From: ICLR.cc/2023/Conference/Program_Chairs
title: Paper Decision
decision: Reject
metareview:_summary,_strengths_and_weaknesses: In this paper, the authors propose a contrastive learning approach toward time series representation learning on top of trend-seasonality decomposition called TS-DC. Experiments on two public benchmark datasets UCR and UEA show the effectiveness of their method.  

Strengths: 
1. This paper is well-written and clear, and the proposed method is very easy to understand. 
2. The idea of utilizing the trend-seasonality decomposition method in time-series representation learning sounds interesting. 
3. After the rebuttal, the experiments become more extensive, and the performance looks good.  

Weaknesses: 
1. This paper is somehow overclaimed. The authors claim that they decompose the original time-series data into trend and seasonality. However, as shown in Figure 10, it is difficult to distinguish the trend and seasonality generated by the model. It seems that the model just roughly divides the original time-series data into positive and negative data by the fully-collected layer according to the KL divergence loss.  
2. The assumptions of this paper are too strong. Generally, the time-series data could be divided into three parts, i.e., trend, seasonality, and remainder, where the trend and seasonality are time-dependent while the remainder is usually time-independent. However, this paper only considers the trend and seasonality, and totally ignored the time-independent variable. 
3. The baselines of this paper only contain the time-series representation learning-related papers, while the seasonality-trend decomposition-related papers are missing, e.g., RobustSTL, Fast RobustSTL etc. Some other methods considering the trend and seasonality, e.g., CoST and LaST, should also be discussed in the paper.
justification_for_why_not_higher_score: First, the seasonality-trend decomposition-related papers are well discussed and compared in this study. Second, the results in Figure 10 and the idea in Figure 2 are not consistent -  it is difficult to distinguish the trend and seasonality generated by the model in Figure 10. Considering some other issues raised by our reviewers, I would recommend rejecting this paper.
justification_for_why_not_lower_score: N/A
summary_of_AC-reviewer_meeting: N/A

From: ICLR.cc/2023/Conference/Paper5699/Authors
title: Response to Reviewer BofU
comment: > Decomposition of time series into trend and seasonality components interactively is not new.
It is pretty close to the work of N-beats. 
The authors may want to add discussions on connection with N-beats and relevant existing work on CL for time series.So audience may have better idea on the contribution of the work.

* Very much appreciate your helpful comments. We hope the following explanations can address your concerns appropriately. 
* In the second part of Related Work, we discuss the difference between our approach and N-BEATS. To make it clearer, in the revised version, we rephrase the second part of Related Work accordingly. 
* Besides, in the first part of Related Work, we put many discussions on relevant works about contrastive learning for time series representation learning. Moreover, we add more discussions on more recent time series CL methods at the end of the first paragraph in Related Work. 
* In addition, in the second paragraph of the Introduction, we have already briefly introduced the relevant CL methods toward unsupervised time series representation learning. 

======================

> Are there any principle way to determine the level of decomposition N?
For example, can we determine N based on the residue error or Fourier analysis.

* Many thanks for your insightful question and suggestion.
* Currently, we do not have such principles to determine the level of decomposition.
* Yes, a heuristic algorithm could be developed to determine N based on the residual error or Fourier analysis. In the future, we will put efforts toward this problem. 

> The S vector in eq. (2) contains integer multipliers of 2\pi in the sin/cos functions (assume L is even). So we will get a vector with only 0 or 1 elements which cannot describe the seasonality in the signal.

* As described in our paper, $ \mathbf{t} = ([1, 2, \cdots, L-1] / L)^T $ and $ \mathbf{S} = [1, cos(2\pi \mathbf{t}), \cdots , cos(2 \pi (\frac{L}{2}-1) \mathbf{t}), sin(2\pi \mathbf{t}), \cdots, sin(2 \pi (\frac{L}{2}-1)\mathbf{t})]$.

* Thus, the elements in vector $\mathbf{t}$ are between 0 and 1, subsequently, there exist non-integer multipliers of $2\pi$ in the $\mathbf{S}$ vector (in eq. (2) in the previous version). Such that, there exist values other than 0 or 1 in the $\mathbf{S}$ vector when $L$ is even. 

>  Eq. (7), the contrastive loss is built based on X and X_n, n=1, 2, …, N. Can we build the contrastive loss based on X and X^s/X^t at different levels?
Trend and seasonality should be quite different and naturally could be used for construct similar/dissimilar pairs.

