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Pascal Welke

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7 papers

2 author rows

TMLR Journal 2025 Journal Article

Expressive Pooling for Graph Neural Networks

Veronica Lachi
Alice Moallemy-Oureh
Andreas Roth
Pascal Welke

Considerable efforts have been dedicated to exploring methods that enhance the expressiveness of graph neural networks. Current endeavors primarily focus on modifying the message-passing process to overcome limitations imposed by the Weisfeiler-Leman test, often at the expense of increasing computational cost. In practical applications, message-passing layers are interleaved with pooling layers for graph-level tasks, enabling the learning of increasingly abstract and coarser representations of input graphs. In this work, we formally prove two directions that allow pooling methods to increase the expressive power of a graph neural network while keeping the message-passing method unchanged. We systemically assign eight frequently used pooling operators to our theoretical conditions for increasing expressivity and introduce a novel pooling method XP, short for eXpressive Pooling, as an additional simple method that satisfies our theoretical conditions. Experiments conducted on the Brec dataset confirm that those pooling methods that satisfy our conditions empirically increase the expressivity of graph neural networks.

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TMLR Journal 2025 Journal Article

Maximally Expressive GNNs for Outerplanar Graphs

Franka Bause
Fabian Jogl
Patrick Indri
Tamara Drucks
David Penz
Nils Morten Kriege
Thomas Gärtner
Pascal Welke

We propose a linear time graph transformation that enables the Weisfeiler-Leman (WL) algorithm and message passing graph neural networks (MPNNs) to be maximally expressive on outerplanar graphs. Our approach is motivated by the fact that most pharmaceutical molecules correspond to outerplanar graphs. Existing research predominantly enhances the expressivity of graph neural networks without specific graph families in mind. This often leads to methods that are impractical due to their computational complexity. In contrast, the restriction to outerplanar graphs enables us to encode the Hamiltonian cycle of each biconnected component in linear time. As the main contribution of the paper we prove that our method achieves maximum expressivity on outerplanar graphs. Experiments confirm that our graph transformation improves the predictive performance of MPNNs on molecular benchmark datasets at negligible computational overhead.

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ICML Conference 2025 Conference Paper

WILTing Trees: Interpreting the Distance Between MPNN Embeddings

Masahiro Negishi
Thomas Gärtner 0001
Pascal Welke

We investigate the distance function learned by message passing neural networks (MPNNs) in specific tasks, aiming to capture the functional distance between prediction targets that MPNNs implicitly learn. This contrasts with previous work, which links MPNN distances on arbitrary tasks to structural distances on graphs that ignore task-specific information. To address this gap, we distill the distance between MPNN embeddings into an interpretable graph distance. Our method uses optimal transport on the Weisfeiler Leman Labeling Tree (WILT), where the edge weights reveal subgraphs that strongly influence the distance between embeddings. This approach generalizes two well-known graph kernels and can be computed in linear time. Through extensive experiments, we demonstrate that MPNNs define the relative position of embeddings by focusing on a small set of subgraphs that are known to be functionally important in the domain.

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KR Conference 2024 Conference Paper

Logical Distillation of Graph Neural Networks

Alexander Pluska
Pascal Welke
Thomas Gärtner
Sagar Malhotra

We present a logic based interpretable model for learning on graphs and an algorithm to distill this model from a Graph Neural Network (GNN). Recent results have shown connections between the expressivity of GNNs and the two-variable fragment of first-order logic with counting quantifiers (C2). We introduce a decision-tree based model which leverages an extension of C2 to distill interpretable logical classifiers from GNNs. We test our approach on multiple GNN architectures. The distilled models are interpretable, succinct, and attain similar accuracy to the underlying GNN. Furthermore, when the ground truth is expressible in C2, our approach outperforms the GNN.

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NeurIPS Conference 2024 Conference Paper

Weisfeiler and Leman Go Loopy: A New Hierarchy for Graph Representational Learning

Raffaele Paolino
Sohir Maskey
Pascal Welke
Gitta Kutyniok

We introduce $r$-loopy Weisfeiler-Leman ($r$-$\ell$WL), a novel hierarchy of graph isomorphism tests and a corresponding GNN framework, $r$-$\ell$MPNN, that can count cycles up to length $r{+}2$. Most notably, we show that $r$-$\ell$WL can count homomorphisms of cactus graphs. This extends 1-WL, which can only count homomorphisms of trees and, in fact, is incomparable to $k$-WL for any fixed $k$. We empirically validate the expressive and counting power of $r$-$\ell$MPNN on several synthetic datasets and demonstrate the scalability and strong performance on various real-world datasets, particularly on sparse graphs.

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ICML Conference 2023 Conference Paper

Expectation-Complete Graph Representations with Homomorphisms

Pascal Welke
Maximilian Thiessen
Fabian Jogl
Thomas Gärtner 0001

We investigate novel random graph embeddings that can be computed in expected polynomial time and that are able to distinguish all non-isomorphic graphs in expectation. Previous graph embeddings have limited expressiveness and either cannot distinguish all graphs or cannot be computed efficiently for every graph. To be able to approximate arbitrary functions on graphs, we are interested in efficient alternatives that become arbitrarily expressive with increasing resources. Our approach is based on Lovász’ characterisation of graph isomorphism through an infinite dimensional vector of homomorphism counts. Our empirical evaluation shows competitive results on several benchmark graph learning tasks.

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AAAI Conference 2022 Conference Paper

Graph Filtration Kernels

Till Schulz
Pascal Welke
Stefan Wrobel

The majority of popular graph kernels is based on the concept of Haussler’s R-convolution kernel and defines graph similarities in terms of mutual substructures. In this work, we enrich these similarity measures by considering graph filtrations: Using meaningful orders on the set of edges, which allow to construct a sequence of nested graphs, we can consider a graph at multiple granularities. A key concept of our approach is to track graph features over the course of such graph resolutions. Rather than to simply compare frequencies of features in graphs, this allows for their comparison in terms of when and for how long they exist in the sequences. In this work, we propose a family of graph kernels that incorporate these existence intervals of features. While our approach can be applied to arbitrary graph features, we particularly highlight Weisfeiler-Lehman vertex labels, leading to efficient kernels. We show that using Weisfeiler-Lehman labels over certain filtrations strictly increases the expressive power over the ordinary Weisfeiler-Lehman procedure in terms of deciding graph isomorphism. In fact, this result directly yields more powerful graph kernels based on such features and has implications to graph neural networks due to their close relationship to the Weisfeiler-Lehman method. We empirically validate the expressive power of our graph kernels and show significant improvements over state-of-the-art graph kernels in terms of predictive performance on various real-world benchmark datasets.

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