Recurrent Graph Neural Networks and Arithmetic Circuits
#Recurrent Graph Neural Networks #Arithmetic Circuits #Deep Learning #Graph Structures #Computational Efficiency
📌 Key Takeaways
- Recurrent Graph Neural Networks (RGNNs) combine graph structures with sequential learning for dynamic data.
- Arithmetic circuits provide a framework for efficient computation and representation in neural networks.
- The integration enhances modeling of complex dependencies and improves computational efficiency.
- Potential applications include time-series analysis on graphs and structured data processing.
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arXiv:2603.05140v1 Announce Type: cross
Abstract: We characterise the computational power of recurrent graph neural networks (GNNs) in terms of arithmetic circuits over the real numbers. Our networks are not restricted to aggregate-combine GNNs or other particular types. Generalizing similar notions from the literature, we introduce the model of recurrent arithmetic circuits, which can be seen as arithmetic analogues of sequential or logical circuits. These circuits utilise so-called memory gat
🏷️ Themes
Neural Networks, Computational Models
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Deep learning
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In machine learning, deep learning focuses on utilizing multilayered neural networks to perform tasks such as classification, regression, and representation learning. The field takes inspiration from biological neuroscience and revolves around stacking artificial neurons into layers and "training" t...
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--> Computer Science > Computational Complexity arXiv:2603.05140 [Submitted on 5 Mar 2026] Title: Recurrent Graph Neural Networks and Arithmetic Circuits Authors: Timon Barlag , Vivian Holzapfel , Laura Strieker , Jonni Virtema , Heribert Vollmer View a PDF of the paper titled Recurrent Graph Neural Networks and Arithmetic Circuits, by Timon Barlag and Vivian Holzapfel and Laura Strieker and Jonni Virtema and Heribert Vollmer View PDF HTML Abstract: We characterise the computational power of recurrent graph neural networks in terms of arithmetic circuits over the real numbers. Our networks are not restricted to aggregate-combine GNNs or other particular types. Generalizing similar notions from the literature, we introduce the model of recurrent arithmetic circuits, which can be seen as arithmetic analogues of sequential or logical circuits. These circuits utilise so-called memory gates which are used to store data between iterations of the recurrent circuit. While GNNs work on labelled graphs, we construct arithmetic circuits that obtain encoded labelled graphs as real valued tuples and then compute the same function. For the other direction we construct recurrent GNNs which are able to simulate the computations of recurrent circuits. These GNNs are given the circuit-input as initial feature vectors and then, after the GNN-computation, have the circuit-output among the feature vectors of its nodes. In this way we establish an exact correspondence between the expressivity of recurrent GNNs and recurrent arithmetic circuits operating over real numbers. Subjects: Computational Complexity (cs.CC) ; Artificial Intelligence (cs.AI); Machine Learning (cs.LG) ACM classes: F.1.1; F.1.3; I.2.m Cite as: arXiv:2603.05140 [cs.CC] (or arXiv:2603.05140v1 [cs.CC] for this version) https://doi.org/10.48550/arXiv.2603.05140 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Laura Strieker [ view email ] [v1] Thu, 5 Mar 2026 13:10:27 UTC ...
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