Many thanks for your constructive suggestions. 

* Yes, we can build the contrastive loss based on $\mathbf{X}$ and $\mathbf{X}^s$ / $\mathbf{X}^t$ at different levels. 
* We have added experiment results and related discussions in Appendix C.4 in the revised paper.


> Eq. (10), w_n is a vector with dimension D. L_c is a real number if I understand correctly.
I am not clear how to multiple them together and get the final loss L_ac which I assume it is also a single real number.

*  Thanks for your careful reviews and we really thank you for pointing out this issue. 
* Actually, $L_c^n$ is a matrix: $ L_c^n \in \mathbb{R}^{L \times D} $. We have clarified the related descriptions in the revised version. Please refer to Eqs. (5), (6), and (9) and corresponding descriptions in the revised draft.

> In sec. 4.2, looks like the proposed method serves only as a feature extractor and is independent of the subsequent classification task.
It is not clear what the classifier is and what the supervised method is in Table 2 and Table 3. The whole setting needs clarification.

*  Yes, the UTSRL model acts like a feature extractor that is independent of downstream models. 
* To improve the clarity of the experiment settings, we add more descriptions about the training procedure toward TS representation learning in Appendix A.1. Besides, we reorganize and rephrase experimental settings and implementation details in Section 4.1 and Appendix A accordingly.


> Fig. 3, visually all sub-figures look no significant difference regarding the clustering except T-Loss.
Maybe it’s due to the dominance of classes 1 and 2.
I would suggest to use another more representative example for illustration.

* Many thanks for your constructive suggestion. We add an extra case study in Appendix C.1.2 on the PenDigits dataset. In this dataset, the time series class labels are more balanced.

From: ICLR.cc/2023/Conference/Paper5699/Authors
title: Response to Reviewer HiGm
comment: > Concerns and questions: As shown in Fig.4, the first components seem to have the most information of the original time series, and the latter ones are more like noises. If we change the number of components decomposed, what the results would be like? It would be great if some experiments can be added to answer this question. Besides, in Section 3.3, how does the non-linear function h_phi is implemented? I think more details need to be added.

We very much thank your advisory comments.
    
1. We have added more experiment results of the TS decomposition under different settings in Appendix C.2 in the revised paper.

    * In particular, in Appendix C.2.3, we conduct extra experiments to probe how the downstream classifier would perform if we change the number of decomposition steps.

    * As shown in the table below, the best number of decomposition steps on different datasets differs, which means we should develop a more intelligent algorithm to determine the suitable N automatically (as mentioned by Reviewer BofU). 

|                       |         ECG500         |        FordB         |      Ham         |  FaceDection     | Heartbeat          |  FaceDection     |
|:---------------------:|:----------------------:|:--------------------:|:----------------:|:----------------:|:------------------:|:----------------:|
| # Decomposition Steps |    ACC &nbsp; UPRC     |   ACC &nbsp; AUPRC   | ACC &nbsp; AUPRC | ACC  &nbsp;AUPRC |  ACC &nbsp; AUPRC  | ACC &nbsp; AUPRC |
|          N=1          | 0.856    &nbsp;  0.723 |      0.520     &nbsp;  0.555    |     0.573     &nbsp;     0.641    |     0.615   &nbsp; 0.667    |     0.703 &nbsp; 0.524    |     0.615   &nbsp; 0.667    |
|          N=2          | 0.846    &nbsp;  0.759 |      0.523    &nbsp;   0.535    |     0.625      &nbsp;    0.638    |     0.608   &nbsp; 0.654    |     0.703 &nbsp; 0.483    |     0.608  &nbsp;  0.654    |
|          N=3          | 0.868    &nbsp;  0.841 |     0.565    &nbsp;    0.573    |     0.531      &nbsp;    0.566    |       0.602 &nbsp; 0.653     |     0.703 &nbsp; 0.503    |       0.602 &nbsp; 0.653     |
|          N=4          | 0.831    &nbsp;  0.736 |     0.506    &nbsp;    0.536    |     0.572      &nbsp;    0.645    |     0.604    &nbsp; 0.645    |     0.703 &nbsp; 0.510    |     0.604   &nbsp; 0.645    |

2. We describe the implementation details of $h_{\phi}$ in Appendix A.2 in previously submitted draft. In the revised paper, we re-organize the descriptions related to implementation details and experiment settings. In particular, we move the implementation details of TS-DC from Appendix to the Implementation Details paragraph in Section 4.1 in the main text.

