SPDM: Geometry-Modulated State Space Modeling with Manifold Constraints for Time Series Forecasting

Siu-Ming Yiu; Xingsheng Chen

REVIEW 1 major objections 1 minor 1 cited by

SPDM: Geometry-Modulated State Space Modeling with Manifold Constraints for Time Series Forecasting

T0 review · 1 major / 1 minor · reviewed 2026-06-27 · grok-4.3

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

Pith's one-line read Treating cross-variable correlations as trajectories on the symmetric positive definite manifold regularizes state-space models for improved multivariate time series forecasting.

desk verdict SPDM folds SPD manifold geometry into SSM selective scanning for multivariate forecasting but the dominance claim rests on unshown ablations. read the letter →

arxiv 2606.09917 v1 pith:JRSHNXBJ submitted 2026-06-06 cs.LG

Xingsheng Chen , Siu-Ming Yiu This is my paper · ORCID

classification cs.LG

keywords statespacemodelsmanifoldconstraintstimeseriesforecastingsymmetricpositivedefinitegeometricregularizationmultivariateselectivescanning

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

The paper proposes embedding manifold constraints into state-space models to better capture evolving correlations in multivariate time series. It projects dynamically changing covariance matrices from the SPD manifold to a tangent space and uses geometric features to modulate the selective parameters of the SSM. This approach preserves the linear-time parallel scan while adding structural regularization from the manifold's geometry. Experiments on eleven benchmarks show state-of-the-art performance, with ablations confirming the geometric constraints as the main driver of gains. A reader would care because it offers a way to incorporate natural geometric structure into efficient sequence models without sacrificing speed.

What carries the argument

Manifold trajectory path that projects covariance matrices from the SPD manifold to Euclidean tangent space, together with geometric gating that modulates SSM internal selective parameters using manifold-derived signals.

What would settle it

Running the eleven benchmark experiments with the manifold trajectory path and geometric gating removed, and finding no performance improvement over standard state-space models, would challenge the central claim.

Watch

Extended reading notes

Core claim

By modeling the correlation structure as a continuous trajectory on the SPD manifold, whose Riemannian features serve as a geometric regularizer, SPDM guides and stabilizes SSM selective scanning through a manifold trajectory path for tangent space projection and a geometric gating scheme for parameter modulation.

Load-bearing premise

Treating the cross-variable correlation structure as a continuous trajectory on the symmetric positive definite manifold acts as a principled geometric regularizer that guides and stabilizes the selective scanning dynamics of state-space models.

Editorial extensions

If this is right

The parameterization preserves the linear-time complexity of parallel scans.
Geometrically constrained state-space dynamics are the dominant architectural factor behind performance gains.
The architecture achieves state-of-the-art forecasting performance on eleven real-world benchmark datasets.
Rich structural constraints from the manifold are embedded while maintaining prediction accuracy and computational efficiency.

Reading between the lines

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

Applying similar manifold constraints could benefit other domains with evolving correlation structures, such as sensor networks or financial time series.
Isolating the contribution of tangent space projection versus geometric gating through targeted ablations would clarify the mechanism.
The linear complexity preservation suggests scalability to longer sequences where geometric regularization might be particularly valuable.

Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

The core move is treating cross-variable correlations as a trajectory on the SPD manifold, projecting it to the tangent space, and using the resulting signals to gate the selective parameters inside an SSM scan. This is the part that does not reduce directly to prior Mamba-style work.

The architecture keeps the linear-time parallel scan while adding two concrete pieces: a manifold trajectory path and a geometric gating scheme. That combination is new enough to be worth testing. The efficiency claim is credible on paper because the projection and gating are designed to sit outside the scan itself.

The reported SOTA on eleven benchmarks is the main empirical hook. If the ablations really isolate the geometric component as the dominant driver, that would be useful for the subfield. The abstract presents the approach as a principled regularizer rather than an ad-hoc addition, which is a reasonable framing.

The main gap is evidentiary. The abstract asserts that geometrically constrained dynamics explain the gains, yet the strength of those further studies cannot be judged from the given text. How the covariances are estimated in practice, how sensitive the Frechet mean is to noise, and whether the tangent-space signals actually stabilize the scan rather than just add parameters are all open questions. Minor implementation details around manifold operations could also affect reproducibility.

