Introducing Spectral Attention for Long-Range Dependency in Time Series Forecasting

Sequence modeling faces challenges in capturing long-range dependencies across diverse tasks. Recent linear and transformer-based forecasters have shown superior performance in time series forecasting. However, they are constrained by their inherent inability to effectively address long-range dependencies in time series data, primarily due to using fixed-size inputs for prediction. Furthermore, they typically sacrifice essential temporal correlation among consecutive training samples by shuffling them into mini-batches. To overcome these limitations, we introduce a fast and effective Spectral Attention mechanism, which preserves temporal correlations among samples and facilitates the handling of long-range information while maintaining the base model structure. Spectral Attention preserves long-period trends through a low-pass filter and facilitates gradient to flow between samples. Spectral Attention can be seamlessly integrated into most sequence models, allowing models with fixed-sized look-back windows to capture long-range dependencies over thousands of steps. Through extensive experiments on 11 real-world time series datasets using 7 recent forecasting models, we consistently demonstrate the efficacy of our Spectral Attention mechanism, achieving state-of-the-art results.

Paper

Similar papers

Peer review

Reviewer weYb5/10 · confidence 4/52024-07-08

Summary

This paper focuses on the exploration of long-term dependency within a whole time series sequence, to address the challenge of the short-term look-back window, which is interesting. Based on the observation, this paper provides Batched Spectral Attention to enable parallel training across multiple timesteps.

Strengths

* The analysis of attention is sufficient to show the FFT graphs. * The method is designed as an easy plug-in module, which benefits various base models.

Weaknesses

* The writing and logical presentation can be strengthened, which is hard to understand, e.g., Fig. 2. (I spent lots of time understanding the formulations and Fig. 2 ) * It is not clear why only the low-frequency components are used, just for long-term dependency, and why the lack of high-frequency components does not affect the short-term vibrations. * The comparison in Table 1 may be a little unfair since more computation and memory are introduced by the BSA. Thus, please provide the computation and memory comparison in Table 1 to further evaluate the superiority of BSA. * I am curious will the performance still be improved when applying BSA as the look-up window T increases or decreases? That is to validate the effectiveness of BSA in more scenarios to demonstrate its generalization ability.

Questions

See weaknesses.

Rating

5

Confidence

4

Soundness

2

Presentation

3

Contribution

3

Limitations

Not sufficient. I can't find the potential negative societal impact of their work in the Conclusion.

Reviewer weYb2024-08-08

Thank you for the response. I raise my scores to 5.

Authorsrebuttal2024-08-12

Dear Reviewer weYb, We are immensely thankful for your constructive feedback. Your helpful and insightful comments would indeed make our paper stronger. - Significantly improve the figures in the paper to make them easier to understand and ensure a more natural flow. - Through a comprehensive study of BSA's computation and memory, we demonstrate the high efficiency of BSA. - Verify that BSA consistently demonstrates high performance even in situations where the look-back window changes. While we hope that our response properly addressed your concerns, we would be happy to provide any additional clarification if necessary. We are also awaiting your advice that could further strengthen our paper. Thank you for your time and effort. Sincerely, Authors

Reviewer pdEA5/10 · confidence 4/52024-07-10

Summary

The paper presents a Spectral Attention mechanism to address the challenge of capturing long-range dependencies in time series forecasting. By preserving temporal correlations among samples and leveraging frequency domain information, the proposed method enhances the forecasting performance of various baseline models. Extensive experiments demonstrate the efficacy of Spectral Attention, achieving state-of-the-art results on multiple real-world datasets.

Strengths

1. Efficacy: The proposed Spectral Attention mechanism significantly improves forecasting performance across multiple real-world datasets. 2. Versatility: The method can be integrated into various baseline models, showcasing its adaptability and broad applicability. 3. Experimental validation: The experiments show consistent performance improvements.

Weaknesses

1. Novelty and Contribution/Missing Related Work * While the paper introduces Spectral Attention as a novel method, using frequency domain analysis in time series forecasting is not a new concept. Notably, there is an existing paper [1] with the same title, "Spectral Attention," also focused on time series forecasting, which is not referenced in the manuscript. This referenced paper employs a global/local perspective: the global Spectral Attention provides comprehensive information about the random process the time series are considered part of, thereby addressing some limitations mentioned in the paper, such as the inability to model long-range dependencies. Furthermore, the referenced work includes spectral filtering, differing from the authors' approach by learning a cut-off frequency while filtering each frequency component independently. Their solution integrates easily into pre-existing architectures. Given the significant similarities and the relevance of this other paper as a precursor to the authors' idea, why is it not cited in the manuscript? The authors must include a thorough discussion of [1], acknowledging its relation and relevance to their work. * Additionally, recent SSM-based approaches should be covered in the related work section. 2. Differentiation from Existing Methods * The paper would benefit from a clearer distinction between Spectral Attention and existing frequency-based methods such as WaveFroM, FEDformer, or the Spectral Attention Autoregressive Model. The unique advantages and innovations of Spectral Attention compared to these methods should be emphasized more explicitly. 3. Computational Complexity * The paper claims that Spectral Attention adds minimal computational overhead. However, the analysis of computational complexity and memory requirements is somewhat superficial. A detailed comparison of training and inference times, as well as memory usage, with and without Spectral Attention, should be provided to substantiate these claims. 4. Integration with Different Models * While the paper demonstrates that Spectral Attention can be integrated with various TSF models, the integration process lacks detail. Specific guidelines or algorithms for integrating Spectral Attention with different architectures should be included. This would facilitate practitioners in applying the proposed method to their models. [1] Moreno-Pino, Fernando, Pablo M. Olmos, and Antonio Artés-Rodríguez. "Deep autoregressive models with spectral attention." Pattern Recognition 133 (2023): 109014.