From: ICLR.cc/2023/Conference/Paper5699/Authors
title: Response to Reviewer 9QzX: Part 3
comment: 
> On the contrary, sec 4.3.1 is a bit short: we wonder what would be the performances of each decomposition level (does-it exist a noise only level that penaliez the performances? What is the impact of the trends extracted after level 1? etc...)


* Really appreciate your constructive comments, we have added in-depth discussions about TS decomposition in Appendix C.2 in the revised paper. 
* In particular, we plot the decomposed trend and seasonality at each decomposition level in Figure 10 in Appendix C.2.2 in the revised draft. As the decomposition proceeds, more noise will get involved in the decomposed components, which could negatively affect the TS decomposition.
* However, as depicted in Figure 11 in Appendix C.2.2, by combining the latter decomposed components, the recovered TS can better fit the original TS. On the other hand, the performance of TS unsupervised representation learning can be improved because of the enhanced robustness. More specifically, the distribution space will be enlarged if noisy negative samples can be contrasted properly.


> Given the contrastive criterion, I don't understand why the ablation is so harmless on univariate TS while it is so harful on multivariate.

* We really appreciate your thoughtful comments and do hope the following explanations can address your question.
* From the ablation studies of the adaptive contrasting reported in the paper, we can draw the following conclusions:
    * For the univariate case, TS decomposition is of high quality. In particular, at the first decomposition level, the trend and seasonality preserve the most informative signals, such that the decaying weights and adaptive weighing do not affect the outcome too much.
    * On the contrary, for multivariate time series data, the perplexing high-dimensional TS is difficult to decompose. Therefore, decomposed components at latter levels can still preserve informative signals to some extent, which means that the weight decaying and adjusting is more important for multivariate TS data w.r.t. TS representation learning.

From: ICLR.cc/2023/Conference/Paper5699/Authors
title: Response to Reviewer 9QzX: Part 2
comment: 
> Is there a link with orthogonal matrix factorization? Or Orthogonal Matching Pursuit (to keep the recursive aspect of the approach)?

* Many thanks for your insightful questions. 
* For your first question, yes, there is a link between our TS decomposition method and orthogonal matrix factorization. 
    * In particular, we extract seasonal features with a set of trigonometric functions $S$ which can be treated as a set of orthogonal functions to exploit the properties of the Fourier Transform.
* Secondly, we address your second question below. 

The decomposition process described in our work absorbs the remainder $X^r$ recursively, such that the complex signals in the time series data can be fully captured.

Similar to traditional signal recovery algorithms, the proposed TS decomposition process works in a greedy way, like Orthogonal Matching Pursuit (OMP), whereas, the parameters that govern the decomposition process in TS-DC are determined in an end-to-end fashion, which is different from existing signal recovery algorithms. 
    
* Besides, we have added more descriptions about the devised decomposition process in Appendix C.2.1 in the revised version, please refer to this part for more details. 
* To extract the seasonal features, we construct a set of trigonometric functions S as the set of orthogonal functions to utilize the properties of Fourier Transform


> The AUPRC metric should be described (even shortly) in the article.

* Thanks for pointing out this issue. We have described the AUPRC metric in Experiment Settings in Section 4.1 accordingly.


> I don't understand the metric & results of table 1: results (ACC around 0.4 on UCR) seem very far from what I read in the literature. I don't get the difference of setting with the cited references.

* As described above, we focus on evaluating the effectiveness of the unsupervised TS representation learning (UTSRL) model. Therefore, to fairly evaluate the UTSRL models under the same setting, we implement our UTSRL model and other baselines using the same backbone encoder and the same downstream model (e.g. classification model). Please refer to the detailed settings of how to train a UTSRL model in Appendix A.1 of the revised paper. 
* Besides, the backbone encoder and downstream classifier adopted in this work are kind of simple and naive, that's why the classification performances reported in Table 1 are not as good as other works.
* In addition, we conduct more experiments on UCR and UEA datasets with different backbone encoders and downstream classifiers. Please refer to the experimental results mentioned above.


> Sec 4.2.3 is not really meaningful, it could be moved to appendix. I also notice that the proposed TSNE does not match what I saw in the literature (in Tonekaboni 2020 for instance).