This is for people already working on SSM extensions for forecasting who want a geometric prior on variable interactions. It is not a general-purpose replacement for simpler models.

I would send it to peer review. The idea is coherent, the complexity claim is important, and the experiments are on real benchmarks even if the current writeup leaves the causal attribution under-specified.

Referee Report

1 major / 1 minor

Summary. The manuscript introduces SPDM, a geometry-modulated state space model for multivariate time series forecasting. It models the evolving cross-variable correlation structure as a trajectory on the symmetric positive definite (SPD) manifold, projects it to the tangent space, and uses the resulting geometric signals to modulate the selective parameters of an SSM architecture inspired by Mamba. The approach aims to preserve the linear-time complexity of the parallel scan while embedding geometric constraints as a regularizer. The authors report state-of-the-art performance on eleven real-world benchmark datasets and attribute the gains to the geometrically constrained dynamics.

Significance. If the results and ablations hold, this could represent a meaningful advance in combining Riemannian geometry with efficient sequence models for time series, providing a way to incorporate correlation evolution without sacrificing computational efficiency. The emphasis on manifold constraints as a stabilizing factor is a promising direction, though its impact depends on the strength of the empirical evidence.

major comments (1)

[Experiments] Experiments section: The assertion that geometrically constrained state-space dynamics are the dominant architectural factor behind performance gains requires explicit ablation results (e.g., quantitative drops when ablating the manifold trajectory path or geometric gating scheme). The abstract states that further studies confirm this dominance, but without the specific metrics, baselines, or controls, it is not possible to evaluate whether the geometric component is load-bearing or if gains could arise from other factors.

minor comments (1)

[Abstract] Abstract: The description of how the projection from SPD manifold to tangent space and the subsequent modulation of selective parameters preserve linear scan complexity would benefit from a brief reference to the relevant equations or pseudocode.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the thoughtful review and for highlighting the need for stronger empirical support of our claims. We address the major comment below and commit to revisions that directly respond to the concern.

read point-by-point responses

Referee: The assertion that geometrically constrained state-space dynamics are the dominant architectural factor behind performance gains requires explicit ablation results (e.g., quantitative drops when ablating the manifold trajectory path or geometric gating scheme). The abstract states that further studies confirm this dominance, but without the specific metrics, baselines, or controls, it is not possible to evaluate whether the geometric component is load-bearing or if gains could arise from other factors.

Authors: We agree that the current presentation does not provide sufficient quantitative detail to substantiate the dominance claim. In the revised manuscript we will add a dedicated ablation subsection in the Experiments section. This will report MSE and MAE on all eleven benchmark datasets for: (i) the full SPDM model, (ii) SPDM without the manifold trajectory path (i.e., covariance matrices processed in Euclidean space), (iii) SPDM without the geometric gating scheme, and (iv) both components removed. We will also include the corresponding Mamba baseline and a non-geometric SSM variant for direct comparison, thereby supplying the requested metrics, controls, and quantitative drops. revision: yes

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; derivation is self-contained

full rationale

The paper proposes an architectural integration of SPD manifold geometry with SSM selective scanning, using tangent-space projections and geometric gating to modulate parameters while preserving linear complexity. No equations or claims reduce a prediction to a fitted input by construction, no self-citation chain is invoked as load-bearing justification for uniqueness or ansatz, and the central mechanism (manifold trajectory guiding SSM dynamics) is presented as an explicit design choice rather than a derived necessity. Experiments are cited as external validation rather than internal tautology. The derivation chain therefore stands on independent geometric and architectural premises.

Assumptions & free parameters 0 free parameters · 2 assumptions · 0 invented entities

Ledger derived exclusively from the abstract since full text unavailable; central claim rests on domain assumptions about manifold geometry providing regularization, with no explicit free parameters or invented entities named.

assumptions (2)

domain assumption Cross-variable correlation structure forms a continuous trajectory on the symmetric positive definite manifold
Central premise stated in the abstract as the basis for guiding SSM dynamics.
domain assumption Riemannian geometric features, tangent space linearity, and Frechet mean centrality act as a principled geometric regularizer for SSM selective scanning
Assumed without further justification in the abstract to stabilize dynamics.

