Pith. sign in

REVIEW 4 major objections 5 minor 31 references

A Dynamic Stiefel Graph Neural Network for Efficient Spatio-Temporal Time Series Forecasting

T0 review · 4 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read A graph neural network that learns a low-rank orthonormal spectral basis on the Stiefel manifold reports the best average forecast accuracy on seven spatio-temporal benchmarks while using far fewer parameters than competing graph and…

desk verdict The Stiefel Fourier trick is worth engaging on the empirical side, but the theoretical claims need serious repair before the paper is credible. read the letter →

arxiv 2506.00798 v1 pith:TMV3HJTH submitted 2025-06-01 cs.LG

Jiankai Zheng , Liang Xie This is my paper
classification cs.LG MSC 68T0705C5062M10
keywords spatio-temporaltimeseriesforecastinggraphneuralnetworksStiefelmanifoldspectralconvolutiondynamicgraphslow-rankfilteringefficientdeeplearning
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper argues that dynamic spatio-temporal forecasting can be made both accurate and cheap by replacing the full graph Fourier transform with a low-rank transform whose columns are orthonormal, a point on the Stiefel manifold. The proposed DST-SGNN learns this transform from a graph rebuilt from each input window, then performs spectral convolution in the reduced basis. The paper proves that this Stiefel Graph Spectral Convolution is not an approximation but exactly a standard graph spectral convolution filtered to the top-$d$ eigenvalues, with smaller eigenvalues set to zero. Because the basis has only $d$ columns, the expensive eigenvalue decomposition of an $N$-node graph collapses to an $O(d^3)$ problem after a linear reparameterization, and stacking multiple convolution layers needs only one transform pair. On seven spatio-temporal datasets, the model reports the best average rank among nine methods, with strongest margins on financial series and long horizons.

What carries the argument

The load-bearing object is the Stiefel Graph Fourier Transform $S(x) = F^T x$, where $F \in \mathrm{St}(n,d) = \{F \in \mathbb{R}^{n \times d} : F^T F = I_d\}$ is chosen to minimize $\mathrm{Tr}(F^T L F)$ for the graph Laplacian $L$. It carries the argument because it keeps only the $d$ most informative spectral directions, turning graph spectral convolution into a low-rank filtered operation (Theorem 2) and reducing the dynamic-graph eigenproblem to a $d$-dimensional one via LDGOSM. The same transform supports the multi-layer identity in Theorem 3, so stacking layers does not multiply the number of forward and inverse transforms.

What would settle it

Train DST-SGNN on a synthetic spatio-temporal process whose true dependency graph is known to contain relationships that cannot be written as $\mathrm{ReLU}(X)\mathrm{ReLU}(X)^T$, for example each node's next value depending on nodes two hops away in a fixed street network, and compare against the same model whose Stiefel basis is learned from the true adjacency matrix. If the dynamic-graph version does not lose forecast accuracy on the synthetic test set, the graph assumption is not decisive; if it loses, the central efficiency-accuracy claim is bounded by that assumption.

Watch

Extended reading notes

Core claim

The load-bearing result is Theorem 2: the convolution $x *_s g = F(F^T x \odot F^T g)$, with $F \in \mathbb{R}^{n \times d}$ and $F^T F = I_d$, equals $P g_\theta(\Lambda) P^T x$, where $P$ holds the eigenvectors of the adjacency matrix, $\Lambda$ the corresponding eigenvalues in descending order, and $\theta_i = p_i^T g$ for eigenvalues at or above the $d$-th while $\theta_i = 0$ below it. Working in the Stiefel basis is therefore exactly a standard graph spectral convolution whose filter coefficients vanish on the low-eigenvalue subspace. The paper then shows how to learn $F$ dynamically: with $A = I + EE^T$ and $E = \mathrm{ReLU}(X)$, the optimization over the Stiefel manifold reduces, through $F = XW$, to a $d \times d$ eigenvalue problem, and the multi-layer version collapses to $S^{-1}(\sum_i S(X) \odot \prod_{j=1}^i S(G_j))$, so extra layers reuse the same transform pair. This combination of an exact filtering equivalence and an efficient dynamic update is what the authors offer as the reason their model forecasts accurately across heterogeneous datasets at low computational cost.

