024 for the cold-start setting. We include the explanation of these methods on anomaly detection in Appendix B.
and SoftCL.T (Lee et al.
5
Results
We present our results on univariate and multivariate classification, well as anomaly detection. Next, we perform ablation studies to evaluate the impact of the main components of our method. We then present a comprehensive sensitivity study for the main hyperparameters of our method.
Table 1: Performance of TimeHUT on univariate and multivariate classification.
125 UCR Datasets
29 UEA Datasets
Model
Acc
Rank
Acc
Rank
DTW
(Franceschi et al.
2019)
72.7
8.72
65.0
10.02
T-Loss |Fanceschi et al.
2019
80.6
6.34
67.5
8.76
TST
Zerveas
2021
64.1
9.79
63.5
10.97
TS-TC
[Elele et al. 2021
75.7
7.50
68.2
9.47
TNC Tonekaboni al.
2021
76.1
7.59
67.7
10.38
MCL
Wickesrrom et a.. 2022
61.2
12.45
TS2Vec
Yue et 2022
83.0
4.78
71.2
7.55
TF-C
Liu et al. 2023
42.0
13.53
Ti-MAF
Li al. 2028
82.3
4.77
InfoTS
Luo et al.
2023
83.8
3.10
72.2
6.60
InfoTS,
Luo et al 2023
84.1
2.71
73.8
5.07
FEAT
Kim et al. 2023
73.1
6.40
SelfDis
P
Pieper et al. (2023)
83.2
3.82
71.8
4.24
Floss Yang al. 2023
84.9
73.9
SoftCL Lee et al.
20244)
85.0
75.1
SMDE Zhang
2024
72.7
6.74
Times RI. (Lau & Chen
2024
84.5
75.2
AutoTCL (Zheng al.
2024]
75.1
4.90
TimeHUT
86.4
2.02
77.3
2.93
Classification. The results of experiments classification are presented in Table 1 where we observe that the proposed TimellUT model outperforms SOTA models for both univariate UCR and multivariate UEA datasets. We achieve an average accuracy and rank of 86.4% and 2.02 for UCR and 77.3% and 2.17 for UEA, respectively. The full classification results for all individual datasets within UCR and UEA are presented in Appendix A (Tables A1 A2 and A3). These results show the efficacy of hicrarchical uniformity-tolernnce latent balancing for classification. Note that some models are specifically designed for either classification or anomaly detection. As result, results for both tasks were not available for all models. We also present UMAP visualizations for the learned representations by our model in Appendix
Table TineHUT performance compared supervised models.
Models
TimeHUT HC2
DrCIF MultiRocket ROCKET HCI
UEA Acc
0.761
0.748
0.732
0.721
0.711
UCR Acc
0.872
0.876
0.868
0.853
0.865
Note that the models in Table D are all self-supervised, similar to our proposed TimeHUT. In Table 2 we extend the comparisons to fully supervised models, namely HIVE-COTE 1.0 (HC1), DrCIF, ROCKET. and HIVE-COTE 2.0 (HC2), as reported in Renault et. al. (2023) and Middlehurst et al. (2021) These comparisons are conducted on 26 UEA datasets (Middlehurst et al. 2021 and 112 UCR datasets (Renault
ct al. 2023 The complete results for all individual datasets on 26 UEA datasets are provided in the Table 3
This experiment demonstrates that, despite our proposed TimeHUT model being trained without labels, it outperforms other models the UEA datasets and achieves competitive performance the UCR datasets.