* Thanks for your suggestions and comments.
* The qualitative analysis of the representations generated by different TSRL (time series representation learning) models is an important way to examine the quality of TSRL models directly.
* Because of the class imbalance of the ECG5000 dataset, the t-SNE plots reported in Section 4.2.3 are not distinguishable as expected. It is indeed difficult to choose a UCR/UEA dataset in which the TS classes are comparable, the clustering effects can be easy to tell, and the performance differences toward downstream tasks are obvious. 
* We report an extra case study of the PenDigits dataset in Appendix C.1.2 and we will choose more representative examples in our final draft. 
* Besides, for your second question, we do not propose t-SNE, t-SNE (t-distributed stochastic neighbor embedding) is a non-linear, unsupervised data exploration approach, which was proposed in 2008. t-SNE is built on top of stochastic methods, therefore, the outcomes are accompanied by randomness to a certain extent. Therefore, the t-SNE plots reported in our work might not be the same as those results in the literature.

From: ICLR.cc/2023/Conference/Paper5699/Authors
title: Response to Reviewer 9QzX: Part 1
comment: > Unexplained gap between presented result and those found in the literature

> " ... I do not understand the differences between the proposed results and those that I found in the cited references. The extent of the discrepancies leads me to reject this article. "

* Many thanks for your constructive comments. In this work, we employ the same encoder as well as the same downstream model to fairly compare the effectiveness of different TS representation learners. 
* In the TS classification experiments, a Transformer-like encoder is adopted as the backbone encoder, and the downstream classifier is an RNN-based model. 
	* Most of the UCR and UEA datasets are relatively small, and the expressiveness of the Encoder and classifier adopted in our experiments cannot be fully leveraged. Therefore, the classification performance in our experiments is not as good as in other works. 
                
        * However, this is not the focus of unsupervised TS representation learning (UTSRL) models. 
        * In the experiments of this work, all UTSRL models and a supervised model are evaluated with the same backbone encoder as well as the same downstream model, such that the effectiveness of UTSRL models can be fairly compared. 
       
* We re-organize and rephrase the related implementation details in Section 4.1 and Appendix A.1 & A.2 in the revised paper accordingly. 

* Moreover, to prove that our proposed UTSRL model can achieve the classification performance reported in other related works, we conduct extra experiments on UCR and UEA datasets with different backbone encoders and downstream classifiers. 
The results are as follows: 


The averaged scores on 128 UCR datasets:


| Encoder | RNN-based | Conv-based | Transformer-based |
|:----------------:|:------------------------------:|:----------------------:|:------------------------------:|
| | ACC &nbsp; AUPRC | ACC &nbsp; AUPRC | ACC &nbsp; AUPRC |
| LSTM | 0.302 &nbsp; 0.284 | 0.343 &nbsp; 0.403 | 0.454 &nbsp; 0.686 |
| SVM | 0.536 &nbsp; 0.321 | 0.758 &nbsp; 0.766 | 0.643 &nbsp; 0.332 |
| KNN | 0.481 &nbsp; 0.308 | 0.721 &nbsp; 0.350 | 0.596 &nbsp; 0.325 |


The averaged classification scores on 30 UEA datasets:


| Encoder | RNN-based | Conv-based | Transformer-based |
|:----------------:|:------------------------------:|:----------------------:|:------------------------------:|
| | ACC &nbsp; AUPRC | ACC &nbsp; AUPRC | ACC &nbsp; AUPRC | 
| LSTM | 0.250 &nbsp; 0.235 | 0.395 &nbsp; 0.472 | 0.399 &nbsp; 0.569 |
| SVM | 0.608 &nbsp; 0.216 | 0.661 &nbsp; 0.227 | 0.623 &nbsp; 0.235 |
| KNN | 0.540 &nbsp; 0.230 | 0.629 &nbsp; 0.226 | 0.590 &nbsp; 0.215 |


> We wonder what is the hypothesis behind the decoposition of the residue: if the trend is a high energy + low frequency signal, it should be explicated at the first step.

* The hypothesis behind the decomposition is that the information will decay as the decomposition proceeds. The decomposed components in earlier steps contain more informative signals. Then, as the number of decomposition steps grows, the latter components will involve more noise.

* We plot the decomposed trend and seasonality at each decomposition level in the revised paper (please refer to Appendix C.2.2). 

    * As shown in Figure 10 in Appendix C.2.2, two datasets ECG5000 and Coffee show different characteristics: ECG5000 is of high energy and low frequency, while Coffee is of low energy and high frequency. 

    * For both two datasets, the trend and seasonality can be explicated at the first decomposition step quite well.