Load-bearing premise

The whole construction rests on the dynamic graph formula $A = I + \mathrm{ReLU}(X)\mathrm{ReLU}(X)^T$: every pair of nodes is assumed to be related only through the outer product of their rectified input features, so if the true spatial dependencies are higher-order, nonlinear, or long-range in a way this graph cannot express, the learned Stiefel basis encodes the wrong relationships and every downstream module inherits that error.

Editorial extensions

If this is right

  • Because SGSC is exactly a filtered spectral convolution, the model inherits the standard semantics of graph spectral methods, and zeroing the small-eigenvalue coefficients acts as built-in denoising rather than a heuristic.
  • LDGOSM's per-step cost is $O(nd^2 + kd^3)$, so when $d \ll n$ the dynamic graph update is approximately linear in the number of nodes, removing the $O(n^3)$ eigendecomposition bottleneck of recomputing the Laplacian spectrum for each window.
  • Multi-layer SGSC computes an $m$-layer convolution with one SGFT and one ISGFT, so deeper spectral stacks add representational capacity without a proportional multiplier on transform cost.
  • In the reported tables, DST-SGNN has the best average MSE rank (2.79) and MAE rank (1.50) across the seven datasets, and its parameter counts, roughly 1.5M to 4.5M, are far below the largest compared models.
  • The reported advantage over baselines widens as the forecast horizon grows on PEMS03 and is largest on the financial datasets CSI300 and exchange rate.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Beyond the paper: because Theorem 2 is an exact equivalence, the Stiefel layer could be dropped into other architectures as a parameter-light spectral filter; the paper only evaluates it inside DST-SGNN, so that transfer remains untested.
  • Beyond the paper: the accuracy ceiling is likely set by the graph model $A = I + \mathrm{ReLU}(X)\mathrm{ReLU}(X)^T$ rather than by the spectral layer, so replacing that graph with a learned or higher-rank construction should improve results if graph quality is the current bottleneck.
  • Beyond the paper: the $O(nd^2)$ scaling argument implies the design should remain practical for thousands of sensors, but the largest dataset tested has 593 nodes; a large-scale deployment test would confirm or refute that extrapolation.
  • Beyond the paper: a frozen $F$ trained once on a representative graph could be tested against the dynamically updated $F$ in LDGOSM; if accuracy barely drops, the dynamic update cost could be eliminated at inference, a possibility the paper does not examine.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The paper proposes DST-SGNN, a spatio-temporal forecasting model that patches and decomposes input series, builds a hyperpatch graph, learns a Stiefel-manifold-constrained graph Fourier matrix via the proposed LDGOSM procedure, and applies a multi-layer Stiefel graph spectral convolution (MSGSC). The authors claim state-of-the-art accuracy on seven spatio-temporal datasets together with reduced time and space complexity relative to existing graph-based and spectral methods. The theoretical contribution is presented as Theorems 1-3, which connect SGSC to classical filtered graph spectral convolution, and Algorithm 1, which is claimed to achieve near-linear O(nd^2) complexity when d is small relative to the number of nodes.

Significance. If the theoretical claims held, the paper would offer a meaningful efficiency contribution: replacing the cubic eigendecomposition of a dynamic graph Laplacian with a linear-time Stiefel-manifold optimization, while providing a filtering interpretation of the learned transform. The empirical evaluation is broad: seven datasets, multiple forecast horizons, ablations against standard spectral and spatial convolution variants, and time/parameter comparisons with several baselines. The public code link is a positive feature. However, the theoretical derivation currently conflates two distinct eigenproblems and the complexity analysis is not tied to the actual data flow in the architecture; these gaps affect the central claims and need to be fixed before the contribution is fully established.