how reviews work

0 comments

Cite this review

Pith. "Pith review of SPDM: Geometry-Modulated State Space Modeling with Manifold Constraints for Time Series Forecasting." pith.science (2026). https://pith.science/paper/JRSHNXBJ

@misc{pith2026260609917,
  author       = {Pith},
  title        = {Pith review of: SPDM: Geometry-Modulated State Space Modeling with Manifold Constraints for Time Series Forecasting},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/JRSHNXBJ}},
  note         = {Machine review of arXiv:2606.09917}
}

read the original abstract

Multivariate time series forecasting requires capturing the continuously evolving correlation structure among interacting variables. Existing state-space models process time series by scanning tokenized temporal or spatial sequences, discarding the evolutionary geometric structure. We address this limitation by introducing manifold constraints into state-space modeling: treating the cross-variable correlation structure as a continuous trajectory on the symmetric positive definite manifold, whose Riemannian geometric features, tangent space linearity, and Frechet mean centrality act as a principled geometric regularizer that guides and stabilizes the selective scanning dynamics of SSMs. We propose SPDM, a geometry-aware SSM architecture that realizes this principle through two cooperating mechanisms: a manifold trajectory path that projects dynamically evolving covariance matrices from the SPD manifold to a Euclidean tangent space, and a geometric gating scheme that directly modulates SSM's internal selective parameters based on geometric signals derived from the manifold trajectory. The parameterization preserves the linear-time complexity of the Mamba parallel scan while embedding rich structural constraints, making the architecture preserve prediction accuracy and computational efficiency simultaneously. Extensive experiments on eleven real-world benchmark datasets establish state-of-the-art forecasting performance, and further studies confirm that geometrically constrained state-space dynamics are the dominant architectural factor behind its performance gains.

Figures

Figures reproduced from arXiv: 2606.09917 by the authors.

**Figure 1.** Framework of SPDM SPDM directly addresses by projecting SPD trajectories to the tangent space and leveraging Mamba’s parallel scan. 2.3. Geometric Deep Learning on Manifolds Geometric deep learning provides a unified framework for generalizing neural networks to non-Euclidean domains. For the SPD manifold specifically, SPDNet [10] and its variants have introduced layers that respect the Riemannian geometry, such as… view at source ↗

**Figure 2.** SPD covariance geometry along the input sequence on ETTm2 with 7 variables. (a) Sample covariance matrix Σ0 at the first window (𝑡 ∈ [0, 15]), exhibiting moderate variances with diagonal range 0.01-0.87 and predominantly positive crossvariable correlations among the high and mid-frequency load series (HUFL-MULL). (b) Covariance matrix Σ20 at the last window (𝑡 ∈ [80, 95]). The variances of HUFL-MULL increase by up … view at source ↗

**Figure 3.** Comparison of efficiency experimental results between SPDM and baselines. GPU memory allocated. All experiments use either unified hyperparameter configurations or those suggested in the official repositories. The main model employs the optimal configuration obtained through hyperparameter search. SPDM consistently achieves the lowest or near-lowest MSE across all three studies while yielding substantial improvemen… view at source ↗

Figures from the paper (3 more)

**Figure 4.** Figure 4: Robustness experimental results on ETTm2 under increasing Gaussian noise [PITH_FULL_IMAGE:figures/full_fig_p011_4.png]

**Figure 5.** Figure 5: Prediction error of SPDM and baselines with increasing lookback length. rebound upward at 𝐿 = 336 or 𝐿 = 720, indicating a fundamental inability to effectively exploit longer historical contexts. S-Mamba, while capable of benefiting from extended lookback windows, yie…

**Figure 7.** Figure 7: presents the scaled prediction results of SPDM, S-Mamba, iTransformer, and PatchTST against the ground truth on the ETTm2 dataset, which reflects electricity transformer temperature and load with 15-minute sampling. The study covering two representative nodes across f…

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Structured Latent Space Modeling over Multi-Scale Temporal Patches for Multivariate Time Series Forecasting
cs.LG 2026-07 conditional novelty 5.0 of 10

A multi-scale patching forecaster with a CNN backbone and smoothness/cross-scale latent penalties claims to beat or match leading baselines on most of 40 long-term forecasting settings at linear cost.