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Published in Transactions on Machine Learning Research (10/2025)
Table 3: Performance comparison TimeHUT, HC2, DrCIF, and ROCKET across UEA datasets.
Accuracy
Dataset
TUmeHUT
HC2
DrCIF
ROCKET
HC1
0.993
0.993
0.980
0.997
0.990
AtrialFibrillaionn
0.533
0.267
0.333
0.200
0.133
BasicMotions
1.000
1.000
1.000
1.000
1.000
Cricket
1.000
1.000
0.986
1.000
0.986
DuckDuckGeese
0.600
0.560
0.5-10
0.500
0.480
ERing
0.926
0.989
0.993
0.985
0.970
EigenWorms
0.962
0.947
0.924
0.908
0.634
Epilepsy
0.964
1.000
0.978
0.978
1.000
ElhanolConeenttatio
0.373
0.772
0.692
0.445
0.791
FaceDetection
0.551
0.660
0.620
0.648
0.656
FingerMovements
0.642
0.530
0.600
0.540
0.550
HandMovement Direction
0.432
0.473
0.527
0.459
0.446
Handwriting
0.582
0.548
0.346
0.567
0.482
Heartbeat
0,810
0.732
0.790
0.741
0.722
LSST
0.586
0.643
0.556
0.622
0.575
Libras
0.883
0.933
0.894
0.900
0.900
MotorImagery
0.660
0.540
0.440
0.510
0.610
NATOPS
0.966
0.894
0.844
0.883
0.889
PEMS-SF
0.855
1.000
1.000
0.821
0.983
PenDigits
0.989
0.979
0.977
0.985
0.934
PhonemeSpectra
0,243
0.290
0.308
0.259
0.321
RacketSports
0.921
0.908
0.901
0.914
0.888
SelleegulationSCPII
0.860
0.891
0.877
0.843
0.853
SelleegllationSCP2
0.583
0.500
0.494
0.494
0.461
StandWalkJump
0.960
0.467
0.533
0.600
0.333
0.916
0.928
0.909
0.931
0.891
Average Accuracy
0.761
0.748
0.732
0.721
0.711
Average Rank
2.60
2.37
3.27
3.10
3.67
Anomaly detection. Table presents the results for anomaly detection on Yahoo and KPI datasets. The experiments are conducted under two distinct settings following Yue et al. (2022). Lee ct al. 2024). and Liu & Chen (2024). In the normal setling, each dataset is divided into two halves based on the lime order, with one half used for training and the other for evaluation. In the cold-start setting, models are pre-trained on the FordA dataset from the UCR and subsequently evaluated on cach individual dataset. The anomaly score is calculated as the LI distance between two representations encoded from both masked and unmasked inputs, as explained in prior works (Yue et al. 2022 Lee et al. 2024 Liu & Chen 2024). We observe that our proposed TimeHUT model achieves state-of thethe-rrtttttt performance terms of F1 for both datasets under the normal setting, with scores of 0. 7.755 and 0.721, respectively. Furthermore, TimeHUT attains an F1 score of 0.779 for the Yahoo dataset in the cold-start setting, demonstrating higher performance than prior works. For the KPI dataset in the cold-start setting, TimeHUUT secures the second-bes F1 score of 0.691.
Forecasting. Finally, to further evaluate our method, we present the mean squared error (MSE) of fore- easting models including our proposed TimeHUT on the univariate ETTh, and ETThy datasets across five prediction horizons (H 24, 48, 168, 336, 720) Appendix (Table A4 which highlights the effectiveness of proposed TimeHUT.
Ablation. We perform ablation studies to analyze the impact of each key module in TimeHUT on 128 UCR and 30 UEA datascts, using accuracy and AUPRC metrics. First we remove the Seter and replace it with similar loss where 7 = 1, effectively turning off the temperature scheduler. Next, we remove the Sete altogether. We then ablate Lnter and only use the LiverSch. And finally we remove both losses and only use HierSSch with 7 The results for this study are presented in Table where we observe that each loss term used to train TimcHUT has a meaningful impact on the final outcome. Moreover, we see a positive impact for using the temperature scheduler instead of constant temperature of 1.
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Table Performance of TimeHUT on anomaly detection.
Yahoo
KPI
Model
F1
Prec.
Rec.
Fi
Prec.
Rec.
SPOT Siffer et al. 2017)
0.338
0.269
0.454
0.217
0.786
0.126
DSPOT Siife et a.. 2017
0.316
0.241
0.458
0.521
0.623
0.447
DONUT Xu et al.
2018
0.026
0.013
0.825
0.347
0.371
0.326
SR (Ren et al. 2019
0.563
0.451
0.747
0.622
0.647
0.598
TS2Vec Yue et al.
2022
0.745
0.729
0.762
0.677
0.929
0.533
SoftCLT Lee al.
2024
0.742
0.722
0.765
0.701
0.916
0.570
TimesURA (Luu & Chen
2024
0.749
0.748
0.750
0.688
0.925
0.546
TimeHUT
0.755
0.746
0.764
0.721
0.899
0.602
Cold-start:
FFT (Rasheed et al. 2009
0.291
0.202
0.517
0.538
0.478
0.615
Twitter-D (Valis al.
2014
0.245
0.166
0.462
0.430
0.411
0.276
Luminol [LinkedIn] 2018
0.388
0.254
0.818
0.571
0.478
0.697
(Ren et al. 2019
0.529
0.404
0.765
0.666
0.670
0.697
TS2Vec Yue et al.
2022
0.726
0.692
0.763
0.676
0.907
0.540
SoftCTT Lee al.
2024
0.762
0.753
0.773
0.707
0.921
0.574
TimeHUT
0.779
0.793
0.765
0.691
0.894
0.563
Table 5: Ablation experiments for the key components of TimeHUT.
128 UCR datasets
30 UEA
datasets
AntierAng
Litiersch
LHieeSch(T=1]
Acc (%)
AUPRC
Acc (%)
AUPRC
86.42
86.23
76.24
74.73
84.64
85.36
74.29
72.55
83.36
83.03
73.71
73.57
84.99
85.31
73.22
72.36
83.00
84.21
71.20
70.74
Sensitivity to hyperparameters. We investigate the effect of the and in Equation on model performance, and present four examples in Figure 2 where we plot the accuracy vs. these parameters for different datasets from UCR and UEA. We observe that while the choice of hyperparameters can expectedly have an impact on the final results, the sensitivity of our model to the optimal set of parameters generally 4%. The detailed hyperparameters for each dataset are presented the Appendix D (Tables A5 A8
Component-wise computational analysis. We also analyze the computational cost of each component of TimeHUT model using the Chinatown dataset in Table 0 The training time overhead yields +2.03% accuracy gain, demonstrating a favorable cost-benefit trade-off.
Table 6: Component-wise computational analysis.
Scenario
Acc Training Time(s) Peak GPU Memory (MB) HIF.OPs/Epoch
Baseline
0.9651
9.36
1330.6
51.2
HHier Angrastagsn
0.9823
11.09
1315.9
60.5
EnierAngreoper Angrepprrd
0.9795
12.34
1341.6
62.7
HHier Ang
0.9828
12.49
1367.6
65.3
HierSch
0.9815
9.53
1332.2
58.5
Hier Aug HierSch
0.9854
12.95
1398.4
69.1
Comparison with different temperature schedulers. We compare various temperature scheduling strategics on the Chinatown and AtriatFibrillation datasots. The base hyperparameters for all schedulers are Tmin 0.1, Tmar 0.75, and Tmaz 10. As shown in Table our Seerarhhial-Schedulle achieves the best accuracy-efficiency trade-off.
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Published in Transactions on Machine Learning Research (10/2025)
Table 7: Comparison of different temperature schedulers on UCR Chinatown and CEA AtrialFibrillationn datasets reporting accuracy, training time, and peak GPU memory values.
Chinatown
AlrialFibrillation
Scheduler
HyperParams
Acc
Time(s)
GPU(MB)
Acc.
Time(s)
GPU(MB)
Exponential
Decay=0.95
0.980
12.83
1376.8
0.417
20.32
3081.4
Sigmoid
Steep=1
0.979
14.11
1421.5
0.412
20.31
3901.2
Warmup-Cosine
Warmup-2
0.962
12.43
1414.9
0.407
19.76
2755.3
Sawtooth-Cyclis
Cycle=T/8
0.979
12.48
1392.1
0.413
19.93
3551.6
Logarithmic
Offset=1
0.980
12.85
1366.2
0.425
20.18
3405.1
Step-Decay
0am
0.977
12.41
1406.3
0.468
19.89
3385.9
Gosine-Restarbe
Period=5
0.974
12.58
1387.7
0.446
20.57
3249.2
Hyperbolie-Taugee Tangent
Steep=2
0.973
12.43
1393.8
0.467
20.72
3251.1
Beerarchical-Schedullee
0.985
12.95
1398.4
0.534
20.13
3171.7
Computational efficiency analysis. We provide an efficiency analysis comparing TimeHUT with other baselines on the UCR Chinatown dataset using NVIDIA RTX 3090. As shown in Table g TimeHUT's training time (12.95s) compared to TS2Vec (9.36s) is justified by accuracy improvements from 0.965 to 0.985. On this particular dataset, TS-TCC shows comparable results to TimeHUT; however, according to Table I1 TSC'''ss average accuracies on 125 UCR and 29 UEA are (75.7, 68.2), which are lower than TimeHUT (86.4, 77.3).
Table 8: Efficiency analysis of TimeHUT vs. other baselines.
Model
Acc
F1-Score
GPU Mem(MB)
PITTOPs/Eppoee Training Tsme(s)
TF-C (Liu et
2023
0.8663
0.8514
1395.4
72.4
10.15
MF-CLR Duan al.
2024
0.8861
0.8726
1376.6
52.3
9.55
CPC
Oord al.
2018
0.9301
0.9181
1377.4
120.2
14.2
T-Loss
|Fancesch et al.
2019
0.9511
0.8191
1594.4
56.3
164.3
TS2
Yue et al
2022
0.9651
0.9684
1330.6
51.2
9.36
CoST Woo et al.
2022
0.9704
0.9609
1420.6
240.6
19.58
TNC
Tonekaboni et al.
2021
0.9772
0.9472
1414.1
192.1
35.91
Times URL (Lu & Chen
2024
0.9744
0.9756
1392.7
113.4
22.62
TS-TCC (Eldele et al.
2021
0.9831
0.9784
1399.4
70.4
13.14
TimeHUT
0.9854
0.9826
1398.4
69.1
12.95
Wilcoxon rank-sum statistical test. Following Ismail- Fawaz et al. (2023). we obtain the difference in av- crage accuracies the 30 UEA datasets for cach pair models. We then count how often Model achieves higher accuracy than Model B (wins), how oflen they are equal (draws), and how often Model achieves higher accuracy (Josses). Moreover, we calculate the statistical significance of the difference between the two models by performing the Wilcoxon signed-rank test across the 30 datascts. The p-values from the Wilcoxon signed-rank test are calculated to assess whether there is statistically significant difference between the me- dian of paired dataset (e.g., < 0.05). We show the Mean-Differena (MD), Wins/Dras /ossses (W/D/L). and Wilcoxon p-value in Table The complete results for all individual models are provided in the Appendix
(Tables A9 and A10
Uniformity vs. tolerance trade-off analysis. Figure presents the comparison of uniformity and tolerance across multiple datasets (e.g., Chinatown, Computers, Dog5Loop Weekeod,,Weee,,,.e. and HouseTTentyy for three different methods: Random initialization, TS2Vec, and TimeHUT. We observe trade-off between uniformity and tolerance where methods with higher uniformity values (e.g., TS2Vec) tend to exhibit lower tolerance values. This occurs because spreading embeddings in the latent space can inadvertently separate similar data points. In contrast, Random initialization shows higher tolerance but lower uniformity, as preserving local relationships may result in clustering within the embedding space. This trade-off highlights the need for a balance between uniformity and tolerance to produce embeddings that generalize effectively. Notably, our TimeHUT model archives balanced trade-off between uniformity and tolerance across most datasets.
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Published in Transactions on Machine Learning Research (10/2025)
97.0
98.0
96.8
AcC
Acc
96.5
97.5
96.2
97.0
96.0
95.8
0.0
2.0
0.0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0
5
0.5
1.0
Ω
1.5
2.0
2.5
3.0
Ct
94.0
94.0
93.0
Acc
93.0
Acc
92.0
92.0
91.0
91.0
2.5
2.0
0.0
0.5
1.5
0.5
1.5
1.0
1.5
2.0
2.5
3
2.0
5
1.0
1.5
2.0
2.5
C
3.0
3.0
Figure 2: The accuracy of TimeHUT versus different values of o; and 6,, on the "Star Light Curves" dataset
"None-Invasive (top left), "China Town" dataset (top right), "Ford-A" dataset (bottom left), and "None- Invasive Fetal ECG Thorax 1" dataset (bottom right).
Performance comparison of various metrics for TimeHUT, including Mean Difference (MD), Win- 8/ s/Draws/Lssses (W/D/L), and statistical significance (p-value).
Table 9:
TimeHUT vs.
MD
W/D/L
p-value
AuL
(Zheng et al.
2024
0.02
20/4/6
0.0188
SelfDis
Pieper et
2023
0.02
18/3/9
0.1073
InfoTS.
Luo et al.
2023
0.03
17/5/8
0.0091
FEAT
Kim al.
2023
0.04
25/2/3
<le-4
SMDE
Zhang et al.
2024
0.04
23/2/5
0.001
InfoTS
Luo
2023)
0.05
21/2/7
0.0002
TS2Vec
Yue et a.l
2022
0.06
25/4/1
<le-
TNC Tonekabooni
al.
2021
0.09
28/0/2
<le4
TS-TCC
Eldele et al. 2021
0.09
28/1/1
<led
T- Losss
Franceschi el al.
2019
0.10
25/2/3
<le4
TST
Zerveas al. 202
0.15
28/1/1
<le-
MCL.
Wickstram al.
2022
0.16
30/0/0
<le-d
TF-C
Lau et al.
2023
0.35
29/0/1
<led
Failure cases. We identify scenarios where TimeHUT encounters limitations. For short sequences (T 20). the hicrarchical contrasting has insufficient temporal context, resulting in suboptimal performance. In the case of very long sequences (T> > 10. 000), the quadratic complexity with respect to sequence length becomes computationally prohibitive. On the other hand, when only limited number of samples per class
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Published in Transactions on Machine Learning Research (10/2025)
61873
Uniformitt
Tolerance
TimettUT
Oiiatron
Hone leytir
Olaepee
Dospoett
Dataset
Dataset
Figure 3: Uniformity and tolerance values for different datasets.
available, the angular margins may become overly restrictive, potentially overseparating natural clusters. In our experiments, TimeHUT showed reduced improvements on datasets such as Screen Type (accuracy: 0.403) and PhonemeSpectra (accuracy: 0.243), which have either very short sequences or complex multivariate distributions where angular margins may overseparate natural clusters.
6 Conclusions
In this work, we propose TimeHUT to learn effective time-series representations. Our proposed method uses two hierarchical loss terms to strike a balance between uniformity and tolerance in the embedding space with the goal of maximizing performance. Our method's use of hierarchical instance-wise and temporal angular margin loss and hierarchical temperature scheduling effectively captures temporal dependencies and distinguishes between positive and negative sequence pairs. The extensive experimentation conducted across hundreds of datasets demonstrated the strong performance of TimeHUT w.r.t. existing methods. Scnsitivity and ablation studies are conducted to assess the impact of different components and hyperparameters.
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Published in Transactions on Machine Learning Research (10/2025)
Appendix
A Additional results
Tables A1 and A2 present the full classification results of our method for all the individual datasets 128
UCR datasets, compared to related prior works, including TST Zerveas et al.
2021). DTW (Franceschi
et al. 2019), TS-TCC (Eldele et al. 2202I,, TNC (Tonekaboni et al. 2021]. T-Loss (Franceschi et al. 2019
Ti-MAE (Li et al., 2023). TS2Vec (Yue et al., 2022), SelfDis (Pieper et al. 2023). FEAT (Kim et al. 2028
and InfoTS (Tuo et a 2023). Among these baselines, TimeHUT achieves the best accuracy on average.
Besides, the full results of TimeHUT for 30 multivariate datasets in the UEA archive are also provided in
Table A3 including models such AuloTCL (Zheng al. 2024). SMDE (Zhang et al. 2024), TF-C (Liu
et al. 2023 and MCL (Wickstrom al.) 2022), where TimeHUT provides the best average accuracy and
average rank. Note that these tables do not contain certain works such as Floss (Yang et al. 2023). SoftCI.T
[eee et al. 2024), and URL (Liu & Chen 2024 given that the breakdown results for all the datasets are not available.
B Related works on anomaly detection
A variety of methods have been developed to address anomaly detection in time series data, each offering unique approaches lo identilying and analyzing outliers in streaming and stalic datasets. SPOT (Siller et al. 2017) is an outlier detection method for streaming univariate time series. It leverages Extreme Value Theory and is not based on preset thresholds or predefined data distributions. It requires only a single parameter to manage the number of false positives. DONUT (Xu et al.) 2018) is an unsupervised anomaly detection algorithm that uses a variational autoencoder. SR (Ren et al. 2019) is designed for time-series anomaly detection, utilizing the spectral residual model in combination with a Convolutional Neural Network. The SR model, originally used in visual saliency detection, enhances the algorithm's performance when paired with CNN. FFT (Rasheed et al. 2009) utilizes the fast Fourier transform to identify regions with high- freuffrey changes. Twitter-AD (Vallis et al.) 2014) automatically detects long-term anomalies by recognizing the irregularities in application and system metrics of cloud data. Luminol (LinkedIn) 2018) is a Python library for time series data analysis, offering two primary features: anomaly detection and anomaly correlation to analyze the potential causes of anomalies. TS2Vec (Zerveas et al. 2021) employs temporal- and instance- wise contrastive losses on two augmented subseries time-serics to capture multi-scale contextual details for anomaly detection. SLf (Lee et al.; 2024) introduces soft assignments to sample pairs for hierarchical contrastive losses to capture the inter- and intra-temporal relationships in the data space. TimesURR (Liu & grquuney-temporal augmentations to preserve the temporal propertics. It constructs hard negative pairs to guide better contrastive learning along with the time reconstruction module to jointly optimize the model for anomaly detection.
Chen 2024) proposes
C Forecasting.
Table A4 presents the mean squared error (MSE) of forecasting models including our proposed TimeHUT
the univariate ETTh, and ETTh; datasets across five prediction horizons (H = 24, 48, 168, 336, 720). TimcHUT consistently achieves the lowest MSE at every horizon and on both datasets (c.g., 0.037 vs. 0.039 for H = 24 on ETTh, and 0.090 vs. 0.090 for H = 24 on ETTh2), with the performance at longer horizons (e.g., 0.115 vs. 0.154 at Н = 336 on ETTh; and 0.195 vs. 0.213 on ETTh2), demonstrating its ability to capture both short- and long-term dependencics. Averagod over all ten configurations, TimcHUT attains an MSE of 0.125, an 8% reduction relative the TS2Vec method, which highlights the effectiveness of our proposed TimeHUT method across multiple scales.
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Published in Transactions on Machine Learning Research (10/2025)
D Hyperparameters
We present the values of hyperparameters including Ci Ct, Tminy Tmaz: and Tmaz for the TimeHUT model across different datasets. Specifically, these values are detailed in Tables A5 and A6 for 128 UCR datasets, Table A7 for 30 UEA datasets, and in Table A8 for anomaly detection.
E UMAP visualization
we present UMAP visualizations for the learned time-series representations by our model. The top-left and bottom-left figures display the representations generated by TS2Voc for the UEA "Basic Motion" datasel and the UCR "Dodger Loop Weekend" dataset, respectively. On the right, we show the representations learned by TimeHUT. Each color corresponds a different class. We observe that the learned reprosentations on the right are more distinctly separated and form tighter clusters.
In Figure A1
10
10
%
Figure A1: UMAP visualization of the learned representations by TimcHUT (right) vs. TS2Vec (left) on "Basic Motion" (top row) and "Dodger Loop Weekend" (bottom row) datasets.
19