major comments (4)
  1. [Sec. 4.4, Eq. (11), Appendix A.1] Equation (11) is presented as the equivalent form of Definition (4), but the degree-normalization term is dropped without explanation. Since L = I_n - D^{-1/2} A D^{-1/2}, substituting F = XW and A = I + EE^T gives an objective involving D^{-1/2}(I + EE^T)D^{-1/2}, not I + EE^T. For A = I + EE^T the degree matrix D is generally not the identity, so the matrix whose top-d eigenvectors LDGOSM actually computes is not the matrix that Theorem 1 identifies as the SGFT matrix. More precisely, Algorithm 1 solves a generalized eigenproblem for the pair (X^T A X, X^T X), which is not the same as the eigenproblem of D^{-1/2} A D^{-1/2}. The authors should either correct the derivation of Eq. (11) or explicitly redefine the graph Laplacian in Definition 1 to use the unnormalized adjacency A.
  2. [Sec. 4.4, Theorem 2 and Appendix A.2] Theorem 2 conflates the eigenvectors of A with those of D^{-1/2} A D^{-1/2}. Theorem 1 constructs F from the normalized adjacency, whereas Theorem 2 defines P and Lambda from the eigenvalues and eigenvectors of A, and the proof of Eq. (20) simply asserts f_i = p_i. These two eigenbases are generally different unless D is a scalar multiple of I. Consequently, Eq. (7)-(8) does not follow from the SGSC as defined, and the claimed filtered-graph-spectral-convolution interpretation is not established. Please state a single matrix whose eigenbasis is used for both F and P, and verify that the filter coefficients in Eq. (8) are defined for that matrix.
  3. [Sec. 4.2, Sec. 4.4, Algorithm 1] The claimed O(nd^2) complexity is not connected to the architecture. Section 4.2 says the hyperpatch graph has (J x N) x p nodes, while the embedding produces X in R^{(JN) x K}; Algorithm 1, however, operates on matrices X, E in R^{n x d} and outputs W in R^{d x d}. The manuscript never specifies how X, E, d, and n relate to the embedded patches, the hyperpatch graph, or the hidden dimension K. If n = (JN)p, the feature matrix fed to LDGOSM should have that many rows, but no such matrix is defined. If n is instead the number of variables, the complexity analysis ignores the hyperpatch graph constructed in Section 4.2. The efficiency claim in Section 4.4 and the time comparisons in Section 5.5 need a precise definition of the matrices entering Algorithm 1 and a per-operation complexity count for the actual model.
  4. [Sec. 4.4, Eq. (10)] The dynamic graph A = I_N + EE^T with E = ReLU(X) is the sole source of spatial structure for the learned transform, but this construction is neither derived nor validated against alternatives. Because every downstream module depends on F learned from this graph, the claim that DST-SGNN dynamically captures spatio-temporal correlations rests on this unvalidated assumption. The authors should either provide a theoretical justification for the outer-product form or add an ablation with different nonlinearities or with an explicitly learned adjacency matrix; without such evidence, the modeling claim is not yet empirically grounded.
minor comments (5)
  1. [Table 2 caption] The caption says the results are summarized on nine datasets, but the table and the abstract report seven datasets; please correct the caption and the surrounding text.
  2. [Appendix A.1, Eq. (15)] In Eq. (15), Tr(F^T F) equals d, not n, because F is n x d and F^T F = I_d; the sentence 'Tr(I_n) = n' is inaccurate, although the optimization is unaffected.
  3. [Appendix A.2, Eq. (19)] The summation in Eq. (19) uses f_2^T x and f_2^T g in every term; the subscripts should follow the summation index i throughout.
  4. [Sec. 4.4, Eq. (6)] The 'Inverse Stiefel Graph Fourier Transform' S^{-1}(x) = Fx is only a left inverse of S, since S(S^{-1}(x)) = x but S^{-1}(S(x)) = FF^T x, which is not x because F is not square orthogonal. The paper should state explicitly that reconstruction after the SGFT is approximate.
  5. [Sec. 4.2, Eq. (1)] After Eq. (1), the text says that hat{X}_{t,j} is the j-th column, but hat{X}_t is a three-way tensor in R^{J x p x N}; the indexing notation should be clarified.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the Stiefel spectral convolution claims are algebraic consequences of the paper's own definitions, and the only self-citations are contextual, not load-bearing.