* Moreover, since the information contained in the remainder keeps being lowered as the decomposition proceeds, the trend and seasonality in following decomposition steps become noisier. We additionally plot the original TS as well as the recovered TS in Figure 11 in Appendix C.2.2, and the recovered TS is realized by fusing the decomposed components. It can be seen that, as the number of decomposition steps climbs up, the recovered time series fit the original data better yet more noises come along. The existence of noise does negatively affect the TS decomposition. However, this is beneficial for contrastive learning, since the robustness of the TS representation learning can be enhanced.

From: ICLR.cc/2023/Conference/Paper5699/Authors
title: Response to Reviewer BQk8: Part2
comment: > Please add equation with all loss terms and provide values for loss weights. How did you tune them?

  * We add the descriptions about the optimization and related objective function in the last paragraph of the Methodology part.
We simply treat them with equal weights since the contributions of these loss terms are not significant.
Furthermore, the loss terms cannot fully stand for the contributions of different modules in TS-DC (please see the added ablation study in Section 4.3.1 of the revised paper).

> Ablation studies are missing.
I would like to see the results, both quantitative and comparison of TSNEE plots when we remove the losses one by one.
What happens when we remove $ L_{decomp} $ ? $ L_{KL} $ ?  $ L_{ac} $ ?

  * Thanks for your suggestion.
Actually, we do conduct some ablation studies already w.r.t. the adaptive contrasting mechanism of our approach (see Table 5).
Besides, we add the ablation study with regards to the loss terms in the final objective in the revised paper (see newly added Section 4.3.1).

> Please make sure paper is proof-read carefully, the writing quality can be improved in terms of typos and certain awkward sentences
popping here and there

* Appreciate your constructive suggestions.
We proofread the paper and fix typos and grammar errors throughout the draft in the revised version.
We do hope the revised paper can reach your standards in terms of writing quality.


================

 MINOR POINTS

> The reference with Pedro Pinheiro should be P. O. Pinheiro et al., please correct

> "a time series decomposition-based contrastive learning" why not write it simply "a time series decomposition-contrastive learning"?

> I would propose to replace $ Z = f_{\theta}(X) \in R^{L \times D} $ with $ f_{\theta}: R^{L \times M} \rightarrow R^{L \times D} $, to make it clear that input is in $ R^{L \times M} $ and output is in $ R^{L \times D} $

> typo adpatively -> adaptively

* We pretty much appreciate your hard work and thoughtful comments.
We have fixed the typos, rephrased the presentations, and fixed the related references according to your helpful suggestions.

From: ICLR.cc/2023/Conference/Paper5699/Authors
title: Response to Reviewer BQk8: Part1
comment: > "Part of these datasets have been z-normalized while the others not, so for the convenience of training andtesting,
we standardize all the datasets and the missing values are replaced with zeros."
Please describe the z-normalization procedure in detail.
I assume that the parameters of z-normalization are derived from the train data and are applied to both train and test data. However,
I have a concern that the z-normalization could be applied to train and test data as whole,
in which case the experimental framework would be rendered invalid.
Until this concern is cleared, it is impossible to consider the acceptance of the paper.

- Notably, we do not apply z-normalization to train and test data as a whole.

- To be specific,

  - The UCR archive was first introduced in 2002 and had been expanded several times [2].
    Before 2018, the UCR archive contains 85 datasets, and the time series were already z-normalized to remove offset and scaling.
    The rationale for this step was discussed in the literature [3] as well as the report of the UCR archive [2].
    In the newly released 43 datasets, the publishers provide the raw data without any normalization when possible.
    For the UCR archive, we split the train data into train set and validate set, and apply the derived mean and std. values of the train set to the validate and test sets, separately.

  - On the other hand, for the UEA archive, we normalize the multivariate time series suggested by [3] and the preprocessing procedure in [4] (https://github.com/hfawaz/dl-4-tsc/blob/master/utils/utils.py), where the normalization is conducted on the time series data one sequence by one sequence.
    That is, the normalization is at the instance level and it is unaware of train/val/test split.

  - Besides, the classification task does not seek to predict the raw un-normalized values, as stated by [2] and [3], the differences between the train set and test set do not affect z-normalized data since z-normalization accounts for offset and scale variance.

  - Moreover, for the classification task, neither information leakage nor misguided prediction would happen when normalizing each individual time series independently in the dataset.