Questions

1. How does the proposed method specifically improve upon the referenced Spectral Attention Autoregressive Model [1]? * A detailed comparative analysis and, if possible, empirical validation are necessary to substantiate the claims of improvement. 2. Can you provide a more detailed explanation of the complexity involved in the spectral attention mechanism? 3. Given that the proposed model operates in the frequency domain, is it capable of handling irregularly sampled data even if the underlying architecture cannot? I am open to raising my score if the authors adequately address these concerns.

Rating

5

Confidence

4

Soundness

2

Presentation

3

Contribution

2

Limitations

Yes

Area Chair qM2o2024-08-12

Discussion

Thank you for being a reviewer for NeurIPS2024, your service is invaluable to the community! The authors have submitted their feedback. Could you check the rebuttal and other reviewers' comments and start a discussion with the authors and other reviewers? Regards, Your AC

Authorsrebuttal2024-08-13

Dear Reviewer pdEA, We sincerely appreciate your valuable feedback and time reviewing our work. Your helpful and insightful comments would indeed make our paper stronger: - Added recommended related studies to the "related work" section and clarified the distinctions from our research. - Clarified the novelty of our BSA method compared to other frequency-utilizing methods - Conducted a thorough analysis of BSA's computational cost and memory efficiency, demonstrating its high efficiency - Provided a detailed description of the BSA implementation process. Again, we thank you for your response to our rebuttal. While we hope that our response properly addressed your concerns, we would be happy to provide any additional clarification if necessary. We also welcome any additional advice you may have that could strengthen our paper. Thank you for your time and effort. Sincerely, Authors

Reviewer A63Y6/10 · confidence 4/52024-07-13

Summary

This paper introduces a new mechanism called "Spectral Attention" designed to address the challenge of long-term dependencies in time series prediction. Traditional models such as linear and Transformer-based predictors face limitations in handling long-term dependencies due to fixed input sizes and the shuffling of samples during training. Spectral Attention enhances model performance by preserving temporal correlations and facilitating long-term information processing. It utilizes low-pass filters to capture long-term trends and supports parallel training across multiple time steps, thus expanding the effective input window. Experimental results demonstrate that this mechanism achieves state-of-the-art prediction performance on multiple real-world datasets, opening new avenues for exploration in time series analysis.

Strengths

1. Aiming at the problem of long-term dependence in time series prediction, this paper proposes a novel Spectral Attention mechanism. 2. This method can be extended to multiple prediction models and achieve performance improvement.

Weaknesses

1. There are some formulas in the paper that do not explain the specific meaning. 2. the source code of the paper is not open, can not verify the effect of the experiment.

Questions

1. the use of sequential sampling instead of random sampling, which will cause the model to generalize in the face of new data or different distribution of data, there is a risk of overfitting? 2. There are some formulas in the paper that do not explain the specific meaning. For example, "The base model can be reformulated as P=f2(F,E) and F,E=f1(X)." What is the meaning of "E"? 3. How is the formula "fSA=f2·SA·f1" derived in the sentence "Our Spectral Attention module takes feature F as input and transforms it into F' of the same size, F' =SA(F), modifying the base model as follows: fSA= f2 · SA · f1"? 4. why was the experiment not conducted on the common ILI "dataset"? 5. Do spectral attention mechanisms significantly increase the computational cost of model training and inference?

Rating

6

Confidence

4

Soundness

2

Presentation

3

Contribution

3

Limitations

no.

Area Chair qM2o2024-08-12

Discussion

Thank you for being a reviewer for NeurIPS2024, your service is invaluable to the community! The authors have submitted their feedback. Could you check the rebuttal and other reviewers' comments and start a discussion with the authors and other reviewers? Regards, Your AC

Authorsrebuttal2024-08-13

Dear Reviewer A63Y, We sincerely appreciate your valuable feedback and the time you dedicated to reviewing our work. Your insightful comments have been very helpful in enhancing the quality of our paper: - Improved the formulas in the paper for better clarity and also revised Figure 2 (as shown in the attached PDF) - Discussed whether the model overfits to the latter part of the training dataset with BSA. - Demonstrated BSA's constant superiority on the ILI dataset - Conducted extensive experiment on computational cost and memory, demonstraing the high efficiency of BSA We are also pleased to demonstrate several important additional experimental results: - BSA consistently demonstrates high performance even when the original 96 lookback window is changed to 192 or 48 (reviewer weYb) - BSA also consistently showed high performance on three additional well-known datasets (PEMS03, Energy-Data, Solar) (global comment) While we hope that our response properly addressed your concerns, we would be happy to provide any additional clarification if necessary. We also welcome any additional advice you may have that could strengthen our paper. Sincerely, Authors

Reviewer pdEA2024-08-12

Response to authors

Thank you for the new experiments carried out by the authors, which have improved the paper. I am raising the score.

Program Chairsdecision2024-09-25

Decision

Accept (poster)

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