UFGTime: Reforming the Pure Graph Paradigm for Multivariate Time Series Forecasting in the Frequency Domain

There are major weaknesses that prevent me from recommending acceptance.

• Soundness of the approach. The proposed approach builds a graph representation by considering the K-nearest neighbors of a representation of the input obtained through an FFT along the temporal dimension. However, in such a representation, each node corresponds to a different frequency and entity. I don't understand why one would want to connect nodes that correspond to different frequencies. For example, with such a representation, signals that have all of their spectrum concentrated at totally different frequencies would get connected. This representation does not preserve the structure of the data, similarly to the method the paper is trying to fix.
• Poor novelty and weak motivation. As noted, the limitation the paper aims to address is specific to a single model. Addressing such a narrow issue isn't sufficient when most state-of-the-art approaches do not have this drawback. Many spatiotemporal graph neural networks utilize sound graph representations of the input, and in many cases, the processing of spatial and temporal dimensions is well integrated (e.g., see [1]). Additionally, several signal processing methods operate on pure graph representations of sets of time series. For instance, [2] uses product graph representations. The visibility graph is another principled graph representation of input time series (e.g., see [3]). All of these representations avoid the issues the proposed method attempts to solve and are more sound than the one presented in the paper. Lastly, the novelty of the graph framelet operator is limited, as it appears to be a straightforward adaptation of an existing method.
• Soundness of the empirical evaluation. The empirical evaluation has some issues. Firstly, there is a growing consensus that the ETT benchmarks used for the experiments in Tab 3 are not significant for evaluating deep learning methods for time series forecasting. For example, in [4], a simple autoregressive linear model trained using ordinary least squares achieves better results than those reported in the table in almost all the considered scenarios. Secondly, some of the results in Table 2 involve baselines that require a predefined input graph, which, according to the appendix, is a kNN graph obtained in an unclear way (e.g., which similarity metric was used to create this graph?).

Given these issues, the paper is far below the acceptance threshold by ICLR standards.

Minor comments

• There must be some reporting errors in Table 3. Looking at the MSE for UFG in ETTH1, the MSE at 192 steps is lower than the MSE at 96, which does not make any sense if the testing is done properly. Differently, the MAE increases as one would expect.

[1] Wu et al., "Traversenet: Unifying space and time in message passing for traffic forecasting" TNNLS 2022
[2] Sabbaqi et al., "Graph-time convolutional neural networks: Architecture and theoretical analysis." PAMI 2023.
[3] Lacasa et al., "From time series to complex networks: The visibility graph" PNAS 2008
[4] Toner et al., "An Analysis of Linear Time Series Forecasting Models." ICML 2024\

• The core motivation of this work feels narrow. While improving upon FourierGNN is a valuable contribution, the paper does not clearly establish why the disjoint modeling architecture in existing GNN-based methods fails critically in practice, or why FourierGNN's approach is inherently superior. A stronger emphasis on the overarching challenges of multivariate time series forecasting would better justify the significance of this work.
• The storytelling could be improved, particularly in the introduction. The two key challenges in FourierGNN are not clearly articulated, and after reading the introduction, it is unclear if this research addresses a significant problem.
• The empirical validation in Sec. 3 is somewhat weak in certain aspects. For instance, the experimental setup for the evaluation in Tab. 1 is unclear, and the performance degradation after permutation looks significant without compared to benchmarking methods, leaving doubt about the strength of the claims. Additionally, the visualization results in Fig. 2 show minimal differences between sparse and fully connected Laplacian patterns without the attention weights.
• The construction of the hyperspectral graph closely mirrors that of the hypervariate graph, with the key distinction being that it bypasses direct modeling of sequential information by transforming time series into discrete frequency components.
• There is a lack of comparative discussion against competitive time series models, particularly recent approaches like PatchTST and TimeMixer. The advantages of UFGTIME over these models are not sufficiently explored, which reduces the clarity around the unique contributions of this research.

• [W1]: Performance improvements achieved by the proposed method are mostly minor compared with FourierGNN for the datasets considered in short-term forecasting.
• [W2]: The proposed method is outperformed by baselines on datasets used for long-term forecasting. Interestingly, in several cases, there is a discrepancy in the performances achieved in terms of MSE and MAE (e.g., MAE scores of the proposed UFGTIME on ETTh2 are the best against baselines, but corresponding MSEs are almost double in value compared to the Autoformer).
• [W4]: The authors focus on the challenges of the pure graph paradigm, yet most graph-based methods for time series before this work [1] were similarly using KNN [3] or differentiable methods (Gumbel softmax) [2] to achieve graph sparsity. Additionally, embeddings were learned based on time series inter-variable correlations or temporal dynamics [2] or as node embeddings [3]. The paper misses an extensive discussion, e.g., in the related work section, on the critical characteristics of the graph modules introduced in the literature to adequately position the proposed UFGTIME's contribution.
• [W5]: The learned graph dependencies are not evaluated qualitatively. Similar to the studies/visualizations for the graph learning module in [3], it would be interesting to assess the validity of learned time series dependencies produced by the proposed graph module.
• [W6]: The proposed method is quite efficient regarding memory/time cost. However, it would be interesting for the discussion to be enhanced with explanations of the complexities of all considered GNN-based baselines. It is unclear to which extent the memory complexity/efficiency of the proposed method is affected by the window size and number of variables in the input, which could provide additional ablation studies.

[1] Yi, K., Zhang, Q., Fan, W., He, H., Hu, L., Wang, P., ... & Niu, Z. (2024). FourierGNN: Rethinking multivariate time series forecasting from a pure graph perspective. Advances in Neural Information Processing Systems, 36.

[2] Shang, C., Chen, J., & Bi, J. (2021). Discrete graph structure learning for forecasting multiple time series. arXiv preprint arXiv:2101.06861.

[3] Wu, Z., Pan, S., Long, G., Jiang, J., Chang, X., & Zhang, C. (2020, August). Connecting the dots: Multivariate time series forecasting with graph neural networks. In Proceedings of the 26th ACM SIGKDD international conference on knowledge discovery & data mining (pp. 753-763).

• The presentation is confusing, often blending obvious claims with unsupported statements and using ambiguous terminology.
• The paper tackles challenges that seem obvious and already addressed in the literature: (1) the importance of maintaining temporal order in time-series processing, and (2) the unsuitability of fully connected graphs in graph-based processing.
• As far as I could understand, the paper’s original contribution is limited to constructing a KNN graph from a spectral representation of the original multivariate time series.