  - For the forecasting task, we do the normalization following the setting that you mentioned, i.e., "the parameters of z-normalization are derived from the train data and are applied to both train and test data".
    In addition, to clarify the normalization settings, we rephrase the descriptions about the normalization settings in Section 4.1 accordingly.

> Work [1] seems related as well please discuss.
  * Thanks for your suggestion, we have added discussions about [1] in the Related Work accordingly.

> $ Z_i $ in (7) is a mistake
  * Very much appreciate your careful comments, we have fixed this typo in the revised paper accordingly.

> "In other words, parameters θ are solely conditioned on X: X → θ."
This does not make any sense and also is easy to confuse with the mathematical definition of mapping. Please rewrite.
 
* We rephrase the related descriptions in the revised version. Thanks for pointing out this issue. 

> Insufficient detail to understand how multivariate case is handled. The architecture depicted in Fig. 1 is inherently unimodal.
How exactly do you handle the multivariate case?

* As claimed in our problem statement, the proposed TS representation learner (TS-DC) is originally devised for multivariate TS.

* TS-DC can naturally handle multivariate as well as univariate cases, and we didn't design any dedicated artifacts for handling multivariate TS.
Many thanks for pointing this out, the dependencies among different variables do help in representing multivariate TS, and we will put more effort toward this direction in our future work.


[1] Ling Yang, Shenda Hong, Unsupervised Time-Series Representation Learning with Iterative Bilinear Temporal-Spectral Fusion, https://arxiv.org/pdf/2202.04770.pdf

[2] Dau, Hoang Anh, Anthony Bagnall, Kaveh Kamgar, Chin-Chia Michael Yeh, Yan Zhu, Shaghayegh Gharghabi, Chotirat Ann Ratanamahatana, and Eamonn Keogh. "The UCR time series archive." IEEE/CAA Journal of Automatica Sinica 6, no. 6 (2019): 1293-1305.

[3] Rakthanmanon, Thanawin, Bilson Campana, Abdullah Mueen, Gustavo Batista, Brandon Westover, Qiang Zhu, Jesin Zakaria, and Eamonn Keogh. "Addressing big data time series: Mining trillions of time series subsequences under dynamic time warping." ACM Transactions on Knowledge Discovery from Data (TKDD) 7, no. 3 (2013): 1-31.

[4] Ismail Fawaz, Hassan, Germain Forestier, Jonathan Weber, Lhassane Idoumghar, and Pierre-Alain Muller. "Deep learning for time series classification: a review." Data mining and knowledge discovery 33, no. 4 (2019): 917-963. https://github.com/hfawaz/dl-4-tsc

From: ICLR.cc/2023/Conference/Paper5699/Authors
title: Overall Response
comment: First of all, we very much appreciate the reviewers' hard work. We very much thanks your positive, constructive, and careful comments and have revised the rebuttal version of our submission accordingly. In particular, we rephrase the implementation details and experiment settings to make the evaluation settings clearer for the audience. We add more in-depth discussions about the time series decomposition, more experiment results about the contrasting mechanism, and more ablation studies. In addition, we explain our normalization settings and evaluation framework to address the concerns raised by Reviewer BQk8 and 9QzX. The detailed replies for all the reviewers can be found below.

From: ICLR.cc/2023/Conference/Paper5699/Reviewer_BQk8
confidence: 4: You are confident in your assessment, but not absolutely certain. It is unlikely, but not impossible, that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work.
summary_of_the_paper: The paper describes a method of learning a time series representation via a contrastive learning approach based on components of neural hierarchical trend-seasonality decomposition.
strength_and_weaknesses: STRENGTHS
- Topic is very interesting 
- Paper is well-written overall, however some typos and awkward sentences are there
- Other than the z-scoring part, the empirical results seem to be extensive and convincing
- The idea seems novel and very neat

WEAKNESSES

- "Part of these datasets have been z-normalized while the others not, so for the convenience of training and testing, we standardize all the datasets and the missing values are replaced with zeros." Please describe the z-normalization procedure in detail. I assume that the parameters of z-normalization are derived from the train data and are applied to both train and test data. However, I have a concern that the z-normalization could be applied to train and test data as whole, in which case the experimental framework would be rendered invalid. Until this concern is cleared, it is impossible to consider the acceptance of the paper.
- Work [1] seems related as well please discuss.
- $Z_i$ in (7) is a mistake
- "In other words, parameters θ are solely conditioned on X: X → θ." This does not make any sense and also is easy to confuse with the mathematical definition of mapping. Please rewrite.
- Insufficient detail to understand how multivariate case is handled. The architecture depicted in Fig. 1 is inherently uni-modal. How exactly do you handle the multivariate case?
- Please add equation with all loss terms and provide values for loss weights. How did you tune them?
- Ablation studies are missing. I would like to see the results, both quantitative and comparison of TSNEE plots when we remove the losses one by one. What happens when we remove $L_{decomp}$? $L_{KL}$? $L_{ac}$?
- Please make sure paper is proof-read carefully, the writing quality can be improved in terms of typos and certain awkward sentences popping here and there