Reference graph

Works this paper leans on

34 extracted references · 10 canonical work pages · cited by 1 Pith paper

[1]

Geometric meansinanovelvectorspacestructureonsymmetricpositive-definite matrices

Arsigny, V., Fillard, P., Pennec, X., Ayache, N., 2007. Geometric meansinanovelvectorspacestructureonsymmetricpositive-definite matrices. SIAM Journal on Matrix Analysis and Applications 29, 328–347

2007
[2]

Riemannian geometry and matrix geometric means

Bhatia, R., Holbrook, J., 2006. Riemannian geometry and matrix geometric means. Linear algebra and its applications 413, 594–618

2006
[3]

Geo-mamba: Geometry- informed state-space learning of functional brain organization

Cao, Y., Dan, T., Yang, Y., Wu, G., 2026. Geo-mamba: Geometry- informed state-space learning of functional brain organization. Med- ical image analysis 112, Article 104081. doi:10.1016/j.media.2026. 104081

work page doi:10.1016/j.media.2026 2026
[4]

arXiv preprint arXiv:2304.08424 , year=

Das,A.,Kong,W.,Leach,A.,Mathur,S.,Sen,R.,Yu,R.,2023.Long- termforecastingwithtide:Time-seriesdenseencoder. arXivpreprint arXiv:2304.08424

work page arXiv 2023
[5]

Robustmanifoldbroad learningsystemforlarge-scalenoisychaotictimeseriesprediction:A perturbation perspective

Feng,S.,Ren,W.,Han,M.,Chen,Y.W.,2019. Robustmanifoldbroad learningsystemforlarge-scalenoisychaotictimeseriesprediction:A perturbation perspective. Neural networks 117, 179–190

2019
[6]

Fu, Y., He, L., Chen, Q., 2026. Manifoldformer: Geometric deep learning for neural dynamics on riemannian manifolds, in: ICASSP 2026-2026 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), IEEE. pp. 6801–6805

2026
[7]

Mamba: Linear-Time Sequence Modeling with Selective State Spaces

Gu, A., Dao, T., 2023. Mamba: Linear-time sequence modeling with selective state spaces. arXiv preprint arXiv:2312.00752

work page Pith review arXiv 2023
[8]

Dygraphformer: Transformer combining dynamic spatio-temporal graph network for multivariate time series forecasting

Han, S., Xun, Y., Cai, J., Yang, H., Li, Y., 2025. Dygraphformer: Transformer combining dynamic spatio-temporal graph network for multivariate time series forecasting. Neural Networks 181, 106776

2025

Show all 34 references

[9]

Long time series of ocean wave predictionbasedonpatchtstmodel

Huang, X., Tang, J., Shen, Y., 2024. Long time series of ocean wave predictionbasedonpatchtstmodel. OceanEngineering301,117572

2024
[10]

A riemannian network for SPD matrixlearning,in:ProceedingsoftheAAAIConferenceonArtificial Intelligence, pp

Huang, Z., Van Gool, L., 2017. A riemannian network for SPD matrixlearning,in:ProceedingsoftheAAAIConferenceonArtificial Intelligence, pp. 2036–2042

2017
[11]

Riemannian curvature of deep neural networks

Kaul, P., Lall, B., 2019. Riemannian curvature of deep neural networks. IEEEtransactionsonneuralnetworksandlearningsystems 31, 1410–1416

2019
[12]

Time series forecasting via direct per-step probability distribution modeling URL:https://arxiv.org/abs/2511

Kong, L., Hong, X., 2025. Time series forecasting via direct per-step probability distribution modeling URL:https://arxiv.org/abs/2511. 23260,arXiv:2511.23260

2025
[13]

Dfimformer: Dynamic frequency-enhanced itransformer for multiscale time series forecast- ing

Li, F., Yu, Y., Zhou, H., Dong, R., 2026. Dfimformer: Dynamic frequency-enhanced itransformer for multiscale time series forecast- ing. Information systems (Oxford) 141, 102747–

2026
[14]

IEEE/CAA Journal of Automatica Sinica 10, 1882–1892

Li,Y.,Fei,C.,Wang,C.,Shan,H.,Lu,R.,2023.Geometryflow-based deep riemannian metric learning. IEEE/CAA Journal of Automatica Sinica 10, 1882–1892

2023
[15]

Bi-mamba4ts: Bidirectional mamba for time series forecasting

Liang, A., Jiang, X., Sun, Y., Lu, C., 2024. Bi-mamba4ts: Bidirectional mamba for time series forecasting. arXiv preprint arXiv:2404.15772