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Published in Transactions on Machine Learning Research (10/2025)
Table A1: Performance of TUmeHUT on the 128 individual datasets from UCR (Part 1).
Datuset
TimelIU
InfoTS,
InfoTS
SelfDis
TS2Vec
Ti-MAE
T-Loss
TNC
TS-TOC
DTW
TST
ACSFI
0.920
0,850
0.850
0.830
0.900
0.820
0.900
0.730
0.730
0.610
0.760
Adiae
0.783
0.735
0.788
0.788
0.762
0.788
0.675
0.726
0.767
0.604
0.550
AllGestueWilmotee
0.796
0.560
0,630
0.776
0.777
0,633
0.763
0,703
0.697
0.716
0.259
0.813
0.623
0.686
0.777
0.793
0.082
0.726
0.699
0.741
0.729
0.423
AllGestureWinntee
0.793
0.633
0.629
0.749
0.716
0.671
0.723
0.646
0,689
0.613
0.447
ArrowHead
0.863
0.874
0.874
0.857
0.857
0.874
0.766
0.703
0.737
0.703
0.771
BME
1.000
1.000
1,000
1.000
0.993
1.000
0.993
0.973
0.933
0.900
0.700
Beef
0.833
0,900
0.833
0.667
0.767
0.900
0.667
0.733
0.600
0.633
0.500
BeetlePly
0.900
0,950
0.950
0.950
0.900
0.900
0.800
0.850
0.800
0.700
1.000
BirdChieken
1.000
0,850
0.900
0.800
0.800
1.000
0.850
0.750
0,650
0.750
0.650
CBF
1,000
1.000
0.999
0.997
1.000
1,000
0.983
0.983
0.998
0.997
0.838
Car
0.933
0.900
0.883
0.850
0.833
0.867
0.833
0.683 0.583
0.733
0.550
Chinstown
0.985
0.985
0.988
0.965
0.965
0.985
0.951
0.977 0,983
0.957
0.936
Coneettaion
0.842
0.825
0.822
0.754
0.832
0.725
0.749
0. 7.7
0.753
0.648
0.562
CinCECGTore
0.848
0.896
0.928
0.654
0.827
0.971
0.713
0. 666
0.671
0.651
0.508
Coffee
1.000
1.000
1.000
1.000
1.000
1,000
1. 1.000
1.000 1.000
1.000
0.821
Computers
0.716
0.720
0.748
0.772
0,600
0.780
0.661
0. 6.6911 0.704
0,700
0.696
Cricket
0.821
0.780
0.774
0.767
0.782
0.674
0.713
0.623
0.731
0.754
0.385
Yricket
0.800
0.774
0.774
0.751
0.749
0.659
0.728
0.597 0.718
0.744
0.467
CricketZ
0.818
0.792
0.787
0.754
0.792
0.718
0.708
0.713
0.754
0.403
Crop
0.768
0.766
0.766
0.763
0.756
0.751
0.722
0.738
0.742
0.665
0.710
DistounSuceedduttion
0.990
0.997
0.997
0.987
0.984
0.984
0.981
0. 0.993
0.977
0.967
0.961
DistalPhalannnOntiinneeee
0.734
0.763
0,763
0.755
0.727
0.763
0.727
0.741
0,755
0.770
0.741
DistalPhalansOttline Interrerr
0.793
0.808
0.801
0.804
0.761
0.793
0.775
0.754
0.754
0.717
0.728
DistalPhalanx I'W
0.734
0.720
0.727
0.748
0.698
0.727
0.676
0.669
0.676
0.580
0.568
ECG200
0.930
0,950
0.930
0.940
0.920
0.910
0.940
0.830
0.880
0.770
0.830
BCG5000
0.945
0.945
0.945
0.940
0.935
0.942
0.933
93937
0.9-1
0.924
0.928
ECGFiveDays
1.000
1.000
1.000
1.000
1.000
0.988
1.000
0.999
0.878
0.768
0.763
BOGHoricontaligqaal
0.591
0,577
0.572
0.608
0.539
0.558
0.605
0. 1/4
0.401
0.503
0.373
0.533
0.459
0.459
0.475
0.503
0.547
0.434
0.392
0.376
0.448
0.298
Earthquakes
0.827
0.821
0.821
0.748
0.748
0.748
0.748
0.748
0.748
0.719
0.748
EleetriDDevices
0.715
0.691
0.702
0.701
0.721
0.685
0.707
7.700
0.686
0.602
0.676
Ethanoll Lvvel
0.588
0.710
0.712
0.670
0.468
0.744
0.382
0.424
0.486
0.276
0 0.260
FaceAll
0.914
0.929
0.929
0.873
0.771
0.850
0.786
0. 766
0.813
0.808
0.504
FaceFour
0.955
0.861
0.818
0.795
0.932
0.875
0.920
0. 0.659
0.773
0. 0,830
0.511
FacesUCR
0.915
0.917
0.913
0.90S
0.921
0.806
0.884
0.789
0.863
0.905
0.5413
Words
0.802
0.809
0.793
0.769
0.771
0.787
0.732
0.653
0.653
0.690 0.525
Fish
0.966
0.949
0.937
0.937
0.926
0.897
0.891
0.817
0.817
0.920
0.720
FordA
0.936
0.925
0.915
0.930
0.936
0.818
0.928
0.930
0.555 0.568
RordB
0.817
0.795
0.785
0.790
0.794
0.652
0.793
0.733 0.815
0.620
0.507
Peesae
0.994
0.998
0.996
0.998
0.986
0.987
0.956
0
0.989
0.899
0.922
PrezzeSSmalTrain
0.988
0.991
0.988
0,980
0.870
0.959
0.933
0. 982
0.979
0.753
0. 0.920
Fungi
1.000
0.866
0.946
0.989
0.957
0.968
1. 1.000
0.527
0.753
0.839
0.366
GestureMdAAia1
0,700
0.592
0.592
0.651
0.608
0.662
0.608
0. 0.131 0,369
0.569
0.208
GestureMidAAirD22
0.608
0.459
0.492
0.631
0.469
0.546
0.546
0.362
0.254
0.608
0.138
GestureMidAArrSS
0.438
0.323
0.315
0.331
0.292
0.400
0.285
0.292 0.177
0.323
0.154
GesturePehhlee21
0.918
0.895
0.802
0.738
0.930
0.901
0.919
0.378
0.395
0.791
0.500
GestuePebble22
0.943
0.905
0.842
0.677
0.873
0.918
0.899
0.316
0.430
0.671
0.380
GunPoint
0.993
1.000
1.000
1.000
0.950
0.993
0.980
0.967 0.993
0.907
0.827
GunPoint
0.997
0.997
1.000
0.994
0.987
0.994
0.994
0.984
0.994
0.918
0.991
GunPoint Feeeeesseeeeeee
1.000
1.000
1,000
1.000
1.000
0.997
0.997
0. 0.991 0.997
0.997
1.000
Young
1.000
1,000
1.000
1.000
1.000
1.000
1 1.000
1.000
1.000
0.838
1.000
Ham
0.781
0.848
0.838
0.733
0.714
0.800
0.724
0. 0.752
0.743
0.467
0.524
HondOOtlinee
0.916
0.946
0.916
0.916
0.922
0.919
0.922
0,930
0.724
0.881
0.735
Haptirs
0.549
0.545
0.546
0.464
0.526
0.484
0.4910
0.474
0.396
0.377
0.357
Herring
0.703
0.703
0.656
0.641
0.641
0.656
0.594
0.594
0.594
0.531
0.594
HouseTwently
0.983
0.941
0.924
0.941
0.916
0.941
0.933
0.782
0.790
0.924
0.815
InlineSkate
0.156
0,420
0.121
0.171
0.415
0.350
0.371
0.378
0.3-17
0
0. 0,257
Insect Tegglaarrraiii Train
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
0.872
1.000
Insect LLsectEGGSuut Ennlaallia
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
0.735
1.000
Insect WrseeetiinhestSonnd
0.611
0.661
0.639
0.590
0.630
0.639
0.597
0.5-19
0.415
0.355
0.266
Ital TaalyPowerDemmn
0.971
0.971
0.966
0.963
0.925
0.967
0.954
0.928
0.955
0.950
0.845
0.885
0.851
0.853
0.861
0.845
0.787
0.789
0.776
0,848
0.795
0.595
Lightning2
0.934
0.934
0.934
0.902
0.869
0.836
0.860
0. 16969
0.836
0.869
0.705
Lightning?
0.877
0.863
0.877
0.808
0.863
0.808
0.795
0.767
0.685
0.726
0.411
Mallat
0.909
0.967
0.974
0.950
0.911
0.956
0.951
0.871
0.922
0.934
0.713
20

