Permutation Equivariant Neural Controlled Differential Equations for Dynamic Graph Representation Learning

Torben Berndt; Benjamin Walker; Tiexin Qin; Jan Stühmer; Andrey Kormilitzin

doi:10.52202/085713-3284

Permutation Equivariant Neural Controlled Differential Equations for Dynamic Graph Representation Learning

Torben Berndt
, Benjamin Walker
, Tiexin Qin
, Jan Stühmer
, Andrey Kormilitzin

Department of Electrical Engineering

Research output: Chapters, Conference Papers, Creative and Literary Works › RGC 32 - Refereed conference paper (with host publication) › peer-review

1 Citation (Scopus)

Abstract

Dynamic graphs exhibit complex temporal dynamics due to the interplay between evolving node features and changing network structures. Recently, Graph Neural Controlled Differential Equations (Graph Neural CDEs) successfully adapted Neural CDEs from paths on Euclidean domains to paths on graph domains. Building on this foundation, we introduce Permutation Equivariant Neural Graph CDEs, which project Graph Neural CDEs onto permutation equivariant function spaces. This significantly reduces the model's parameter count without compromising representational power, resulting in more efficient training and improved generalisation. We empirically demonstrate the advantages of our approach through experiments on simulated dynamical systems and real-world tasks, showing improved performance in both interpolation and extrapolation scenarios. © 2025 Neural information processing systems foundation. All rights reserved.

Original language	English
Title of host publication	39th Conference on Neural Information Processing Systems (NeurIPS 2025)
Editors	D. Belgrave, C. Zhang, H. Lin, R. Pascanu, P. Koniusz, M. Ghassemi, N. Chen
Publisher	Neural Information Processing Systems (NeurIPS)
Pages	108931-108966
Number of pages	36
ISBN (Print)	9798331338275
DOIs	https://doi.org/10.52202/085713-3284
Publication status	Published - Dec 2025
Event	39th Annual Conference on Neural Information Processing Systems (NeurIPS 2025) - San Diego Convention Center, San Diego, United States Duration: 2 Dec 2025 → 7 Dec 2025 https://neurips.cc/Conferences/2025

Publication series

Name	Advances in Neural Information Processing Systems
Volume	38
ISSN (Print)	1049-5258

Conference

Conference	39th Annual Conference on Neural Information Processing Systems (NeurIPS 2025)
Abbreviated title	NeurIPS 2025
Place	United States
City	San Diego
Period	2/12/25 → 7/12/25
Internet address	https://neurips.cc/Conferences/2025

Bibliographical note

Full text of this publication does not contain sufficient affiliation information. With consent from the author(s) concerned, the Research Unit(s) information for this record is based on the existing academic department affiliation of the author(s).

Funding

This work is supported by the Helmholtz Association Initiative and Networking Fund on the HAICORE@KIT partition. Benjamin Walker is funded by the Hong Kong Innovation and Technology Commission (InnoHK Project CIMDA).

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10.52202/085713-3284

https://papers.nips.cc/paper_files/paper/2025/hash/8d54ecfb4ffc95c8994c479671a46b66-Abstract-Conference.html

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Berndt, T., Walker, B., Qin, T., Stühmer, J., & Kormilitzin, A. (2025). Permutation Equivariant Neural Controlled Differential Equations for Dynamic Graph Representation Learning. In D. Belgrave, C. Zhang, H. Lin, R. Pascanu, P. Koniusz, M. Ghassemi, & N. Chen (Eds.), 39th Conference on Neural Information Processing Systems (NeurIPS 2025) (pp. 108931-108966). (Advances in Neural Information Processing Systems; Vol. 38). Neural Information Processing Systems (NeurIPS). https://doi.org/10.52202/085713-3284

Berndt, Torben ; Walker, Benjamin ; Qin, Tiexin et al. / Permutation Equivariant Neural Controlled Differential Equations for Dynamic Graph Representation Learning. 39th Conference on Neural Information Processing Systems (NeurIPS 2025). editor / D. Belgrave ; C. Zhang ; H. Lin ; R. Pascanu ; P. Koniusz ; M. Ghassemi ; N. Chen. Neural Information Processing Systems (NeurIPS), 2025. pp. 108931-108966 (Advances in Neural Information Processing Systems).