MINOR POINTS

- The reference with Pedro Pinheiro should be P. O. Pinheiro et al., please correct
- "a time series decomposition-based contrastive learning" why not write it simply "a time series decomposition-contrastive learning"?
- I would propose to replace $Z = f_θ(X) \in R^{L \times D}$ with $f_\theta: R^{L \times M} \to R^{L \times D}$, to make it clear that input is in $R^{L \times M}$ and output is in $R^{L \times D}$
- typo adpatively -> adaptively


[1] Ling Yang, Shenda Hong, Unsupervised Time-Series Representation Learning with
Iterative Bilinear Temporal-Spectral Fusion, https://arxiv.org/pdf/2202.04770.pdf
clarity,_quality,_novelty_and_reproducibility: - I have no concerns about clarity, paper is clearly written
- Datasets are public, code is provided, hyperparameter settings and hardware requirements are described well. I have no reproducibility concerns
- Quality is good overall, but ablation studies are missing
- Novelty is excellent
summary_of_the_review: I very much like the paper overall, however I have two serious concerns

- I have strong concern about z-normalization, which has potential to invalidate the entire experimental framework. I cannot recommend the paper for acceptance unless this concern is cleared.
-  Ablation studies are missing.

I am willing to increase the score to accept if authors carefully address my concerns and I do hope that the authors cooperate during the rebuttal period.
correctness: 4: All of the claims and statements are well-supported and correct.
technical_novelty_and_significance: 4: The contributions are significant, and do not exist in prior works.
empirical_novelty_and_significance: 3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.
flag_for_ethics_review: NO.
details_of_ethics_concerns: n/a
recommendation: 3: reject, not good enough

From: ICLR.cc/2023/Conference/Paper5699/Reviewer_9QzX
confidence: 2: You are willing to defend your assessment, but it is quite likely that you did not understand the central parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.
summary_of_the_paper: nstead of relying only on contrastive learning, the authors propose to introduce the classical tricks from NLP & vision, namely masking and data augmentation to improve signal representation learning.
The first step of the architecture consists in a decomposition in trend and periodicity (both are forced to be distinct through KL but should enable the reconstruction of the signal). Then, the authors introduce a recursive approach, decomposing residues in the same manner.
The contrast criterion is introduced between the different decomposition scales, inside a single signal.

Then the authors propose an experimental section on UCR and UEA. Results are evaluated in ACC and AUPRC first. Then they propose a qualitative analysis of the latent space. They also provide some ablation studies regading the specific contrastive loss.
strength_and_weaknesses: **Strength** 

Interesting decomposition approach


**Weaknesses**

Unexplained gap between presented result and those found in the literature


==

We wonder what is the hypothesis behind the decoposition of the residue: if the trend is a high energy + low frequency signal, it should be explicated at the first step.

Is there a link with orthogonal matrix factorization? Or Orthogonal Matching Pursuit (to keep the recursive aspect of the approach)?

The AUPRC metric should be described (even shortly) in the article.

I don't understand the metric & results of table 1: results (ACC around 0.4 on UCR) seem very far from what I read in the literature. I don't get the difference of setting with the cited references.

Sec 4.2.3 is not really meaningful, it could be moved to appendix.
I also notice that the proposed TSNE does not match what I saw in the literature (in Tonekaboni 2020 for instance).

On the contrary, sec 4.3.1 is a bit short: we wonder what would be the performances of each decomposition level (does-it exist a noise only level that penaliez the performances? What is the impact of the trends extracted after level 1? etc...)