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Published in Transactions on Machine Learning Research (10/2025)
Table A2: Performance of TimeHUT on the 128 individual datasets from UCR (Part 2).
Dataset
TimelIUT
InfoTS,
InfoTS
SelfDis
TS2Vec
Ti-MAE
'T-oss
TNC
TS-TCC
DTW
TST
Meat
0,967
0.967
0.967
0.967
0.950
0.967
0.950
0.917
0.883
0.933
0,900
Modicallmaages
0.828
0.920
0.820
0.803
0.789
0.771
0.750
0.754
0.747
0.737
0.632
MelbourrePedestrian
0.964
0.964
0.962
0.958
0.959
0.949
0.944
0.942
0.949
0.791
0.741
Middle Pww.annOOttinnnggoooeeoooo
0.662
0.662
0.662
0.641
0.636
0.675
0.656
0.643
0.630
0.500
0.617
MinkdePPhalanss WwwalnnnOOllinerreeee
0.869
0.859
0.859
0.852
0.838
0.811
0.825
0.818 0.818
0.698
0.753
0.617
0.636
0.617
0.623
0.584
0.623
0.591
0.571 0.610
0.506
0.506
MixedSSuapesRegulel Regulaz Train
0.929
0.940
0.935
0.922
0.917
0.922
0.903
0.911 0.855
0.842
0.879
MixedStapesSnallTTiin
0.894
0.892
0.887
0.877
0.961
0.875
0.860
0,813 0.735
0,780
0.828
MoteStrain
0.925
0.873
0.873
0.880
0.861
0.913
0.851
0.825 0.843
0.835
0.768
0
0.911
0.911
0.924
0,930
0
0.878
0.898
0.898
0,790
0.471
Non Www.rasivveFetalECCCCTTToe
0,953
0.943
0.944
0.930
0.938
0.9:38
0.919
0.912 0.913
0.865
0.832
OSULeal
0.864
0.760
0.760
0.806
0.851
0.736
0.760
0.728 0.723
0.591
0.545
OliveOll
0,933
0.933
0.933
0.567
0,900
0,933
0.867
0.833 0.800
0.833
0.800
PLAID
0.553
0.356
0.355
U.444
0.561
0.458
0.555
0.495 0.445
0.840
0.419
PhalangeeulliusCoooeee
0.819
0.826
0.826
0.834
0.809
0.772
0.784
0.787 0.804
0.728
0.773
Phoneme
0.320
0.272
0.281
0.266
0.312
0,229
0,276
0.180 0.242
0.228
0.139
PickupGesture WitmoteZ
0,940
0.820
0.820
0,700
0,820
0,8-10
0.740
0.620 0.600
0,660
0.240
Pigg SinAAirwe AerAnwyyrresssurr
0.817
0.433
0.432
0. 793
0.630
0.2440
0.510
0.413 0.380
0.106
0.120
PigArtPressure Pressure
0.971
0.820
0.830
0.904
0.966
0.760
0.928
0.808 0.524
0.245
0.774
PigCVP
0,928
0.654
0.653
0.889
0.312
0.750
0.758
0.619 0.615
0.151
0.596
Plane
1.000
1.000
1.000
1.000
1.000
1.000
0.990
1.000 1.000
1.000
0.933
Power
1.000
0.995
1.000
0,961
0.961
1.000
0.900
0.933 0.961
0.878
0.911
0.859
0.883
0.883
0,583
0.834
0.863
0.844
0.854 0.839
0.805
0.854
Proximal Caciinaalllaaaan Out
0.914
0.924
0.927
0.883
0.887
0.876
0.859
0.866 0.873
0.784
0.770
PhalaxTiP
0.8419
0.819
0.814
0.824
0.824
0.829
0.771
0.810 0.800
0.761
0.780
Refrigerrationeeviiss
0.645
0.624
0.624
0.571
0. 0.589
0.611
0.515
0.565 0.563
0.464
0.483
Rock
0,820
0.760
0.760
0.8-10
0,700
0.660
0.580
0,580 0.600
0,600
0.680
ScreeTType
0.483
0.510
0.493
01.48
0.411
0.579
0.416
0.509
0.419
0.397
0.419
HeugHandGendeerCo
0,973
0.939
0.914
0.900
0.963
0.838
0,890
0.882 0.837
0.802
0.725
Semglland Mallaanddooeenntt Ch2
0
0.833
0.836
0.713
0,960
0.700
0.789
0.593 0.613
0.584
0.420
Semn GemngHandSubjettCC
0.958
0.945
0.924
0.813
0.951
0.813
0.853
0.771 0.753
0.727
0.484
GeskuGGeetueWinmee
0,960
0.920
0.920
0,900
0.940
0,900
0.920
0.820 0.860
0.860
0.760
Shapelet
1.000
0.856
0.856
1.000
1.000
0.911
0.672
0.589 0.683
0.650
0.489
ShapesAAll
0
0.855
0.852
0.855
0.902
0.840
0.848
0.788 0.773
0.7G8
0.733
SmaalKKicchenApppiiane
0.768
0.773
0.773
0.699
0.731
0.7.1
0.677
0.725 0.691
0.643
0.592
SmoothSubspaee
0.987
1.000
1.000
1.000
0.9I0
0.5993
0.960
0.913 0.953
0.827
0.827
0.965
0.921
0.927
0.918
0.903
0.912
0.902
0.804 0.899
0.725
0.724
Sony SonyAAIBORoboSSurfeee
0.902
0.953
0.953
0.858
0.871
0.934
0.889
0.834 0.907
0.831
0.745
StarLightCurves
0.975
0.973
0.973
0.979
0.969
0.972
0.961
0.968
0.967
0.907
0.9:1
Strawberry
0. 0.968
0.978
0.978
0.978
0.962
0.970
0.954
0.951 0.965
0.941
0.916
SwedishLeal
0.946
0.954
0.950
0.962
0.941
0.938
0.914
0.880
0.923
0.792
0.738
Symbols
0.982
0.979
0.979
0.971
0.976
0.961
0. 0.963
0.885
0.916
0.950
0.786
SymtheticComtrol
1.000
1.000
1,000
1.000
0.987
0.993
0.987
1.000
0.990
0.999
0.490
ToeSegmeutationl
0.969
0.930
0.934
0.9417
0.917
0.890
0.939
0.864
0.930
0.772
0.807
ToeSegmentation2
0.946
0.923
0.915
0.908
0.892
0.908
0.900
0.831
0.877
0.838
0.615
Trace
1.000
1.000
1.000
1.000
1.000
1.000
0.990
1.000
1.000
1.000
1.000
TwoLeadECG
0.989
0.999
0.998
0.999
0.986
0.985
0.999
0.993
0.976
0.905
0.871
TwoPatterus
1.000
1.000
1.000
1.000
1.000
0.994
0.999
1.000 0.999
1.000
0.466
UMD
1.000
1.000
1.000
1.000
1.000
1.000
0. 0.993
0.993 0.986
0.993
0.910
UWaveGrsturel Jibrary All
0.947
0.966
0.967
0.878
0.930
0.956
0.896
0.903 0.692
0.892
0.475
WWweGestureLibrray
0.823
0.820
0.819
0.823
0.795
0.814
0.785
0.781
0.733
0.728
0.569
UWaveGesturel Library Y
0.736
0.745
0.736
0.762
0.719
0.736
0.710
0.697
0.641
0.634
0.348
UWaveGrssuueLibbrrryr
0.771
0.768
0.768
0.769
0.770
0.749
0.757
0.721
0.690
0.658
0.635
Wafer
0.999
0.999
0.998
0.998
0.998
0.996
0.992
0.991
0.991
0.980
0.991
Wine
0.907
0.963
0.963
U.944
0.87U
U.9K07
0.815
0.759
0.778
0.574
0.500
WordSynonyms
0.723
0.715
0.704
0.699
0.676
0.705
0.691
0.630
0.531
0.649
0.422
Worms
0.818
0.766
0.753
0.792
0.701
0.779
0.727
0.623 0.753
0.581
0.455
Worms TwoClass
0.883
0.818
0.857
0.844
0.805
0.792
0.792
0.727
0.758
0.623
0.584
Yoga
0.903
0.937
0.869
0.872
0.887
0.834
0.837
0.812
0.791
0.837
0.830
DosggerLoopDay
0.675
0.675
0.675
0.613
0.562
0.613
0.500
0.200
DodgerLoopGamee
0.920
0.971
0.9-12
0.913
0.841
0.739
0.877
0.696
Dodger Werkend
0.964
0.986
0.986
0.978
0.966
0.978
0.949
0.732
On the first detasets:
Average Accuracy
0.864
0.841
0.838
0.832
0.830
0.823
0.806
0.761
0.757
0.727
0.641
Average Rank
2.020
2.710
3.100
3.820
1.780
4.770
6.310
7,590
7,500
8.720
9.790
21

