Recurrent Graph Neural Networks and Arithmetic Circuits
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. Generalising 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 (recurrent) GNNs work on labelled graphs, we construct arithmetic circuits that obtain encoded labelled graphs as real valued tuples and then compute the same functi...
| Authors | Timon Barlag, Vivian Holzapfel, Laura Strieker et al. |
|---|---|
| Primary category | cs.CC |
| Published | 5 March 2026 |
| Last updated at source | 4 May 2026 |
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