SimMTM: A Simple Pre-Training Framework for Masked Time-Series Modeling

Time series analysis is widely used in extensive areas. Recently, to reduce labeling expenses and benefit various tasks, self-supervised pre-training has attracted immense interest. One mainstream paradigm is masked modeling, which successfully pre-trains deep models by learning to reconstruct the masked content based on the unmasked part. However, since the semantic information of time series is mainly contained in temporal variations, the standard way of randomly masking a portion of time points will seriously ruin vital temporal variations of time series, making the reconstruction task too difficult to guide representation learning. We thus present SimMTM, a Simple pre-training framework for Masked Time-series Modeling. By relating masked modeling to manifold learning, SimMTM proposes to recover masked time points by the weighted aggregation of multiple neighbors outside the manifold, which eases the reconstruction task by assembling ruined but complementary temporal variations from multiple masked series. SimMTM further learns to uncover the local structure of the manifold, which is helpful for masked modeling. Experimentally, SimMTM achieves state-of-the-art fine-tuning performance compared to the most advanced time series pre-training methods in two canonical time series analysis tasks: forecasting and classification, covering both in- and cross-domain settings.

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Peer review

Reviewer 5Qee7/10 · confidence 3/52023-07-04

Summary

This paper presents SimMTM, a simple pre-training framework for masked time-series modeling. The core idea is to train the model to reconstruct the time series by aggregating information from multiple masked series rather than one single masked series. While the temporal pattern is destroyed in a single masked series, multiple masked series contain complementary information, making the reconstruction process more accessible. The aggregation of point-wise representations is weighted by their series-wise similarities. The proposed loss adds the reconstruction loss with a contrastive loss on the series representations. The author provides extensive empirical studies on both time series classification and time series forecasting tasks to evaluate the learned representations.

Strengths

The proposed method is sound and well-motivated. Reconstructing the original time series from multiple randomly masked series is novel, in my opinion. The write-up is easy to follow. The overview figure is also illustrative and helps the understanding. The empirical evaluation is comprehensive and convincing.

Weaknesses

1. In Eq 4, the sum over the variable $s'$ is confusing without carefully reading the text below it. In my opinion, it would be more clear to have the sum over $z'$ and have $s' = Projector(z')$ on the right. 2. Eq 7 is not precise. I understand that the authors mean the intra-similarity of samples should be maximized. However, the sets before and after $~$ are the same, and therefore they are already "close". Please considering revise eq 7.

Questions

The paper says, "For each time series, the reconstruction is not only based on its own masked series." I wonder how much does the method benefit from aggregating representations from other time series?

Rating

7: Accept: Technically solid paper, with high impact on at least one sub-area, or moderate-to-high impact on more than one areas, with good-to-excellent evaluation, resources, reproducibility, and no unaddressed ethical considerations.

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.

Soundness

3 good

Presentation

3 good

Contribution

3 good

Limitations

Yes

Reviewer L1Yx8/10 · confidence 3/52023-07-05

Summary

Pre-training models have been using self-supervised learning in various fields (NLP, Vision). However, masked modeling, a representative method of self-supervised learning, was difficult to apply to time-series tasks. Randomly masked data is difficult to show good performance because semantic information of time series including temporal changes is broken. Thus, SimMTM recovers the masked point in time through weighted aggregation of multiple neighbors outside the manifold. This not only restores simple, but also reconstructs complementarily, leading to good performance. SimMTM performs forecasting and classification (in-domain, cross-domain) on various datasets and shows good performance.

Strengths

1. They explained the problem of masked modeling in time-series data well from the time-series point of view. 2. Also, to apply masked modeling to time-series data, the characteristics of time-series were well utilized. In other words, masked modeling was not simply applied to time-series, but the characteristics of time-series data were well understood and applied accordingly. 3. Experiments were conducted on various tasks of the pre-training model, and remarkable performance improvements were achieved.

Weaknesses

It seems that there is a part that does not match the notation in the formula and Figure 2.

Questions

Regarding weakness, I don't know what $z'$ means in Eq.4 and line 154. No explanation of $s'$ in "$z'$ represents the corresponding point-wise representation of $s'$". Does $s'$ mean series-wise representations $S$?

Rating

8: Strong Accept: Technically strong paper, with novel ideas, excellent impact on at least one area, or high-to-excellent impact on multiple areas, with excellent evaluation, resources, and reproducibility, and no unaddressed ethical considerations.

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.