---

Published in Transactions on Machine Learning Research (10/2025)
Table A3: Performance of TimeHUT on the 30 individual datasets from UEA.
Dataset
TimeHT
AutoTCL
SellDis
InfoTS,
FEAT
SMDE
InfoT'S
Tee
TNC
TS-TCC
T-Loss
DTW
TST
MCL
TF-C
ArtSeulary Wordiecooiitionn
0.933
0.988
0.91X)
0.553
0.991
0.963
0.987
0.988
0.973
0.953
0.943
0.987
0.977
0.963
0.263
AtrialFibeillaion
0.533
0.467
0.267
0.267
0.293
0.200
0,200
0.200
0.133
0.267
0.133
0.067
0,400
0.200
BasicMotions
1.000
1.000
0.925
1.000
1,000
0.975
0.975
0.975
0.975
1,000
1.000
0.975
0.975
0.700
0.850
Character Souncctrrimjjccoriiss Trajectories
0.997
0.976
0.994
0.987
0.993
0.992
0.974
0.995
0.967
0.985
0.993
0.989
0.975
0.938
0.061
Cricket
1.000
1.000
1.000
1,000
0.969
1,000
0.986
0.972
0.958
0.917
0.972
1.000
1.000
0.861
0.263
Geeeee
0.600
0.700
0.480
106000
0.564
0,600
0,5:10
0.680
0.460
0.350
0.650
0.600
0.620
0,160
0.220
ElgenWorms
0.962
0.901
0.931
0.748
0.811
0.839
0.733
0.841
0.340
0.779
0.840
0.618
0.748
0.526
0.366
Epilopey
0.964
0.978
0.986
0.903
0.948
0.971
0.971
0.964
0.957
0.957
0.971
0.964
0.949
0.695
0.526
ERing
0.926
0,944
0.919
0.953
0.896
0.900
0.940
0.874
0.852
0.904
0.133
0.3
0.874
0.825
0.500
EthanolConeetrraion
0.373
0.354
0.460
0.323
0.322
0.289
0.281
0.308
0.297
0.285
0.205
0.323
0.262
0.251
0.251
PeceDetection
0.551
0.581
0.541
0.525
0,530
0.548
0.531
0.501
0.536
0.344
0.513
0.529
0.534
0.517
0.510
Moveennossmentts
0.642
0.640
0.590
0.620
0.488
0.530
0,630
0,480
0.470
0.460
0.580
0.560
0.530
0.530
BesdMMooemenDDieetiiin
0.132
0,432
0.132
0.511
0.378
0,378
0,392
0.338
0.321
0:213
0.351
0,231
0,213
0,283
0.216
Handwrising
0.582
0.384
0.428
0.554
0.542
0.418
0.452
0.515
0.249
0.498
0.451
0.286
0.225
0.308
0.137
Heartbeat
0.810
0.785
0.751
0.771
0.746
0.746
0.722
0.683
0.746
0.751
0.741
0.717
0.746
0.634
0.722
JapaneseVowels
0.981
0,981
0.978
0,986
0.983
0,970
0
0.981
0.978
0.930
0.989
0.919
0,978
0,875
0,408
Libras
0.883
0.833
0.900
0.889
0,889
0.850
0.883
0.867
0.817
0.822
0,883
0.870
0.656
0.655
0.438
LSST
0.586
0.354
0.610
0.593
0.518
0.618
0.591
0.537
0.595
0.474
0.509
0.551
0.108
0.104
0.223
MosorImapery
0.060
0.570
0.520
0.610
0.562
0.620
0.630
0.510
0.500
0.610
0.580
0.500
0.500
0.450
0.500
NATOPS
0.966
0.944
0.972
0.939
0.921
0.916
0.933
0.928
0.911
0.822
0.917
0.883
0.850
0.733
0.550
PEMS-SF
0.855
0.838
0.884
0.757
0.874
0.509
0.751
0.682
0.890
0.734
0.676
0.711
0.740
0.849
0.346
PenDigits
0.987
0.989
0.989
0.991
0.989
0.979
0.974
0,981
0.560
0,973
0.708
PhonemeSpectrs
0.213
0,218
0.292
0. 22233
0.216
0.218
0,249
0.233
0.207
0:252
0.222
0,151
0,085
0,102
0.292
RacketSpports
0.921
0.914
0.908
0.829
0.898
0.842
0.855
0.855
0.776
0.816
0.855
0.803
0.800
0.776
0.644
SellRegulationSCP
0.800
0.891
0.800
0.887
0.852
0,804
0.874
0.812
0.799
0.823
0.843
0.775
0.754
0.774
0.658
SellTegglattionSCP2
0.583
0.578
0.600
0.572
0.562
0.577
0.578
0.578
0.550
0.533
0.539
0.539
0.550
0.505
0.500
SpolonArabic Digits
0.995
0.925
01.922
0.982
0,986
0.977
0.947
0.968
0.9131
0.970
0.905
0,963
0.923
0.961
0.104
StandWalkJump
0.600
0.533
0.533
0.167
0.533
0.533
0.467
0.467
0.400
0.333
0.333
0,200
0.267
0.266
0.333
0.919
0,929
0.906
0.759
0.753
0,875
0.575
0.565
Inseet InseetWingbes Wingbeat
0.406
0.488
0.449
0.472
0.462
0.553
0.470
0.466
0.469
0.264
0.156
0.105
0.276
0.100
On the first 29 datasets:
Average Accuracy
0.773
0.751
0.748
0.738
0.731
0.727
0.732
0.712
0.677
0.082
0.675
0.650
0.635
0.612
0.420
Averae Rank
2.93
4.90
4.24
5.07
6.40
6.74
6.60
7.55
10.38
9.47
8.76
10.02
10.97
12:45
13:53
Table A4: Forecasting Performance on ETThI and ETTh2 (MSE)
Datasel
TimeHUT
TS2Vee
lalormer
LogTrans
N-BEATS
TCN
TS- TCC
LSTTee
0.037
0.039
0.098
0.103
0.094
0.075
0.103
0.108
0.054
0.062
0.158
0.167
0.210
0.227
0.139
0.175
BTTh;
168
0.098
0.134
0.183
0.207
0.232
0.316
0.253
0.396
336
0.115
0.154
0.222
0.230
0.306
0.408
0.155
0.468
720
0.138
0.163
0,269
0.273
0.322
0.390
0.190
0,659
21
0.090
0.090
0.093
0.102
0.198
0.103
0.239
3.55.
48
0.122
0.124
0.155
0.169
0.234
0.142
0.260
3.190
ETTh
168
0.188
0.208
0.232
0.246
0.331
0:227
0.291
2.80 2,800
336
0.195
0.213
0.263
0.267
0.431
0.296
0.336
2.753
720
0.206
0.214
0.277
0.303
0.437
0.325
0.362
2.878
Average
0.125
0.136
0.198
0.213
0.290
0.227
0.234
1.299
22

