Graph Adaptive Autoregressive Moving Average Models

Moshe Eliasof, Alessio Gravina, Andrea Ceni, Claudio Gallicchio, Davide Bacciu, Carola-Bibiane Schönlieb
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:15232-15265, 2025.

Abstract

Graph State Space Models (SSMs) have recently been introduced to enhance Graph Neural Networks (GNNs) in modeling long-range interactions. Despite their success, existing methods either compromise on permutation equivariance or limit their focus to pairwise interactions rather than sequences. Building on the connection between Autoregressive Moving Average (ARMA) and SSM, in this paper, we introduce GRAMA, a Graph Adaptive method based on a learnable ARMA framework that addresses these limitations. By transforming from static to sequential graph data, GRAMA leverages the strengths of the ARMA framework, while preserving permutation equivariance. Moreover, GRAMA incorporates a selective attention mechanism for dynamic learning of ARMA coefficients, enabling efficient and flexible long-range information propagation. We also establish theoretical connections between GRAMA and Selective SSMs, providing insights into its ability to capture long-range dependencies. Experiments on 26 synthetic and real-world datasets demonstrate that GRAMA consistently outperforms backbone models and performs competitively with state-of-the-art methods.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-eliasof25a, title = {Graph Adaptive Autoregressive Moving Average Models}, author = {Eliasof, Moshe and Gravina, Alessio and Ceni, Andrea and Gallicchio, Claudio and Bacciu, Davide and Sch\"{o}nlieb, Carola-Bibiane}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {15232--15265}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/eliasof25a/eliasof25a.pdf}, url = {https://proceedings.mlr.press/v267/eliasof25a.html}, abstract = {Graph State Space Models (SSMs) have recently been introduced to enhance Graph Neural Networks (GNNs) in modeling long-range interactions. Despite their success, existing methods either compromise on permutation equivariance or limit their focus to pairwise interactions rather than sequences. Building on the connection between Autoregressive Moving Average (ARMA) and SSM, in this paper, we introduce GRAMA, a Graph Adaptive method based on a learnable ARMA framework that addresses these limitations. By transforming from static to sequential graph data, GRAMA leverages the strengths of the ARMA framework, while preserving permutation equivariance. Moreover, GRAMA incorporates a selective attention mechanism for dynamic learning of ARMA coefficients, enabling efficient and flexible long-range information propagation. We also establish theoretical connections between GRAMA and Selective SSMs, providing insights into its ability to capture long-range dependencies. Experiments on 26 synthetic and real-world datasets demonstrate that GRAMA consistently outperforms backbone models and performs competitively with state-of-the-art methods.} }
Endnote
%0 Conference Paper %T Graph Adaptive Autoregressive Moving Average Models %A Moshe Eliasof %A Alessio Gravina %A Andrea Ceni %A Claudio Gallicchio %A Davide Bacciu %A Carola-Bibiane Schönlieb %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-eliasof25a %I PMLR %P 15232--15265 %U https://proceedings.mlr.press/v267/eliasof25a.html %V 267 %X Graph State Space Models (SSMs) have recently been introduced to enhance Graph Neural Networks (GNNs) in modeling long-range interactions. Despite their success, existing methods either compromise on permutation equivariance or limit their focus to pairwise interactions rather than sequences. Building on the connection between Autoregressive Moving Average (ARMA) and SSM, in this paper, we introduce GRAMA, a Graph Adaptive method based on a learnable ARMA framework that addresses these limitations. By transforming from static to sequential graph data, GRAMA leverages the strengths of the ARMA framework, while preserving permutation equivariance. Moreover, GRAMA incorporates a selective attention mechanism for dynamic learning of ARMA coefficients, enabling efficient and flexible long-range information propagation. We also establish theoretical connections between GRAMA and Selective SSMs, providing insights into its ability to capture long-range dependencies. Experiments on 26 synthetic and real-world datasets demonstrate that GRAMA consistently outperforms backbone models and performs competitively with state-of-the-art methods.
APA
Eliasof, M., Gravina, A., Ceni, A., Gallicchio, C., Bacciu, D. & Schönlieb, C.. (2025). Graph Adaptive Autoregressive Moving Average Models. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:15232-15265 Available from https://proceedings.mlr.press/v267/eliasof25a.html.

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