Soundness

3 good

Presentation

3 good

Contribution

3 good

Limitations

In fact, there is no limit to this work

Reviewer ZNHw5/10 · confidence 3/52023-07-06

Summary

The authors propose SimMTM, a novel representation learning method for time-series data based on random masking. They experimentally verify the effectiveness of the proposed method from both in-domain and cross-domain perspectives. Comprehensive comparative experiments with existing methods are conducted, demonstrating the effectiveness of the proposed approach.

Strengths

The authors have conducted extensive comparative experiments with existing methods and quantitatively demonstrated the effectiveness of the proposed method. In addition to in-domain generalization, they also focus on cross-domain generalization. This verification is indispensable for validating the effectiveness of deep representation learning assuming large-scale open data.

Weaknesses

**Presentation quality** The current presentation style of this paper is confusing. Particularly, there is a lack of consistency in the representation of formulas and symbols, making it very difficult to grasp the overall logic of the paper. Some specific examples include: 1. In Equation 3, the symbol $\times$ is used to denote both the Cartesian product and scalar multiplication when defining the domain of $R$. 2. The transposition notation in Equation 3 is counterintuitive as $\mathbf{s}$ is defined as a row vector. 3. Equation 7 is overly verbose and exacerbates the difficulty in reading, as it does not contribute to the subsequent. It would be sufficient to simply declare that only the situation where $i = k$ is treated as positive pairs. 4. While $\mathbf{s}$ is defined as a single vector, $\mathbf{s}^+$ is defined as a set of vectors. Some other points that I could not make from the paper are discussed below in the Questions section. **Comparison with prior literature** The comparison with prior literature is insufficient. For example, references [1, 2] can be cited as representative examples of representation learning methods for deep neural networks under time-series data. In particular, a model that generalized the method in [2] as a generalized contrastive learning method not limited to the time-series domain was proposed later. Both [2] and [3] have superior theoretical guarantees for identifiability from the perspective of nonlinear ICA. The authors should clearly indicate the proposed model's advantages over these approaches. **References** 1. Hyvarinen, A., & Morioka, H. (2016). Unsupervised feature extraction by time-contrastive learning and nonlinear ICA. *Advances in neural information processing systems*, *29*. 2. Oord, A. V. D., Li, Y., & Vinyals, O. (2018). Representation learning with contrastive predictive coding. *arXiv preprint arXiv:1807.03748*. 3. Hyvarinen, A., Sasaki, H., & Turner, R. (2019, April). Nonlinear ICA using auxiliary variables and generalized contrastive learning. In *The 22nd International Conference on Artificial Intelligence and Statistics* (pp. 859-868). PMLR.

Questions

- What is the definition of $\operatorname{Encoder}(\mathcal{X})$? Typically, a function $f \colon X \rightarrow Y$ can use all the information in $X$ to calculate $Y$, but it seems that the Encoder function defined here applies the same function in parallel to some dimension. However, it is not clear from the text which dimension this parallel processing applies to. For example, there would be at least two possibilities: $\operatorname{Encoder}(\mathcal{X})$ is kind of a “syntax suger” for either $\bigcup\_i \operatorname{Encoder}( \\{x\_i\\} \cup \\{\bar{x}\_i^j \\}\_{j} )$ or $\bigcup\_i ( \\{ \operatorname{Encoder}(x\_i) \\} \cup \\{ \operatorname{Encoder}(\bar{x}\_i^j) \\}\_{j} )$. The same can be said about the definitions of the Projector and Decoder. - Although I understood the training pipeline of the proposed method, I had questions regarding its behavior at inference time. Does the proposed method compute internal representations from the true sequence and $M$ randomly masked sequences at inference time, similar to training time? Or does it only use the true sequence without random masking at inference time? Additionally, how is training conducted during the fine-tuning stage in the pipeline? - The authors mention the analysis of a quantity called the CKA value in line 262 of Section 4.4, but it is unclear what this quantity actually is. While there is an explanation of Pre-training/Fine-tuning CKA in the caption of Table 5, if the CKA value mentioned in the main text refers to these, its meaning should be clearly explained in the text as well. Moreover, I did not understand why a small $| \Delta_{\mathrm{CKA}} |$ leads to “acquiring adaptive representations for different tasks” (l.264). In principle, it should be possible to drastically change the internal representation by fine-tuning while maintaining the degree of change in the internal representation along the evolution of the layers. Suppose $x_\mathrm{first}$ and $x_\mathrm{last}$ be the representation in the first and the last layer at the pre-training phase, respectively. We can consider one idealistic situation that the representations after fine-tuning are given as $y_{\mathrm{first}} = x_{\mathrm{first}} + \delta_{\mathrm{task}}$ and $y_{\mathrm{last}} = x_{\mathrm{last}} + \delta_{\mathrm{task}}$ with a task-dependent fixed vector $\delta$. In such a situation, the values of Pre-training/Fine-tuning CKA would be nearly the same, and the difference in CKA values would go to zero by construction. However, the internal representations drastically change depending on the task choice. In this context, I believe there is a logical gap in the authors' argument. - In masked modeling-based representation learning, the proposed method uses the true sequence without masking, along with the input. This setup is generally considered to make it more challenging to avoid trivial local solutions that merely output the input as is. Can it be said that such a phenomenon does not occur? Moreover, if a trivial local solution can be avoided, what factors of the proposed method enable this? - As a naive control condition for the idea of using multiple different random masks, it is possible to consider the variant of using only one random mask that reduces the masked portion $r$, or takes the position of the mask to have a specific rules that is not completely iid. Can the proposed method be claimed to be effective against such variants? In particular, the model structure of using multiple random masks is expected to have at least some overhead in terms of training/inference computation time compared to such simple control conditions.