---

Published in Transactions on Machine Learning Research (10/2025)
Table A5: Hyperparameters for the 128 individual datasets of UCR (Part 1).
TimelUUT
Dataset
Acc
AUPRC
m. Tmin
Finez maz
ACSF1
0.920
0.933
0.0 / 0.0
0.76
0.4
0.66
Adiac
0.783
0.774
0.47 / 2.68
0.7
0.01
0.62
10
CeGGsstrrWimmotee
0.796
0.790
10.0 / 0.48
0.77
0.2
0.77
32
AleGesture WiimoteY
0.817
7.99 0.0
0.61
0.5
WiimoteZ Wilmott
0.793
0.796
7.61 2.09
0.32
0.91
13
ArrowHeaad
0.863
0.914
2.34 1.27
0.76
0.62
BME
1.000
1.000
8.17
4.17
0.63
0.01
0.75
20
Beef
0.833
0.869
3.01
0.46
0.49
0.21
0.86
16
HeetleFly
0.900
0.971
8.69
7.46
0.76
0.09
0.91
26
BirdChicken
1.000
1.000
0.47
1.48 0.64
0.09
0.56
37
CDF
1.000
1.000
4.52 / 6.89
0.57
0.0
0.94
46
Car
0.933
0.935
0.0 / 0.24
0.8
0.2 0.56
Chinatown
0.985
0.999
10.0 7.53
0.3
0.05
0.76
Concentoonntnttaatioonn
0.842
0.827
1.28
0.69
CinCECGToro
0.848
0.910
5.28
7.62
0.44
0.57
Coffre
1,000
1.000
5.34
8:51
0.55
0.88
37
Computers
0.716
0.756
8.29
2.26
0.77
0.22
0.74
14
CricketX
0.821
0.829
0.0 10.0
0.65
0.17
0.6 38
Y
0.800
0.801
3.87
7.79
0.73
0.12 0.96
CricketZ
0.818
0.829
10.0 0.87 0.79
0.31
0.77 39
Crop
0.768
0.761
0.0 10.0 / 0.8
0.3
/ 0.63
DiatonsSiseReeuatiion
0.990
0.983
9.89 2.68 0.64
0.21
0.97
Distal CaaaaPaaaaaxuOtiinneeeeCoooooo
0.734
0.744
1.72 9.06 0.52
0.23
0.82
DistalPhalanxOun Oalaaxouttheerrreeee
0.793
0.841
5.15 2.37
0.31
DistalPhalanxTTVV
0.734
0.550
8.45 1.46
0.67
0.72
LodgerLLopDay
0.675
0.653
8.34 9.28
0.64
0.28
1.0
28
GomgerLoop
0.920
0.971
8.67
8.14
0,63
0.37
0.82
Dodgerl Loop Werkend
0.964
0.981
1.55
8.77
0.42
0.0
0.86
45
ECG200
0.930
0.982
2.48 5.82
0.39
0.1
0.5
37
ECG5000
0.945
0.561
0.0
10.0
0.45
0.0S
L.
18
ECGFiveDays
1.000
1.000
5.98
7.08
0.51
0.27
0.66
EOCHorizontaliguaall
0.594
0.625
5.48
1.4
0.62
0.22
0.54
17
FOGrerticalSignal
0.533
0.513
2.1
183
0.50
0.03
0.83
10
Earthquakes
0.622
4.31
0.46
EleetrieDDevies
0.745
0.650
0.84 0.0 0.3
0.16
0.57
EthanolLevel
0.588
0.559
0.16 1.36 0.65
0.08
0.51
FaceAll
0.914
0.905
10.0 / 0.0 0.41
0.15
0.5 50
FaceFour
0.955
0.990
6.0 / 5.73 0.62
0.03
0.84
FaceSUC
0.945
0.945
0.0 / 3.54 0.7
0.05
0,56
36
Fifty-Wrds
0.802
0.722
2.02 6.94
0.32
0.39
0.59
47
Fish
0.966
0.980
4.12 / 10.0
0.74
0.1
0.5
FordA
0.936
0.981
0.94 / 0.0
0.33
0.64
FordB
0.898
1.8 / 1.97 0.33
0.23
0.74
FreeseRRegulaTrain
0.994
0.996
1.32 4.69 0.76
FrelserSmalllrain
0.988
0.992
L.73 / 5.79
0.45
0.65
35
Fungi
1.000
1.000
1.85 3.17
0.69
0.1
0.67
29
Ar
0.700
0.719
0.0 7,82 0.32
0.31
0.53
24
GestureMiiAAis22
0.608
0.672
0.39 / 6.08 / 0.47
0.11
0.62
31
GestureMidAirD3
0.438
0.503
0.36 3.72
0.79
0.05
0.83
22
GesturePebble211
0.913
0.969
0.0 0.55
0.8
0.06
0.99
38
GesturaPebblee22
0.943
0.960
4.98 / 2.3 0.55
0.16
0.69
GunPoint
0.993
0.909
9.18 0.71
0.54
0.34
0.72
GunPPint.Ar Spaa
1.000
0.0 / 10.0
0.45
0.09
0.78
50
GuunPoinMMaieeeessseeen
1,000
1.000
5,91 2.66 0.59
Gun Ola Yousus
1.000
1.000
2.16 8.84 0.75
0.26
0.64
Hant
0.781
0.878
4.98 6.76
0.72
0.04
0.8
11
HandQuelines
0.946
0.966
8.79 / 1.91
0.4
0.09
0.7
10
Haptics
0.519
0.563
0.0 / 3.22 0.46
0.07
0.74
45
Herring
0.703
0.613
6.22 4.47
0.62
0.0
0.5 26
House Twenty
0.983
0.985
0.12 / 0.0
0.34
0.08
0.53
50
InlineSkate
0.156
0.123
7,85 10.0 0.3
0.1 0.63
1.000
1.000
9.19
4.05 0.55
0.33
0.94
1.000
3.0
0.07
WingheatSundd
0.641
0.659
4.61 5.35
0.77
0.29
23

---

Published in Transactions on Machine Learning Research (10/2025)
Table A6: Hyperparameters for the 128 individual datasets of UCR (Part 2).
TimellUT
Dataset
Ace
AUPRC
Twin
Tiae Tiar
Italy ItalyPower Demand
0.971
0.974
7.39
10.0
0.65
0.03
0.99
Largek MichenApplianee
0.885
0.900
5.74
0.7
0.58
0.85
Lightning?
0.934
0.978
1.41
6.16
0.34
0.01
0.6
Lightning7
0.877
0.927
9.64
4.48
0.58
0.22
0.99
30
Mallat
0.969
0.983
0.41/
10.0
0.66
0.02
0.7
Meat
0.967
1.000
9:33 / 5.65 0.66
0.07
0.92 16
Medicallmages
0.828
0.816
0.72 0.0
0.64
0.03
0.58
Melbourne Podessrian
0,964
0.962
10.0
1.92/ 0.77 0.23
0.61 33
0.662
0.532
2.12
9.61
0.8
0.12
0.74
0,869
0.924
2
6.81
0.21
0.617
0.423
1.57
5:34
0.8
0.21
0.74
MixeeSSapeeRegglat Train
0.929
0.952
5.1
8.41
0.33
0.24
0.9
24
0.894
0.927
4.95 9.89
0.31
0.4
0.91
MoteStrain
0.925
0.967
4.43 9.69
0.75
0.03
0.83
22
ConlavasiveeetalBCCCTOoo
0.948
0.946
1.1 9.14
0.57
0.21
0.54
48
NouInvasive FetalliCe horax2
0.953
0.951
0.0 / 1.92
0.78
0.02
0.74
26
OSULeaf
0,864
0.587
2.96 / 3.95
0.69
0.02
0.58
32
OlivOOil
0.933
0.910
5.19 / 5.78 0.62
0.09
0.67
30
PLAID
0.553
0.523
0.0 0.0
0.8
0.02
0.93
PhalangesOutlinesCorrc
0.819
0.897
0.54
1.3 0.66
0.36
0.55
Phoneme
0.320
0.146
0.0 0.06
0.8 0.01
0.69
PickopGestureWWn WiimoteZ
0,940
0.947
7.53
6.34
0.76
0.29
0.86
43
PigAirwayPei Pressure
0.817
0.838
9.95
0.0
0.7 0.35
1.0
18
PigAAtPrressve
0.971
0.981
5.86
0.03
0.62
0.25
0.76
35
PigCVP
0.928
0.936
5.92
0.35
/ 0.8 / 0.18
0.96
22
Plane
1.000
1.000
7.08
0.06
0.41
0.14
0.57
17
PowerCons
1.000
1.000
0.0
7.37
0.37
0.33
0.5
PreximalPhallannnnttiieeeee Grooup
0.859
0.713
2.44
/ 0.63
0.46
0.26
0.56
17
ProxinalPiasluuxuuutllCCCC
0.914
0.964
7.67
10.0
0.57
0.17
0.64
ProxinalPbslanxIW
0,549
0.631
4.34
0.55
0.1
InfrigerationDevice
0.645
0.630
0.0 0.76
0.74
0.85
Rock
0,820
0.504
4.31
0.49
0.54
0.19
0.78
17
Screen Type
0.403
0
1.62
3:41
0.39
0.26
0.73
41
SengHanuGGnnde:h22
0.973
0.991
6,46
5.33
0.3
0.18
0.88
30
SemggHaaddMoveemeatti
0,911
0.921
1.61
10.0
0.38
0.29
0.73
29
SengHHaadSahheshhh2
0.958
0.963
4.68
2.35
/ 0.AL
0.39
0.84
20
Shakeresttuee WiimoteZ
0.960
0.971
4.54
7.4T 0.58
0,26
0.75
38
ShapeletSim
1.000
1.000
3.87 / 0.36 0.65
0.12
0.74
ShapesAll
0.908
0.922
10.0 / 3.7 0.4
0,5
wwwalliitchenApplinnne
0.768
0.825
10.0 0.0 0.75
0.14
SmoothSSuseace
0.987
0.995
5.2 0.36 0.42 0.08
0.84
Sony AlBoAAooootSurfeeee
0.965
0.996
5.71 6.88
0.8
0.02
0.99
10
0.902
0.985
4.16 / 10.0
0.8
0.01
/ 0.53
45
StarLightCurves
0.975
0,982
10.0
0.2
0.79
0,21
1.0
33
Strawberry
0.968
0.997
0.0
10.0
0.5
0.28
0.5
37
SwrdishLeaf
0.946
0.944
2.55
6.61
/ 0.76
0.37
0.51
16
Symbols
0.982
0.989
6.38
3.52
0.47
0.4
0.73
SyutheticControl
1.000
1.000
0.25
9.78
0.33
0.14
0.74
ToeSegmentationl
0,969
0.988
10.0
6.39
0.4
0,95
TonSegmennation2
0.946
0.944
5.23
6.56 0.66
0.29
0.92
Trace
1.000
1.000
9.03
6.29 0.33
0.24
0.61
TwoLGG
0.989
1.000
0,0 9.41 0.8
0.2
0.5
TwoPatterns
1.000
1.000
3.0 3.0
0.5 0.07
0.8 30
UMD
1.000
1.000
9.75 / 5.93
0.A1 0.08
0.85 12
UWaveGesttre Library All
0.947
0.966
5:33
4.61
0.3 0.09
1.0
UWaveGest La X
0.823
0.620
1.59 / 6.69
0.42
0.08
0.8
WesteGestuee
0.736
0.734
3.14 / 8.18
0.44
0.25
LO 35
0.771
0.778
8.33
0.23
0.76
Wafer
0.999
1.000
1.98
1.83
0.62
0.02
0.77
38
Wine
0.907
0.970
4.31
8.83
0.71
0.08
0.9
14
WordSynonyms
0.723
0.585
2.56
6.52
0.76
0.17
0.5
48
Worms
018188
0.828
3.61
0.0
0.75
0.21
1.0
WornsTToClass
0.883
0.873
0.76
2.79
0.34
0.21
0.68
50
Yogs
0.903
0.924
8.48
/ 0.53
0.52
0.39
0.68
100
Average on all 128 datascts
0.864
0.862
24

