connecting
the dots

  Marek Černý

I am a Ph.D. student under the supervision of Prof. Floris Geerts at  UAntwerp in Flanders. My research centers on whatever connects structural graph theory with the expressive power of graph neural networks. This effort has various impact areas, including drug discovery, material science, or spatiotemporal analytics.

Previously, I graduated with highest honors in discrete models and algorithms from Charles University. My thesis relating topology and neural networks was advised by Bastian Grossenbacher-Rieck and Robert Šámal. Simultaneously, I was a research engineer in deep learning, computer vision, and temporal-spatial networks at several global companies and start-ups.

Contact

Feel free to contact me via email `me at marekcerny dot com`. Follow me on Bluesky, view my CV on LinkedIn, or check out some stuff on my GitHub and Scholar. I proudly use OrgPad. Inquiries regarding research ideas or experiences are warmly welcome.

News

Caterpillar GNNs 🐛

Abstract. Message-passing graph neural networks (MPGNNs) dominate modern graph learning. Typical efforts enhance MPGNN’s expressive power by enriching the adjacency-based aggregation. In contrast, we introduce an efficient aggregation over walk incidence-based matrices that are constructed to deliberately trade off some expressivity for stronger and more structured inductive bias. Our approach allows for seamless scaling between classical message-passing and simpler methods based on walks. We rigorously characterize the expressive power at each intermediate step using homomorphism counts over a hierarchy of generalized caterpillar graphs. Based on this foundation, we propose Caterpillar GNNs, whose robust graph-level aggregation successfully tackles a benchmark specifically designed to challenge MPGNNs. Moreover, we demonstrate that, on real-world datasets, Caterpillar GNNs achieve comparable predictive performance while significantly reducing the number of nodes in the hidden layers of the computational graph:

Press ↑/↓ to switch graphs, ←/→ to change height.

Demo. Comparison of computational graphs (EA) efficient aggregation Ch (ours), and (MP) message-passing for the selected graph. Connections between layers are given by (EA) t-th efficient graph matrices; (MP) copies of the adjacency matrix and the global readout. We use computational graphs for smaller examples of PROTEINS (TUDataset) in this demo. For detailed explanation, we refer to the paper (e.g., Fig. 12).