full rationale

The derivation chain is self-contained. Definition 1 defines SGSC as F(F^T x ⊙ F^T g) with F minimizing Tr(F^T L F) on the Stiefel manifold; Theorem 1 is the standard Rayleigh–Ritz characterization of the top-d eigenvectors, proved in Appendix A.1, and Theorem 2 expands the Hadamard product to obtain exactly P gθ(Λ) P^T x with θ_i = p_i^T g for retained eigenvalues and zero otherwise. This is an algebraic equivalence following from the definitions, not a fit of the forecast target. The dynamic adjacency A = I_N + EE^T is a modeling choice, attributed to external work by Yang et al., 2024, and the LDGOSM objective (11) is a constrained optimization problem whose solution is derived in Appendix A.3; the O(nd^2) complexity statement is a complexity analysis, not a circular reuse of the target. The only self-citations are [Zheng et al., 2025], used for context about full spatio-temporal graphs in Section 2.2 and as provenance for the CSI300 dataset in Section 5.1; neither supports a load-bearing premise of the method. Forecasting results are obtained on held-out test splits against external baselines, so no fitted input is renamed as a prediction. I therefore find no significant circularity.

Assumptions & free parameters 5 free parameters · 4 assumptions · 0 invented entities

The method combines standard deep learning components (patching, decomposition, linear layers) with a few domain-specific assumptions. The only tuned quantities are hyperparameters; no new physical or mathematical entities are introduced.

free parameters (5)
  • patch size p and stride s = Not explicitly reported
    Hyperparameters of the Patching module (Section 4.2); values are not stated in the paper.
  • hidden dimension K (d_model) = 128
    Selected via grid search on validation set; 128 was optimal on CSI300 and Solar (Appendix B.1).
  • number of MSGSC layers (HP stacking layers) = 2
    Selected via grid search; 2 layers gave the best performance on CSI300 and Solar (Appendix B.2).
  • learning rate = 0.0001
    Fixed training hyperparameter (Section 5.1).
  • input window size T = 96, 192, or 336
    Experimental setting varied across datasets.
assumptions (4)
  • domain assumption Dynamic graph adjacency A = I_N + E E^T with E = ReLU(X) captures the spatio-temporal relationships
    Introduced in Section 4.4 (Eq. 10); assumes pairwise dependencies are expressible as outer products of ReLU features.
  • domain assumption Top-d eigenvectors of the graph matrix form a useful Fourier basis
    Standard spectral filtering assumption; the paper truncates to d components to reduce complexity.
  • domain assumption SeriesDecomp from Autoformer separates trend and seasonality
    The paper uses Autoformer's decomposition block (Section 4.2) without modification, assuming it yields meaningful components.
  • ad hoc to paper The Stiefel manifold constraint F^T F = I_d is a beneficial inductive bias
    The paper introduces this constraint (Definition 1) to ensure orthonormal columns; it is not derived from the data.

how reviews work

0 comments
Cite this review

Pith. "Pith review of A Dynamic Stiefel Graph Neural Network for Efficient Spatio-Temporal Time Series Forecasting." pith.science (2026). https://pith.science/paper/TMV3HJTH

@misc{pith2026250600798,
  author       = {Pith},
  title        = {Pith review of: A Dynamic Stiefel Graph Neural Network for Efficient Spatio-Temporal Time Series Forecasting},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/TMV3HJTH}},
  note         = {Machine review of arXiv:2506.00798}
}
read the original abstract

Spatio-temporal time series (STTS) have been widely used in many applications. However, accurately forecasting STTS is challenging due to complex dynamic correlations in both time and space dimensions. Existing graph neural networks struggle to balance effectiveness and efficiency in modeling dynamic spatio-temporal relations. To address this problem, we propose the Dynamic Spatio-Temporal Stiefel Graph Neural Network (DST-SGNN) to efficiently process STTS. For DST-SGNN, we first introduce the novel Stiefel Graph Spectral Convolution (SGSC) and Stiefel Graph Fourier Transform (SGFT). The SGFT matrix in SGSC is constrained to lie on the Stiefel manifold, and SGSC can be regarded as a filtered graph spectral convolution. We also propose the Linear Dynamic Graph Optimization on Stiefel Manifold (LDGOSM), which can efficiently learn the SGFT matrix from the dynamic graph and significantly reduce the computational complexity. Finally, we propose a multi-layer SGSC (MSGSC) that efficiently captures complex spatio-temporal correlations. Extensive experiments on seven spatio-temporal datasets show that DST-SGNN outperforms state-of-the-art methods while maintaining relatively low computational costs.