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abstract = "Dynamic graphs exhibit complex temporal dynamics due to the interplay between evolving node features and changing network structures. Recently, Graph Neural Controlled Differential Equations (Graph Neural CDEs) successfully adapted Neural CDEs from paths on Euclidean domains to paths on graph domains. Building on this foundation, we introduce Permutation Equivariant Neural Graph CDEs, which project Graph Neural CDEs onto permutation equivariant function spaces. This significantly reduces the model's parameter count without compromising representational power, resulting in more efficient training and improved generalisation. We empirically demonstrate the advantages of our approach through experiments on simulated dynamical systems and real-world tasks, showing improved performance in both interpolation and extrapolation scenarios. {\textcopyright} 2025 Neural information processing systems foundation. All rights reserved.",

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Berndt, T, Walker, B, Qin, T, Stühmer, J & Kormilitzin, A 2025, Permutation Equivariant Neural Controlled Differential Equations for Dynamic Graph Representation Learning. in D Belgrave, C Zhang, H Lin, R Pascanu, P Koniusz, M Ghassemi & N Chen (eds), 39th Conference on Neural Information Processing Systems (NeurIPS 2025). Advances in Neural Information Processing Systems, vol. 38, Neural Information Processing Systems (NeurIPS), pp. 108931-108966, 39th Annual Conference on Neural Information Processing Systems (NeurIPS 2025), San Diego, California, United States, 2/12/25. https://doi.org/10.52202/085713-3284

Permutation Equivariant Neural Controlled Differential Equations for Dynamic Graph Representation Learning. / Berndt, Torben; Walker, Benjamin; Qin, Tiexin et al.
39th Conference on Neural Information Processing Systems (NeurIPS 2025). ed. / D. Belgrave; C. Zhang; H. Lin; R. Pascanu; P. Koniusz; M. Ghassemi; N. Chen. Neural Information Processing Systems (NeurIPS), 2025. p. 108931-108966 (Advances in Neural Information Processing Systems; Vol. 38).

Research output: Chapters, Conference Papers, Creative and Literary Works › RGC 32 - Refereed conference paper (with host publication) › peer-review

TY - GEN

T1 - Permutation Equivariant Neural Controlled Differential Equations for Dynamic Graph Representation Learning

AU - Berndt, Torben

AU - Walker, Benjamin

AU - Qin, Tiexin

AU - Stühmer, Jan

AU - Kormilitzin, Andrey

N1 - Full text of this publication does not contain sufficient affiliation information. With consent from the author(s) concerned, the Research Unit(s) information for this record is based on the existing academic department affiliation of the author(s).

PY - 2025/12

Y1 - 2025/12

N2 - Dynamic graphs exhibit complex temporal dynamics due to the interplay between evolving node features and changing network structures. Recently, Graph Neural Controlled Differential Equations (Graph Neural CDEs) successfully adapted Neural CDEs from paths on Euclidean domains to paths on graph domains. Building on this foundation, we introduce Permutation Equivariant Neural Graph CDEs, which project Graph Neural CDEs onto permutation equivariant function spaces. This significantly reduces the model's parameter count without compromising representational power, resulting in more efficient training and improved generalisation. We empirically demonstrate the advantages of our approach through experiments on simulated dynamical systems and real-world tasks, showing improved performance in both interpolation and extrapolation scenarios. © 2025 Neural information processing systems foundation. All rights reserved.

AB - Dynamic graphs exhibit complex temporal dynamics due to the interplay between evolving node features and changing network structures. Recently, Graph Neural Controlled Differential Equations (Graph Neural CDEs) successfully adapted Neural CDEs from paths on Euclidean domains to paths on graph domains. Building on this foundation, we introduce Permutation Equivariant Neural Graph CDEs, which project Graph Neural CDEs onto permutation equivariant function spaces. This significantly reduces the model's parameter count without compromising representational power, resulting in more efficient training and improved generalisation. We empirically demonstrate the advantages of our approach through experiments on simulated dynamical systems and real-world tasks, showing improved performance in both interpolation and extrapolation scenarios. © 2025 Neural information processing systems foundation. All rights reserved.

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DO - 10.52202/085713-3284

M3 - RGC 32 - Refereed conference paper (with host publication)

SN - 9798331338275

T3 - Advances in Neural Information Processing Systems

SP - 108931

EP - 108966

BT - 39th Conference on Neural Information Processing Systems (NeurIPS 2025)

A2 - Belgrave, D.

A2 - Zhang, C.

A2 - Lin, H.

A2 - Pascanu, R.

A2 - Koniusz, P.

A2 - Ghassemi, M.

A2 - Chen, N.

PB - Neural Information Processing Systems (NeurIPS)

T2 - 39th Annual Conference on Neural Information Processing Systems (NeurIPS 2025)

Y2 - 2 December 2025 through 7 December 2025

ER -

Berndt T, Walker B, Qin T, Stühmer J, Kormilitzin A. Permutation Equivariant Neural Controlled Differential Equations for Dynamic Graph Representation Learning. In Belgrave D, Zhang C, Lin H, Pascanu R, Koniusz P, Ghassemi M, Chen N, editors, 39th Conference on Neural Information Processing Systems (NeurIPS 2025). Neural Information Processing Systems (NeurIPS). 2025. p. 108931-108966. (Advances in Neural Information Processing Systems). doi: 10.52202/085713-3284

Permutation Equivariant Neural Controlled Differential Equations for Dynamic Graph Representation Learning

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