---

Published in Transactions on Machine Learning Research (10/2025)
Table AT: Hyperparameters for the 30 individual datasets of UFA.
TimeHUT
Dotaset
AUPRC
G//o//mn Tunin Tuii
Tmaz
Toos
Articulary Rordoooggntnonn
0.993
0.6
0.36
0.64
AtrialFibiilltion
0.533
0.440
2.04
0.08
0.67
0.26 0.68
DasicMotions
1.000
1,000
3.0
0.07
CharacterTraaeccon
0.997
0.998
0.32 ] 1.1
0.26
Cricket
1.000
1,000
5:24 9.16 0.377
0.37 / 0.33 0.87
DuesDecGGesse
0.600
0.630
0.1 1.0 0.5
0.0 1.0 1.0
ERing
0.926
0.969
0.0 / 0.75 0.68 0.0
1.0 17
RigenWorms
0.962
0.951
10.0 / 5.15 0.51
0.2
/ 0.91
Epilepsy
0.964
0.973
0.41 0.12 0.52
0.28
0.6 34
0.373
0.361
0.78
0.52
0.11
0.5
PereDetection
0.551
9.04
10.0
0.74
0.38
0.66
FlvgerMovements
0.612
0.652
0.0
0.5
0.1
0.6
HandMovement Directtoo Direction
0.432
0.461
3.42 / 0.0
0.38
Handwriting
0.582
0.586
4.51 0.0 0.8
0.07
0.62
Heartheat
0.810
0.586
1.64 5.66 0.46
0.22 0.66
33
Lnsect Wingbeat
0.466
0.453
0.0 / 0.0
0.3
0.24
0.99
JapaneseVowede
0.984
0.996
9:33 / 8.55
0.47
0.33
0.68 33
LSST
0.586
0.407
2.59 / 0.0 0.34
0.16 0.88
Libras
0.853
0.892
7.76
5.46 0.68
0.09
0.72 20
Motormaagery
0.660
0.5/ 0.2 0.5
0.0
1.0
NATOPS
0.966
0.985
0.5
0.4/
PEMS-SF
0.855
0.894
8.8 9.3
0.6
0.95
PenDigits
0.989
0.995
2.8 5.59
0.67
0.05
0.92 26
PhoneneSpectra
0.243
0.195
7.18 3.93
0.8 0.35
0.5 22
RacketSports
0.921
0.905
0.82 / 4.83
0.57
0.09
0.63
48
SellRegusstioSCPPI
0.860
0.935
0.95 / 0.0 0.49
0.0
0.53 /3
SelfltogalationSCPP
0.583
0.566
0.0 / 4.06
0.35
0.02
05
SpokenArabicDiglla.
0.995
0.998
8.45
/ 8.92 0.49
0.15 0.94
StandWalkJump
0.600
0.437
0.2 0.2
05
urw
0.46
/ 0.8
0.08
Average on datasets:
Table A8: Hyperparameters for anomaly detection.
Dataset
Precision
Rerall
cafes/ma /ma mmaa/Tae Tugin Twex Umas
Yahoo
0.755
/ 0.02 /
1.0
KPI
0.721
0.809
0.602
4.4
0.08
0.50 0.21
0.5 44.0
Cold-start:
Yahno
0.779
0.793
0.765
10.00
6.27
0.76
0.03
0.99 39
KPI
0.691
0.894
0.563
2.35
0.87
0.62
0.32 / 0.55
25

---

Published in Transactions on Machine Learning Research (10/2025)
Algorithm 1: PyTorch-like pseudo-code for TimeHUT
B: Batch size
2
T: Length of the time-series
tau, min, tau_nax, onega, signa: Temperature scheduling parametere
a_a: Angular margin
Input:
Time-series dataset = [x1, x2...., x_h,..., xn]
Model parameters \theta Dutput: Learned representations [z1, z2, ..,..., z_i,..., zn]
Step Preprocessing
for in X:
a1, b1, a2, randon_ str___rop__ii randon_crop_indicce([]]]. Randomly crop indices subseries
xi[i] x_i[ai:bi] First subseries
x2[i] x_i
subseries
15
21[1] encoder (x1 [i]) # Encode firet subseries
16
22[1] encoder (x2(i]) # Encode second subseries
17
18
Step 2: Bierarchical Contrastive Loss Calculation
for t, t² in overlapping taap:ingttimmmttapallaaaal (21 22[[)): # Iterate over timestampa of instance i s(it_i't) aim(ai 22[i] [t]) # Positive pairs
s(it_i't!) sim(21[3]tt) 22[1] [t(]) Negative pairs across subseries
s(it_it') = sim [t], z1 (t')) # Negative pairs within subseries
s(it_i't',, s(it_it')) for 1 (B): Iterate over all instances in the batch s(it_i't) sim [i] [t], =2[i] [t]) Positive pairs
L_memp =
s(it_j't) sim [t], (t]) Negative pairs within the batch (cropped)
s(it_jt) sim(zi(a) [t]] Negative pairs within the batch I_Inst centaacc_contrasttinn (os((((t__(__)))) s(it_j't), s(it_jt))
Step Temperature Scheduling sau_sigma lambda sigma: (tau haa__ma-tta__min) cos 2omeeaa sigma 2) tau_min
35
for enbedding.pair in embedding_.eirreett 22):
34
I. TempSch L_temp "tau_ssfp Sau_sigma(e1gg) (eigma)
35
I. InstSch L_inst tau__iigmaette (sigma)
Step 4: Hierarchical Angular Margin Losa Calculation
for t, t² in werrlapping..innsttappaaaa timestamps 22[i]): # Iterate over timestampa of instance 1
(-1) (1) \0ax(0, \max(0,
22 # Positive pairs
Negative pairs across subseries
Negattve pairs within subseries L_Teppnng = compute_angulae aagpue__anularrrrrgg..eeeeee www.s/aarrnnnnaaaeeaaeeeeee (argl s(it_i't'), s(i__it'), m_a)
(-t)
for i (B): Iterate all instances in the batch (Acos" (ooo""""a__it,
Positive pairs
\max(0, m_a (c1) (ett)tttt(ttt Negative pairs within batch (cropped) \max(0, m_a \cos (cos (-I)(e_((tt, I. I_stAnng compute_ane srapute_angular_mate (artitn s(it_j't), s(it_jt), m_a)
Negative pairs within
50
Step Combine Loeses
51
L. HierSch sum(L sum(L_teem__ee temp_sch L, inst_sch) (len(X)
52
L. Hierrrng sum [am(L_tenn tam__tempp_ng____ L, i_inst_ang) (1en(X)
Iotal Hierrhhh L_Hiirrng
Step 6: Model Optimization theta optimize T_tal))
26