Rating

5: Borderline accept: Technically solid paper where reasons to accept outweigh reasons to reject, e.g., limited evaluation. Please use sparingly.

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.

Soundness

3 good

Presentation

2 fair

Contribution

3 good

Limitations

The limitations of this paper are adequately discussed in the appendix. Furthermore, the effectiveness of the proposed method can be confirmed from various perspectives through exhaustive comparative experiments. However, as mentioned earlier, there are major concerns primarily about the presentation of the paper. These are points that affect the reproducibility of the results and the authors' claims, so it would be necessary to resolve all problems of unclear logical progression for this paper to be accepted.

Authorsrebuttal2023-08-19

Request of Reviewer's attention and feedback

Dear Reviewer, We kindly remind you that it has only 2 days until the Reviewer-author discussion ends. Please let us know if our response has addressed your concerns. Due to the word limit of Rebuttal, we will be happy to answer your concerns further or deal with any additional issues/questions in the discussion period. Following your suggestion, we have answered your concerns and improved the paper in the following aspects: - We **have rewritten or modified some formulas and corrected some writing errors** to improve presentation quality. - We **have compared SimMTM and three generalized representation learning methods you mentioned TCL(2016), CPC(2018), and PCL(2019)**. We further demonstrate the state-of-the-art performance of SimMTM. - We **explained the training pip-line of pre-training and fine-tuning**, **the definition of Encoder**, **What is $\text{CKA}$, and why we use $|\Delta_{\text{CKA}}|$ to measure the difference in representation-learning property between pre-training and fine-tuning models**. - We further **analyzed the relationship between masked ratios and numbers** and **compared the effect of different masked rules**. Since we cannot submit the revised version during the reviewing phase, we guarantee to resolve all the writing issues and include all the above updates in the revised paper. Thanks again for your valuable review. We are looking forward to your reply.

Authorsrebuttal2023-08-21

We are anticipating your feedback.

Dear Reviewer ZNHw, Thanks again for your valuable and constructive review, which has inspired us to improve our paper further substantially. Following your suggestions, we have modified some formulas and writing errors to improve presentation quality, compared the three generalized representation learning methods you mentioned, analyzed the relationship between masked ratios and numbers, compared the effect of different masked rules, and discussed all your mentioned weaknesses in every detail. We do our best to solve your concerns in the limited time and characters. We hope that this new version has addressed your concerns to your satisfaction. We eagerly await your reply and are happy to answer any further questions. **We kindly remind you that the reviewer-author discussion phase will end by Aug 21st at 1 pm EDT, just 4 hours left. After that, we may not have a chance to respond to your comments**. Sincere thanks for your dedication! Authors

Reviewer xbHA5/10 · confidence 4/52023-07-07

Summary

This paper proposes a simple pre-training framework for masked time-series modeling. Instead of reconstructing origin data directly, which is unsuitable for time series, this paper recovers masked time points by the weighted aggregation of multiple neighbors outside the manifold. The reviewer appreciates the novelty method proposed, but is still concerned about some results.

Strengths

1) The method is of novelty. The multi-level aggregation and representation method is appealing. 2) Experimentally, both high-/low-level tasks benefit from this method.

Weaknesses

1. The experimental results need more justification (see Questions). 2. The relationship with manifold learning needs more description. What is the progress in this aspect? 3. The masked parts in Figure 1 and Figure 1 in Supplement material should be annotated and more results should be listed. A well-trained network usually predicts low-frequency results. Why the result of TST in the right-upper part in Figure 1 in Supplement material contains too many high-frequency parts?