Given the contrastive criterion, I don't understand why the ablation is so harmless on univariate TS while it is so harful on multivariate.

clarity,_quality,_novelty_and_reproducibility: The model is clear, the reported performances are very low wrt the literature.
summary_of_the_review: This article describe a new signal decomposition approach based on an original contrastive crtiterion. The whole article is well written and interesting, but I do not understand the differences between the proposed results and those that I found in the cited references. The extent of the discrepancies leads me to reject this article.
correctness: 3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.
technical_novelty_and_significance: 3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.
empirical_novelty_and_significance: Not applicable
flag_for_ethics_review: NO.
recommendation: 3: reject, not good enough

From: ICLR.cc/2023/Conference/Paper5699/Reviewer_HiGm
confidence: 3: You are fairly confident in your assessment. It is possible that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.
summary_of_the_paper: This paper proposes TS-DC, a contrastive learning approach for time series representation learning based on trend-seasonality decomposition. The key idea of TS-DC is to decompose the time series into pairs of additive trend and seasonality recursively, and then reconstruct the original time series with these trend and seasonality components. The final loss includes loss based on KL-divergence, decomposition procedure and adaptive contrasting. 

strength_and_weaknesses: Strength: TS-DC uses recursive decomposition instead of negative samples in contrastive learning for time series. This method gets the contrastive learning rid of additional biases brought by negative sampling and avoids data augmentation. This paper brings a new perspective to relative research fields. The experiments are comprehensive. 

Concerns and questions: As shown in Fig.4, the first components seem to have the most information of the original time series, and the latter ones are more like noises. If we change the number of components decomposed, what the results would be like? It would be great if some experiments can be added to answer this question. Besides, in Section 3.3, how does the non-linear function h_phi is implemented? I think more details need to be added. 
clarity,_quality,_novelty_and_reproducibility: Good
summary_of_the_review: This paper brings a new perspective to relative research fields. The experiments are comprehensive.
correctness: 3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.
technical_novelty_and_significance: 3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.
empirical_novelty_and_significance: 3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.
flag_for_ethics_review: NO.
recommendation: 6: marginally above the acceptance threshold

From: ICLR.cc/2023/Conference/Paper5699/Reviewer_BofU
confidence: 3: You are fairly confident in your assessment. It is possible that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.
summary_of_the_paper: In this paper, the authors propose a new method TS-DC for unsupervised time series representation learning. In the TS-DC method, original multivariate time series is decomposed into trend and seasonality components iteratively. Then three losses L_decomp (based on decomposition error), L_{KL} (quantifies distance between distributions of the trend and seasonality components), and L_ac (use contrastive positive/negative pairs to extract complex signals in original data at different decomposition level) are designed and used to get the optimal representations. Experimental results look promising.
strength_and_weaknesses: Strength
The whole framework looks pretty novel and applying contrastive learning (CL) at different decomposition level of the original data provides a new way to unleash the power of CL.

Weakness
Decomposition of time series into trend and seasonality components interactively is not new. It is pretty close to the work of N-beats. The authors may want to add discussions on connection with N-beats and relevant existing work on CL for time series. So audience may have better idea on the contribution of the work.
clarity,_quality,_novelty_and_reproducibility: Overall, the paper is well written and clear. 
Novelty looks pretty good as I mentioned in the strength of the work. 
Reproducibility is feasible with the submitted code.

summary_of_the_review: 1. Are there any principle way to determine the level of decomposition N? For example, can we determine N based on the residue error or Fourier analysis.
2. The S vector in eq. (2) contains integer multipliers of 2\pi in the sin/cos functions (assume L is even). So we will get a vector with only 0 or 1 elements which cannot describe the seasonality in the signal.
3. Eq. (7), the contrastive loss is built based on X and X_n, n=1, 2, …, N. Can we build the contrastive loss based on X and X^s/X^t at different levels? Trend and seasonality should be quite different and naturally could be used for construct similar/dissimilar pairs.
4. Eq. (10), w_n is a vector with dimension D. L_c is a real number if I understand correctly. I am not clear how to multiple them together and get the final loss L_ac which I assume it is also a single real number.
5. In sec. 4.2, looks like the proposed method serves only as a feature extractor and is independent of the subsequent classification task. It is not clear what the classifier is and what the supervised method is in Table 2 and Table 3. The whole setting needs clarification.
6. Fig. 3, visually all sub-figures look no significant difference regarding the clustering except T-Loss. Maybe it’s due to the dominance of classes 1 and 2. I would suggest to use another more representative example for illustration.  

correctness: 3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.
technical_novelty_and_significance: 3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.
empirical_novelty_and_significance: 2: The contributions are only marginally significant or novel.
flag_for_ethics_review: NO.
recommendation: 6: marginally above the acceptance threshold