Figures

Figures reproduced from arXiv: 2506.00798 by the authors.

Figure 1
Figure 1. Framework diagram of the DST-SGNN model. [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

31 extracted references · 22 canonical work pages

  1. [1]

    Uci machine learning repository,

    [Asuncion et al., 2007] Arthur Asuncion, David Newman, et al. Uci machine learning repository,

    work page 2007

  2. [3]

    The MSGSC has the following equivalent com- putational form: M SGSC(X, G) = S−1( mX i=1 S(X) ⊙ iY j=1 S(Gj)) (29) Proof. S mX i=1 X∗sG1∗sG2∗s · · · ∗sGi ! = mX i=1 S(X∗sG1∗sG2∗s · · · ∗sGi) = mX i=1 S(X) ⊙ iY j=1 S(Gj) (30) Therefore, M SGSC(X, G) = mX i=1 X∗sG1∗sG2∗s · · · ∗sGi = S−1   mX i=1 S(X) ⊙ iY j=1 S(Gj)   (31) B Parameter Analysis B.1 The im...

    work page 2027

  3. [4]

    Spectral temporal graph neural network for multivariate time-series forecast- ing

    [Cao et al., 2020] Defu Cao, Yujing Wang, Juanyong Duan, Ce Zhang, Xia Zhu, Congrui Huang, Yunhai Tong, Bix- iong Xu, Jing Bai, Jie Tong, et al. Spectral temporal graph neural network for multivariate time-series forecast- ing. Advances in neural information processing systems , 33:17766–17778,

    work page 2020

  4. [6]

    Convolutional neural networks on graphs with fast localized spectral filtering

    [Defferrard et al., 2016] Micha¨el Defferrard, Xavier Bres- son, and Pierre Vandergheynst. Convolutional neural networks on graphs with fast localized spectral filtering. Advances in neural information processing systems , 29,

    work page 2016

  5. [12]

    Modeling long-and short-term temporal patterns with deep neural networks

    [Lai et al., 2018] Guokun Lai, Wei-Cheng Chang, Yiming Yang, and Hanxiao Liu. Modeling long-and short-term temporal patterns with deep neural networks. In The 41st international ACM SIGIR conference on research & devel- opment in information retrieval, pages 95–104,

    work page 2018

  6. [13]

    Multichannel spatial– temporal graph convolution network based on spectrum decomposition for traffic prediction

    [Lei et al., 2024] Tianyang Lei, Kewei Yang, Jichao Li, Gang Chen, and Jiuyao Jiang. Multichannel spatial– temporal graph convolution network based on spectrum decomposition for traffic prediction. Expert Systems with Applications, 238:122281,

    work page 2024

  7. [14]

    Cyclenet: enhancing time series forecasting through modeling peri- odic patterns

    [Lin et al., 2024] Shengsheng Lin, Weiwei Lin, Xinyi Hu, Wentai Wu, Ruichao Mo, and Haocheng Zhong. Cyclenet: enhancing time series forecasting through modeling peri- odic patterns. arXiv preprint arXiv:2409.18479,

    arXiv 2024

  8. [15]

    itransformer: Inverted transformers are effective for time series forecasting

    [Liu et al., 2023] Yong Liu, Tengge Hu, Haoran Zhang, Haixu Wu, Shiyu Wang, Lintao Ma, and Mingsheng Long. itransformer: Inverted transformers are effective for time series forecasting. arXiv preprint arXiv:2310.06625,

    arXiv 2023

Show all 31 references
  1. [16]

    A time series is worth 64 words: Long-term forecasting with transformers

    [Nie et al., 2022] Yuqi Nie, Nam H Nguyen, Phanwadee Sinthong, and Jayant Kalagnanam. A time series is worth 64 words: Long-term forecasting with transformers. arXiv preprint arXiv:2211.14730,

    2022 arXiv

  2. [18]

    Fred- former: Frequency debiased transformer for time series forecasting

    [Piao et al., 2024] Xihao Piao, Zheng Chen, Taichi Mu- rayama, Yasuko Matsubara, and Yasushi Sakurai. Fred- former: Frequency debiased transformer for time series forecasting. In Proceedings of the 30th ACM SIGKDD Conference on Knowledge Discovery and Data Mining , pages 2400–2410,

