DYMAG: Rethinking Message Passing Using Dynamical-systems-based Waveforms

Dhananjay Bhaskar, Xingzhi Sun, Yanlei Zhang, Charles Xu, Arman Afrasiyabi, Siddharth Viswanath, Oluwadamilola Fasina, Guy Wolf, Michael Perlmutter, Smita Krishnaswamy
Proceedings of the 1st Conference on Topology, Algebra, and Geometry in Data Science(TAG-DS 2025), PMLR 321:236-268, 2026.

Abstract

We present DYMAG, a graph neural network based on a novel form of message aggregation. Standard message-passing neural networks, which often aggregate local neighbors via mean-aggregation, can be regarded as convolving with a simple rectangular waveform which is non-zero only on 1-hop neighbors of every vertex. Here, we go beyond such local averaging. We will convolve the node features with more sophisticated waveforms generated using dynamics such as the heat equation, wave equation, and the Sprott model (an example of chaotic dynamics). Furthermore, we use snapshots of these dynamics at different time points to create waveforms at many effective scales. Theoretically, we show that these dynamic waveforms can capture salient information about the graph, including connected components, connectivity, and cycle structures. Empirically, we test DYMAG on both real and synthetic benchmarks to establish that DYMAG outperforms baseline models on recovery of graph persistence, generating parameters of random graphs, as well as property prediction for proteins, molecules and materials. Our code is available at \url{https://github.com/KrishnaswamyLab/DYMAG}.

Cite this Paper

BibTeX
@InProceedings{pmlr-v321-bhaskar26a, title = {DYMAG: Rethinking Message Passing Using Dynamical-systems-based Waveforms}, author = {Bhaskar, Dhananjay and Sun, Xingzhi and Zhang, Yanlei and Xu, Charles and Afrasiyabi, Arman and Viswanath, Siddharth and Fasina, Oluwadamilola and Wolf, Guy and Perlmutter, Michael and Krishnaswamy, Smita}, booktitle = {Proceedings of the 1st Conference on Topology, Algebra, and Geometry in Data Science(TAG-DS 2025)}, pages = {236--268}, year = {2026}, editor = {Bernardez Gil, Guillermo and Black, Mitchell and Cloninger, Alexander and Doster, Timothy and Emerson, Tegan and Garcı́a-Rodondo, Ińes and Holtz, Chester and Kotak, Mit and Kvinge, Henry and Mishne, Gal and Papillon, Mathilde and Pouplin, Alison and Rainey, Katie and Rieck, Bastian and Telyatnikov, Lev and Yeats, Eric and Wang, Qingsong and Wang, Yusu and Wayland, Jeremy}, volume = {321}, series = {Proceedings of Machine Learning Research}, month = {01--02 Dec}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v321/main/assets/bhaskar26a/bhaskar26a.pdf}, url = {https://proceedings.mlr.press/v321/bhaskar26a.html}, abstract = {We present DYMAG, a graph neural network based on a novel form of message aggregation. Standard message-passing neural networks, which often aggregate local neighbors via mean-aggregation, can be regarded as convolving with a simple rectangular waveform which is non-zero only on 1-hop neighbors of every vertex. Here, we go beyond such local averaging. We will convolve the node features with more sophisticated waveforms generated using dynamics such as the heat equation, wave equation, and the Sprott model (an example of chaotic dynamics). Furthermore, we use snapshots of these dynamics at different time points to create waveforms at many effective scales. Theoretically, we show that these dynamic waveforms can capture salient information about the graph, including connected components, connectivity, and cycle structures. Empirically, we test DYMAG on both real and synthetic benchmarks to establish that DYMAG outperforms baseline models on recovery of graph persistence, generating parameters of random graphs, as well as property prediction for proteins, molecules and materials. Our code is available at \url{https://github.com/KrishnaswamyLab/DYMAG}.} }
Endnote
%0 Conference Paper %T DYMAG: Rethinking Message Passing Using Dynamical-systems-based Waveforms %A Dhananjay Bhaskar %A Xingzhi Sun %A Yanlei Zhang %A Charles Xu %A Arman Afrasiyabi %A Siddharth Viswanath %A Oluwadamilola Fasina %A Guy Wolf %A Michael Perlmutter %A Smita Krishnaswamy %B Proceedings of the 1st Conference on Topology, Algebra, and Geometry in Data Science(TAG-DS 2025) %C Proceedings of Machine Learning Research %D 2026 %E Guillermo Bernardez Gil %E Mitchell Black %E Alexander Cloninger %E Timothy Doster %E Tegan Emerson %E Ińes Garcı́a-Rodondo %E Chester Holtz %E Mit Kotak %E Henry Kvinge %E Gal Mishne %E Mathilde Papillon %E Alison Pouplin %E Katie Rainey %E Bastian Rieck %E Lev Telyatnikov %E Eric Yeats %E Qingsong Wang %E Yusu Wang %E Jeremy Wayland %F pmlr-v321-bhaskar26a %I PMLR %P 236--268 %U https://proceedings.mlr.press/v321/bhaskar26a.html %V 321 %X We present DYMAG, a graph neural network based on a novel form of message aggregation. Standard message-passing neural networks, which often aggregate local neighbors via mean-aggregation, can be regarded as convolving with a simple rectangular waveform which is non-zero only on 1-hop neighbors of every vertex. Here, we go beyond such local averaging. We will convolve the node features with more sophisticated waveforms generated using dynamics such as the heat equation, wave equation, and the Sprott model (an example of chaotic dynamics). Furthermore, we use snapshots of these dynamics at different time points to create waveforms at many effective scales. Theoretically, we show that these dynamic waveforms can capture salient information about the graph, including connected components, connectivity, and cycle structures. Empirically, we test DYMAG on both real and synthetic benchmarks to establish that DYMAG outperforms baseline models on recovery of graph persistence, generating parameters of random graphs, as well as property prediction for proteins, molecules and materials. Our code is available at \url{https://github.com/KrishnaswamyLab/DYMAG}.
APA
Bhaskar, D., Sun, X., Zhang, Y., Xu, C., Afrasiyabi, A., Viswanath, S., Fasina, O., Wolf, G., Perlmutter, M. & Krishnaswamy, S.. (2026). DYMAG: Rethinking Message Passing Using Dynamical-systems-based Waveforms. Proceedings of the 1st Conference on Topology, Algebra, and Geometry in Data Science(TAG-DS 2025), in Proceedings of Machine Learning Research 321:236-268 Available from https://proceedings.mlr.press/v321/bhaskar26a.html.

Related Material