---

Published in Transactions on Machine Learning Research (10/2025)
Table A9: Mean Difference (MD) values for TimeHUT and competing methods.
TimeHUT
AutuTCL
SelIDis
InfoTS,
InfoTS
T92
TS-TCC
MCL
TimeHUT
0.00
0.02
0.02
0.03
0.01
0.04
0.06
0.06
0.09
0.09
0.10
0.15
0.16
0.35
AutoTCL
SeliDis
-002
-0.00
0.00
0.01
0.02
0.02
0.03
0.01
0.07
0.08
0.12
0.14
0.14
0.33
FEAT
-0.11
-0.02
-0.02
-0.01
0.00
0.01
0.02
0.05
0.05
0.06
0.10
0.12
0.12
0.31
InfoTS
-0.05
10.03
-0.02
-0.02
-0.01
-0.01
0.00
0.01
0.01
0.05
0.06
0.10
0.11
0.30
TS2Vec
TNC
-0.09
01.07
-0.07
-0.06
-0.05
-0.01
-0.03
-0.03
0.00
-0.00
0.01
0.06
0.07
0.26
TS-TCC
T-Loss
-0.10
11.08
-0.08
-0.06
-0.06
-0.06
-0.05
-0.05
-0.01
-0.00
0.00
0.01
0.06
0.25
TST
MCL
-0.16
-0.14
-0.14
-0.13
41.12
-0.11
-0.10
-0.11
-0.07
-0.07
-0.06
-0.02
0.00
0.19
Table A10: P-value matrix for TimeHUT and competing methods.
AutoTCl. TimeHl.T
SeiDis
InfoTS,
Infol'S
TS2Vee
TNC
TST
MCL
TimeHUT AutoTCL.
0.088
0.1073
0.0091
<1e-
0.001
0.00012
<le-
<le-1
<le-
<led
<led
<led
<le-
0.8288
0.4123
0.0877
0.0362
0.0036
<1o4
0.0003
0.0004
<1e4
<164
SelDDss
0.1073
0.8288
0.5700
0.0798
0.0382
0.0497
0.0019
<lo-4
0.0002
0.0007
<lo4
<le44
<lo-4
0.0091
0.5700
<1o4
<1o4
0.0004
<1e4
<164
FEAT
<lo4
0.0687
0.0798
0.3805
0.9808
0.3707
0.0174
0,0001
0.0002
0.0091
0.0001
<le-4
<1c-4
SMIE
InfoTS
0,0002
0,0862
0.6497
0.0296
0.3599
0.3809
0.2355
0.0008
0.0035
0.0057
0,0002
<le1
<le-
T82Voc
<lo4
TNC
<lei
<le-
<le4
<le4
0.0001
<3e-1
0.0003
0.0026
0.7051
0.1592
0,0207
0.0051
<le-
TS-TCC
<lo4
0,003
0.0022
<le4
0.0345
T-Loss
<lo4
0.0044
0.0007
0.0004
0.0081
0.013
0.0057
0.0808
0.4502
0.6004
0.0647
0.0113
0.001
TST
<le4
<le-
<led
0.0001
<lc4
<led
0.0001
0.0009
0.0207
0.0201
0,0647
0.2891
0.005
MCL
<led
<led
<led
<led
<le-1
<1e-1
<le-1
0.0051
0.0026
0.0113
0.2501
0.2891
0.0009
TE-C
<le4
<1e4
<1e4
<1e4
<1e4
<364
<1e4
<1e-
<1e-1
<1e4
0.0001
0.0005
0.0009
27


Reviews:
[{"review_id": "lh9Wkxi4tk", "reviewer": "Reviewer_K7oc", "summary": "", "questions": "", "limitations": "", "rating": null, "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": "", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "The authors propose a method called TimeHUT for learning time-series representations by hierarchical uniformly-tolerance balancing of contrastive representations. Two distinct losses are proposed to learn strong representations for balancing between uniformly and tolerance in the embedding space. The authors conducted experiments on 128 UCR and 30 UAE datasets for univariate and multivariate classification, as well as Yahoo and KPI datasets for anomaly detection, which shows the effectiveness of TimeHUT.", "claims_and_evidence_yn": "Yes", "claims_explanation": "The modeling capability of the proposed method TimeHUT is well supported by the empirical performance.", "audience_yn": "Yes", "audience_explanation": "This manuscript deals with balancing between uniformality and tolerance in time series contrastive learning which is now a hot topic im machine learning.", "requested_changes": "1. I find that Figure 1 is not easy to read. I suggest the authors polish the caption and use more precise components in the figure. \n\n2. Although TMLR does not require each paper to be highly novel, this work's technological novelty can be made clearer and deeper by first providing a clear discussion of modeling insights from related works and then discussing some theoretical aspects of TimeHUT.\n\n3. The authors provide a block of PyTorch-like pseudo-code for TimeHUT. However, I find it still inconvenient for readers to conduct sufficiently reproducible experiments for many reasons, such as detailed parameter settings. Why not directly share the code on platforms like GitHub?\n\n4. The use of hierarchical information may add significant computational complexity. I suggest that the authors discuss the time cost of TimeHUT.\n\n5. Are there failure cases where TimeHUT significantly adds a computational burden or introduces inappropriate inductive biases that hinder efficiency or effectiveness?", "broader_impact_concerns": "I did not find any obvious ethical and societal issues.", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "XiMQRyoQvx", "reviewer": "Reviewer_hKUk", "summary": "", "questions": "", "limitations": "", "rating": null, "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": "", "claims_and_evidence": "No", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "The paper proposes **TimeHUT**, a self-supervised framework for time-series representation learning that:\n\n1. **Stacks three existing ingredients**\n    - multi-scale (instance + temporal) contrastive objectives from **TS2Vec**;\n    - a **periodic cosine temperature scheduler** that alternates between uniformity- and tolerance-favouring regimes;\n    - an **angular-margin loss** (ArcFace-style) applied hierarchically to enforce a minimum angle between negatives.\n2. **Reports experimental results** on 128 UCR and 30 UEA classification datasets and on Yahoo/KPI anomaly-detection benchmarks, showing small (≈1–2 pp) average gains over recent SSL baselines.\n3. **Provides ablations** indicating that removing either the scheduler or the angular margin reduces classification accuracy.\n\n**Key strengths**\n\n- Well-executed engineering recipe that can be dropped into any TS2Vec-like codebase.\n- Consistently non-negative performance deltas on a large public benchmark suite.\n\n**Key weaknesses**\n\n- ★ **Limited methodological novelty** – all three components are direct borrowings from prior work; TimeHUT contributes only their combination.\n- **Marginal empirical improvements** relative to the added compute/hyper-parameter burden.\n- **No analysis of efficiency** (training time, memory, etc.).", "claims_and_evidence_yn": "No", "claims_explanation": "Novelty claims are not supported: the hierarchical contrast is directly adopted from TS2Vec; temperature scheduling and angular margins are well-established techniques; and there is no comparison to prior scheduler- or margin-based self-supervised learning methods applied to the same datasets.", "audience_yn": "Yes", "audience_explanation": "Researchers who care about pragmatic ways to squeeze a bit more accuracy out of TS2Vec-style pipelines may appreciate the plug-and-play recipe and the extensive benchmark sweep. The work is less attractive to readers looking for conceptual advances.", "requested_changes": "1. **Clarify and justify novelty.** Rewrite the abstract and Related-Work sections to make explicit that the hierarchical contrast, temperature schedule, and angular-margin loss are all taken from prior work\n2. **Provide an efficiency analysis.** Report wall-clock training time, peak GPU memory, and FLOPs/epoch for TimeHUT versus other baselines.", "broader_impact_concerns": "I do not see immediate ethical red flags.", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "5gqvRq3Soe", "reviewer": "Reviewer_4fMT", "summary": "", "questions": "", "limitations": "", "rating": null, "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": "", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "This work introduces a method to embed time series through a contrastive self-supervised learning methods. Through the design of a dedicated loss, the authors try to balance several behaviors to obtained good representations of the time series. Namely, they try to balance uniformity (maximization of the spreading of the representation) with tolerance (such that small variations of a sample have a close representation), while also maintaining a sufficient distance between negative pairs. They benchmark their method on several datasets and tasks, and compare it with several prior methods. Moreover, the authors add an ablation of the different part of the proposed loss.", "claims_and_evidence_yn": "Yes", "claims_explanation": "This work introduces a loss which allows to find embeddings of time series which balance several appealing properties, such as uniformity and tolerance. The paper is well written, the concepts are well explained, and the proposed loss is well motivated. The relation with previous works is also well described. The experiments demonstrate very good performance on classification tasks compared to previous works, and on several datasets. Moreover, these good results are also shown on anomaly detection tasks, where the results are competitive with previous works. Finally, there is also an extensive ablation showing the influence of each of the key components of the method, the analysis of the trade-off between uniformity and tolerance, and the sensitivity to different hyperparameters.\n\nI am not very familiar with this literature, so I do not see major weaknesses. I think it is a nice work, using a well motivated loss to solve the task of self-supervised learning for time series, and which evaluated the method thoroughly, with comparisons with other methods on several benchmarks, and ablation studies. Maybe a slight weakness would be that it relies a lot on previous works, combining several components of different works. Nonetheless, it is done in a smart way and it is well justified.", "audience_yn": "Yes", "audience_explanation": "This paper proposes a method to perform self-supervised learning on time series which is a lot of interests to a wide audience. The authors introduce a loss demonstrating state of the art results, and show that each component of their loss provides improvements through ablation studies, and do an extensive comparison with previous works. Thus, their results are also of interest to TMLR's audience.", "requested_changes": "I don't have major requested changes. A minor one would be to use with better care the \\citep vs \\citet in the citation format.\n\n\nTypos:\n- p2: \"Following we summarize key recent papers in this area.\"", "broader_impact_concerns": "None", "additional_comments": "", "extra_scores": {}, "extra_text": {}}]

Author rebuttal:

Decision: Accept (poster)