    2024

  3. [19]

    Saurous, and Matthew Hoffman

    [Saad et al., 2024] Feras Saad, Jacob Burnim, Colin Car- roll, Brian Patton, Urs K ¨oster, Rif A. Saurous, and Matthew Hoffman. Scalable spatiotemporal prediction with bayesian neural fields. Nature Communications , 15(1):7942,

    2024

  4. [20]

    Spatial-temporal synchronous graph convolutional networks: A new framework for spatial- temporal network data forecasting

    [Song et al., 2020] Chao Song, Youfang Lin, Shengnan Guo, and Huaiyu Wan. Spatial-temporal synchronous graph convolutional networks: A new framework for spatial- temporal network data forecasting. In Proceedings of the AAAI conference on artificial intelligence, volume 34, pag...

    2020

  5. [21]

    Modwavemlp: Mlp-based mode decomposition and wavelet denoising model to defeat complex structures in traffic forecasting

    [Sun et al., 2024] Ke Sun, Pei Liu, Pengfei Li, and Zhifang Liao. Modwavemlp: Mlp-based mode decomposition and wavelet denoising model to defeat complex structures in traffic forecasting. In Proceedings of the AAAI Conference on Artificial Intelligence , volume 38, pages 9035–9043,

    2024

  6. [22]

    Timemixer: Decomposable mul- tiscale mixing for time series forecasting

    [Wang et al., 2024a] Shiyu Wang, Haixu Wu, Xiaoming Shi, Tengge Hu, Huakun Luo, Lintao Ma, James Y Zhang, and Jun Zhou. Timemixer: Decomposable mul- tiscale mixing for time series forecasting. arXiv preprint arXiv:2405.14616,

    arXiv

  7. [23]

    Timexer: Empow- ering transformers for time series forecasting with exoge- nous variables

    [Wang et al., 2024b] Yuxuan Wang, Haixu Wu, Jiaxiang Dong, Guo Qin, Haoran Zhang, Yong Liu, Yunzhong Qiu, Jianmin Wang, and Mingsheng Long. Timexer: Empow- ering transformers for time series forecasting with exoge- nous variables. arXiv preprint arXiv:2402.19072,

    arXiv

  8. [24]

    Autoformer: Decomposition transform- ers with auto-correlation for long-term series forecast- ing

    [Wu et al., 2021] Haixu Wu, Jiehui Xu, Jianmin Wang, and Mingsheng Long. Autoformer: Decomposition transform- ers with auto-correlation for long-term series forecast- ing. Advances in neural information processing systems , 34:22419–22430,

    2021

  9. [25]

    Timesnet: Temporal 2d-variation modeling for general time series analysis

    [Wu et al., 2022] Haixu Wu, Tengge Hu, Yong Liu, Hang Zhou, Jianmin Wang, and Mingsheng Long. Timesnet: Temporal 2d-variation modeling for general time series analysis. arXiv preprint arXiv:2210.02186,

    2022 arXiv

  10. [26]

    Fits: Modeling time series with 10k parameters

    [Xu et al., 2023] Zhijian Xu, Ailing Zeng, and Qiang Xu. Fits: Modeling time series with 10k parameters. arXiv preprint arXiv:2307.03756,

    2023 arXiv

  11. [27]

    Fedgtp: Exploiting inter-client spatial dependency in fed- erated graph-based traffic prediction

    [Yang et al., 2024] Linghua Yang, Wantong Chen, Xiaoxi He, Shuyue Wei, Yi Xu, Zimu Zhou, and Yongxin Tong. Fedgtp: Exploiting inter-client spatial dependency in fed- erated graph-based traffic prediction. InProceedings of the 30th ACM SIGKDD Conference on Knowledge Discovery a...