2024
[16]

Liu, Y., Hu, T., Zhang, H., Wu, H., Wang, S., Ma, L., Long, M.,
[17]

arXiv preprint arXiv:2310.06625

itransformer:Invertedtransformersareeffectivefortimeseries forecasting. arXiv preprint arXiv:2310.06625

arXiv
[18]

The illusion of state in state-space models

Merrill, W., Petty, J., Sabharwal, A., 2024. The illusion of state in state-space models. arXiv preprint arXiv:2404.08819

2024
[19]

Ridge regression on riemannian manifolds for time-series prediction URL:https://arxiv.org/abs/2411.18339, arXiv:2411.18339

Nava-Yazdani, E., 2025. Ridge regression on riemannian manifolds for time-series prediction URL:https://arxiv.org/abs/2411.18339, arXiv:2411.18339

2025
[20]

Adaptive sliding window normalization

Papageorgiou, G., Tjortjis, C., 2025. Adaptive sliding window normalization. Information systems (Oxford) 129, 102515–

2025
[21]

Clus- tering brain-network time series by riemannian geometry

Slavakis, K., Salsabilian, S., Wack, D.S., Muldoon, S.F., Baidoo- Williams, H.E., Vettel, J.M., Cieslak, M., Grafton, S.T., 2017. Clus- tering brain-network time series by riemannian geometry. IEEE Transactions on Signal and Information Processing over Networks 4, 519–533

2017
[22]

Attention is all you need

Vaswani,A.,Shazeer,N.,Parmar,N.,Uszkoreit,J.,Jones,L.,Gomez, A.N., Kaiser, Ł., Polosukhin, I., 2017. Attention is all you need. Advances in neural information processing systems 30

2017
[23]

Koopman neural forecaster for time series with temporal distribution shifts URL: https://arxiv.org/abs/2210.03675,arXiv:2210.03675

Wang, R., Dong, Y., Arik, S.Ö., Yu, R., 2023. Koopman neural forecaster for time series with temporal distribution shifts URL: https://arxiv.org/abs/2210.03675,arXiv:2210.03675

2023
[24]

Contrastive learning enhanced by graph neural networks for universal multivariate time series representation

Wang, X., Xing, Q., Xiao, H., Ye, M., 2024. Contrastive learning enhanced by graph neural networks for universal multivariate time series representation. Information Systems 125, 102429

2024
[25]

Is mamba effective for time series forecasting? Neurocomputing 619, 129178

Wang, Z., Kong, F., Feng, S., Wang, M., Yang, X., Zhao, H., Wang, D., Zhang, Y., 2025. Is mamba effective for time series forecasting? Neurocomputing 619, 129178

2025
[26]

URL:https://openreview.net/forum?id=ju_Uqw384Oq

Wu,H.,Hu,T.,Liu,Y.,Zhou,H.,Wang,J.,Long,M.,2023.Timesnet: Temporal 2d-variation modeling for general time series analysis, in: The Eleventh International Conference on Learning Representations. URL:https://openreview.net/forum?id=ju_Uqw384Oq

2023
[27]

Advancesinneuralinformationprocessingsystems34,22419–22430

Wu,H.,Xu,J.,Wang,J.,Long,M.,2021.Autoformer:Decomposition transformers with auto-correlation for long-term series forecasting. Advancesinneuralinformationprocessingsystems34,22419–22430

2021
[28]

Repetitive contrastive learning enhances mamba’s selectivity in time series prediction

Yan, W., Cao, H., Tan, Y., 2025. Repetitive contrastive learning enhances mamba’s selectivity in time series prediction. Neural Networks , 108290

2025
[29]

Fa- mamba: Frequency attention driven mamba for multimodal remote sensing classification

Yang, D., Li, D., Ma, J., Lu, Y., Li, Y., Fang, L., Xie, W., 2026. Fa- mamba: Frequency attention driven mamba for multimodal remote sensing classification. Neural Networks , 108931

2026
[30]

Fast sequential clustering in Riemannian manifolds for dynamic and time-series-annotated multilayer networks