Questions

In terms of experimental results, why Random init. outperforms TF-C in Table 2? Does SimMTM use a stronger baseline? Is it an unfair comparison? Maybe TF-C or other methods will outperform SimMTM with the same baseline. It seems that the model learns directly aggregate information from different masked series, which learns more temporal information than other semantic information.

Rating

5: Borderline accept: Technically solid paper where reasons to accept outweigh reasons to reject, e.g., limited evaluation. Please use sparingly.

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.

Soundness

2 fair

Presentation

4 excellent

Contribution

3 good

Limitations

The authors should discuss more implications about using large-scale pre-training in forecasting in terms of fairness.

Reviewer xbHA2023-08-19

Thanks for the response

Thanks for the response. At this stage, I will keep my score unchanged.

Area Chair mxUn2023-08-21

Thanks for the updated opinion reviewer xbHA, however, could you give more detailed reasoning as why you have your score unchanged? The authors have made an effort to respond to your comments, so please at least point out which part is not satisfying enough.

Area Chair mxUn2023-08-21

Mixed reviews

Dear reviewers (and especially reviewer ZNHw), Thanks for the hard work so far! This paper received mixed reviews and the authors have responded multiple times. We need to ideally reach a consensus in the rebuttal period, and at least should have active discussions, updated recommendations, and acknowledgment that you have read the response. Can you please check other reviews and the author rebuttal and see if your opinion has changed? Please give your reasoning in as much detail as possible. AC

Reviewer ZNHw2023-08-22

Thank you for your response

Thank you for responding to my questions and concerns. Regarding presentation quality, I think the paper will be easier to read if revisions are made based on the comments. Thanks for adding the experimental comparison to the previous studies I have pointed out. After confirming the experimental results, I acknowledge the experimental advantage of this paper over these papers. About questions **Q1&Q2** I understood the procedure of this work. Thank you for your response. **Q3** I am still not fully convinced. Regarding CKA, the authors stated as > Centered Kernel Alignment (CKA) is a statistical measure between representations that identify correspondences in models with different initializations. We can use it to measure the representation-learning property of deep models by calculating between a model's first and last layer representations. A larger indicates the model tends to learn high-level representations, which is widely used in previous works [1,2,3]. First, CKA itself is a general metric that evaluates the similarity between two representations, not limited to the models with different initialization or layers. I acknowledge that CKA itself is widely used to evaluate the similarity of model representations. However, I was still not convinced by the authors' statement that evaluating the CKA of the first and last layers of a model can tell whether the model has acquired "high-level representations." It seems to me that high CKA simply means high representaion similarity between layers, but how could this lead to the acquisition of "high-level representaion” as an entire model? **Q4** I understood the authors' point. **Q5** > As mentioned in Q2, masked modeling involves only pre-training, so there is no computational overhead problem in fine-tuning and inference. Thank you for making clear this point. However, I asked about *some overhead in terms of both training/inference computation time.* The computational overhead of training time because of using multiple masking should be clearly documented in the manuscript. Overall, the additional experiments and notational revisions made the paper's contribution clear. But, I still have a bit concern on the interpretation of CKA studies. Therefore, let me raise my score to 5.

Authorsrebuttal2023-08-22

Thanks for Your Response and Raising the Score

We thank Reviewer ZNHw for providing a detailed valuable rebuttal review and feedback, which enables us to understand your concerns clearly. We are delighted to further clarify the remaining two questions: **(1)** About the CKA: we adopt this concept following the usage of the previous works [1, 2]: - Xie et al. [1] use the CKA to measure the attention similarity among different layers in vision Transformer, specially "measure the representation diversity in the model." - TimesNet [2], which also focuses on time series (**closer to our paper**), adopts the CKA similarity between bottom and top layers to define "high-level" and "low-level" representations (or tasks) quantitively ($\underline{\text{Section 4.6 of their official paper}}$). Intuitively, since the bottom layer representations are usually be viewed as containing the "low-level" or detailed information, a smaller CKA similarity means the top layer contains the different information from the bottom layer, so-called "high-level" or abstract information. Many thanks for your valuable question. We will rephrase this part in every detail by adding new explanations and proper citations to make the concept more clear. **(2)** About the training overhead: Thanks for pointing out this item. We will discuss the training overhead in the $\underline{\text{Conclusion}}$ section as a limitation and place it in the future work. Many thanks for your dedication! We guarantee to resolve all the writing issues and include all the mentioned updates in the final version. ===== [1] Xie,et al, Revealing the Dark Secrets of Masked Image Modeling. CVPR, 2022. [2] Wu,et al, TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysis. ICLR, 2023.

Program Chairsdecision2023-09-21

Decision

Accept (spotlight)

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