    2024

  12. [28]

    Geoexplainer: Interpreting graph convo- lutional networks with geometric masking

    [Yu et al., 2024] Rui Yu, Yanshan Li, Huajie Liang, and Zhiyuan Chen. Geoexplainer: Interpreting graph convo- lutional networks with geometric masking. Neurocomput- ing, 605:128393,

    2024

  13. [29]

    Multi- resolution time-series transformer for long-term forecast- ing

    [Zhang et al., 2024] Yitian Zhang, Liheng Ma, Soumyasun- dar Pal, Yingxue Zhang, and Mark Coates. Multi- resolution time-series transformer for long-term forecast- ing. In International Conference on Artificial Intelligence and Statistics, pages 4222–4230. PMLR,

    2024

  14. [30]

    Multi-resolution patch-based fourier graph spectral network for spatiotemporal time series forecasting

    [Zheng et al., 2025] Jiankai Zheng, Liang Xie, and Haijiao Xu. Multi-resolution patch-based fourier graph spectral network for spatiotemporal time series forecasting. Neu- rocomputing, 638:130132,

    2025

  15. [2007]

    Beyond spatio-temporal representations: Evolv- ing fourier transform for temporal graphs

    [Bastos et al., 2024] Anson Bastos, Kuldeep Singh, Ab- hishek Nadgeri, Manish Singh, and Toyotaro Suzu- mura. Beyond spatio-temporal representations: Evolv- ing fourier transform for temporal graphs. arXiv preprint arXiv:2402.16078,

    2024 arXiv

  16. [2016]

    Istgcn: Inte- grated spatio-temporal modeling for traffic prediction us- ing traffic graph convolution network

    [Gupta et al., 2023] Arti Gupta, Manish Kumar Maurya, Nikhil Goyal, and Vijay Kumar Chaurasiya. Istgcn: Inte- grated spatio-temporal modeling for traffic prediction us- ing traffic graph convolution network. Applied Intelli- gence, 53(23):29153–29168,

    2023

  17. [2018]

    Llgformer: Learnable long-range graph transformer for traffic flow prediction

    [Jin et al., 2025] Di Jin, Cuiying Huo, Jiayi Shi, Dongxiao He, Jianguo Wei, and Philip S Yu. Llgformer: Learnable long-range graph transformer for traffic flow prediction. In Proceedings of the ACM on Web Conference 2025 , pages 2860–2871,

    2025

  18. [2020]

    Ad- dressing spatial-temporal heterogeneity: General mixed time series analysis via latent continuity recovery and alignment

    [Chen and Zhao, 2024] Jiawei Chen and Chunhui Zhao. Ad- dressing spatial-temporal heterogeneity: General mixed time series analysis via latent continuity recovery and alignment. In The Thirty-eighth Annual Conference on Neural Information Processing Systems,

    2024

  19. [2021]

    Semi-supervised classification with graph convolutional networks

    [Kipf and Welling, 2016] Thomas N Kipf and Max Welling. Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907,

    2016 arXiv

  20. [2022]

    Ma-gcn: A memory augmented graph convolutional net- work for traffic prediction

    [Peng and Zhang, 2023] Dunlu Peng and Yongsheng Zhang. Ma-gcn: A memory augmented graph convolutional net- work for traffic prediction. Engineering Applications of Artificial Intelligence, 121:106046,

    2023

  21. [2023]

    Orthogonal weight normalization: Solution to optimization over mul- tiple dependent stiefel manifolds in deep neural networks

    [Huang et al., 2018] Lei Huang, Xianglong Liu, Bo Lang, Adams Yu, Yongliang Wang, and Bo Li. Orthogonal weight normalization: Solution to optimization over mul- tiple dependent stiefel manifolds in deep neural networks. In Proceedings of the AAAI Conference on Artificial Intel...

    2018

  22. [2024]

    Multi-head multi-order graph attention networks

    [Ben et al., 2024] Jie Ben, Qiguo Sun, Keyu Liu, Xibei Yang, and Fengjun Zhang. Multi-head multi-order graph attention networks. Applied Intelligence , pages 1–16,

    2024

  23. [2025]

    Re- versible instance normalization for accurate time-series forecasting against distribution shift

    [Kim et al., 2021] Taesung Kim, Jinhee Kim, Yunwon Tae, Cheonbok Park, Jang-Ho Choi, and Jaegul Choo. Re- versible instance normalization for accurate time-series forecasting against distribution shift. InInternational Con- ference on Learning Representations,

    2021

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.