Ye, C., Slavakis, K., Nakuci, J., Muldoon, S.F., Medaglia, J., 2021. Fast sequential clustering in Riemannian manifolds for dynamic and time-series-annotated multilayer networks. IEEE Open Journal of Signal Processing 2, 190–206

2021
[31]

Are transformers effective for time series forecasting?, in: Proceedings of the AAAI conference on artificial intelligence, pp

Zeng, A., Chen, M., Zhang, L., Xu, Q., 2023. Are transformers effective for time series forecasting?, in: Proceedings of the AAAI conference on artificial intelligence, pp. 11121–11128

2023
[32]

Multivariate time series forecasting under hyperbolic space hierarchical constraints URL:https://openreview

Zhang, K., Xu, Y., 2026. Multivariate time series forecasting under hyperbolic space hierarchical constraints URL:https://openreview. net/forum?id=vuzL4ImPKW

2026
[33]

Crossformer: Transformer utilizing cross- dimension dependency for multivariate time series forecasting, in: The Eleventh International Conference on Learning Representations

Zhang, Y., Yan, J., 2023. Crossformer: Transformer utilizing cross- dimension dependency for multivariate time series forecasting, in: The Eleventh International Conference on Learning Representations. URL:https://openreview.net/forum?id=vSVLM2j9eie

2023
[34]

Fedformer: Frequency enhanced decomposed transformer for long- term series forecasting URL:https://arxiv.org/abs/2201.12740, arXiv:2201.12740

Zhou, T., Ma, Z., Wen, Q., Wang, X., Sun, L., Jin, R., 2022. Fedformer: Frequency enhanced decomposed transformer for long- term series forecasting URL:https://arxiv.org/abs/2201.12740, arXiv:2201.12740. X. Chen and S.M. Yiu:Preprint submitted to ElsevierPage 13 of 13

2022

Pith tools

Reviewed June 27, 2026 · model on record in the stance chip above.

[1] [1]

Geometric meansinanovelvectorspacestructureonsymmetricpositive-definite matrices

Arsigny, V., Fillard, P., Pennec, X., Ayache, N., 2007. Geometric meansinanovelvectorspacestructureonsymmetricpositive-definite matrices. SIAM Journal on Matrix Analysis and Applications 29, 328–347

2007

[2] [2]

Riemannian geometry and matrix geometric means

Bhatia, R., Holbrook, J., 2006. Riemannian geometry and matrix geometric means. Linear algebra and its applications 413, 594–618

2006

[3] [3]

Geo-mamba: Geometry- informed state-space learning of functional brain organization

Cao, Y., Dan, T., Yang, Y., Wu, G., 2026. Geo-mamba: Geometry- informed state-space learning of functional brain organization. Med- ical image analysis 112, Article 104081. doi:10.1016/j.media.2026. 104081

work page doi:10.1016/j.media.2026 2026

[4] [4]

arXiv preprint arXiv:2304.08424 , year=

Das,A.,Kong,W.,Leach,A.,Mathur,S.,Sen,R.,Yu,R.,2023.Long- termforecastingwithtide:Time-seriesdenseencoder. arXivpreprint arXiv:2304.08424

work page arXiv 2023

[5] [5]

Robustmanifoldbroad learningsystemforlarge-scalenoisychaotictimeseriesprediction:A perturbation perspective

Feng,S.,Ren,W.,Han,M.,Chen,Y.W.,2019. Robustmanifoldbroad learningsystemforlarge-scalenoisychaotictimeseriesprediction:A perturbation perspective. Neural networks 117, 179–190

2019

[6] [6]

Fu, Y., He, L., Chen, Q., 2026. Manifoldformer: Geometric deep learning for neural dynamics on riemannian manifolds, in: ICASSP 2026-2026 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), IEEE. pp. 6801–6805

2026

[7] [7]

Mamba: Linear-Time Sequence Modeling with Selective State Spaces

Gu, A., Dao, T., 2023. Mamba: Linear-time sequence modeling with selective state spaces. arXiv preprint arXiv:2312.00752

work page Pith review arXiv 2023

[8] [8]

Dygraphformer: Transformer combining dynamic spatio-temporal graph network for multivariate time series forecasting

Han, S., Xun, Y., Cai, J., Yang, H., Li, Y., 2025. Dygraphformer: Transformer combining dynamic spatio-temporal graph network for multivariate time series forecasting. Neural Networks 181, 106776

2025