Unified view on random walk and Weisfeiler-Leman kernels, improving accuracy.
problem Improving graph kernel methods for better classification accuracy.
method Define and analyze walk-based node refinement methods, relate to Weisfeiler-Leman test, and introduce new walk-based kernels.
result Walk-based kernels are as expressive as Weisfeiler-Leman subtree kernel but support non-strict neighborhood comparison.
Weisfeiler-Leman struggles with graph isomorphism; enhanced architectures improve generalization.
problem Graph isomorphism problem and limited expressivity of 1-WL. method Augmenting 1-WL and MPNNs with subgraph information, employing margin theory, and introducing provable generalization kernels. result Increased expressivity of graph neural networks and kernels does not necessarily correlate with improved generalization performance.
Line graph transformation aids graph isomorphism tests by excluding challenging graph properties.
problem Limited theoretical understanding of line graph transformation's impact on GNN models.
method Examined CFI and strongly regular graphs, showing line graph transformation helps WL tests distinguish these graphs.
result Line graph transformation aids WL tests in distinguishing challenging graph properties.
New MPNNs match 2-WL, faster distinguishing graphs.
problem Improving graph neural network expressiveness.
method Introducing ℓ-walk MPNNs and second-order GNNs. result Walk MPNNs match 2-WL and can distinguish graphs faster.
Geometric GNNs improve graph discrimination through GWL.
problem Discriminating geometric graphs embedded in Euclidean space.
method Proposed a geometric version of the Weisfeiler-Leman test (GWL) for geometric graphs.
result Characterized the expressive power of geometric GNNs based on physical symmetries.
Unified framework for subgraph-enhanced GNNs, improving prediction accuracy and reducing computation time.
problem Limited understanding of subgraph-enhanced GNNs and their relation to the Weisfeiler-Leman hierarchy.
method Theoretical framework, theoretical expressivity results, and data-driven subgraph sampling methods.
result Data-driven subgraph-enhanced GNNs outperform non-data-driven methods in predictive performance.
ISP improves GNN expressivity by stratifying nodes based on graph invariants.
problem Graph Neural Networks struggle with expressivity and structural heterogeneity.
method Invariant-Stratified Propagation (ISP) using ISP-WL and ISPGNN.
result ISP achieves enhanced expressivity beyond 1-WL, with theoretical guarantees and practical improvements.
We investigate graph neural networks for multi-relational data.
problem Understanding and improving graph neural networks for multi-relational data.
method Aligning Relational GCN and Compositional GCN with the Weisfeiler-Leman test to understand their expressive power and introduce a new k-RN architecture. result The k-RN architecture overcomes the expressiveness limitations of Relational GCN and Compositional GCN. Graph kernels based on the 1-dimensional Weisfeiler-Leman algorithm and corresponding neural architectures recently emerged as powerful tools for (supervised) learning with graphs. However, due to the purely local nature of the algorithms, they might miss essential patterns in the given data and can only handle binar…
Weisfeiler and Leman enhance graph learning for machine learning tasks.
problem Learning from graph data in machine learning.
method Weisfeiler and Leman algorithm applied to graph and node representation learning.
result The algorithm improves graph and node representation learning in machine learning.
Graphs indistinguishable by GNNs are fully characterized.
problem Limited expressiveness of GNNs in distinguishing non-isomorphic graphs.
method Theory of covering spaces to characterize GNN equivalence classes.
result Arbitrarily many non-isomorphic graphs that GNNs cannot distinguish.
Graph neural networks (GNNs) have emerged recently as a powerful architecture for learning node and graph representations. Standard GNNs have the same expressive power as the Weisfeiler-Leman test of graph isomorphism in terms of distinguishing non-isomorphic graphs. However, it was recently shown that this test cannot…
In recent years, graph neural networks (GNNs) have emerged as a powerful neural architecture to learn vector representations of nodes and graphs in a supervised, end-to-end fashion. Up to now, GNNs have only been evaluated empirically -- showing promising results. The following work investigates GNNs from a theoretical…
Enhances graph neural networks with spectral and topological information.
problem Improving graph neural networks' expressivity beyond Weisfeiler-Leman hierarchy.
method Integrates spectral information into Persistent Homology diagrams.
result SpectRe is strictly more expressive than PH and spectral information alone.
GNNs with random node initialization are shown to be universally expressive.
problem Limitations of standard GNNs in distinguishing graphs.
method Random node initialization (RNI) to enhance GNNs' expressive power.
result GNNs with RNI are proven to be universally expressive.
kth-order invariant graph networks are as powerful as kth-order WL in distinguishing graphs.
problem Measuring the expressive power of graph neural network formalisms.
method Considered kth-order invariant graph networks (k-IGNs) and compared their expressive power to kth-order WL.
result k-IGNs and k-WL are equally powerful in distinguishing graphs.
PathNNs improve graph neural networks by distinguishing non-isomorphic graphs.
problem Limitations of standard GNNs in distinguishing non-isomorphic graphs.
method Proposes PathNNs that aggregate paths to update node representations.
result Two variants of PathNNs are strictly more powerful than 1-WL algorithm.
The paper connects GNNs to VC dimension theory to study their generalization performance.
problem Understanding GNNs' ability to make meaningful predictions beyond the training set.
method Using Vapnik-Chervonenkis (VC) dimension theory in two settings: no upper bound on graph order and known upper bound.
result Tight connections between GNNs' bitlength, number of colors, and VC dimension in different settings.
ESAN improves graph neural networks by processing subgraphs.
problem Limitations of MPNNs in graph isomorphism.
method ESAN represents graphs as sets of subgraphs and processes them with equivariant architectures.
result ESAN increases the expressive power of GNNs and more expressive architectures.
Graph Substructure Networks (GSN) improves GNN expressivity by counting subgraph isomorphisms.
problem Limited expressivity of GNNs in detecting and counting graph substructures.
method Topologically-aware message passing scheme based on substructure encoding.
result GSN is strictly more expressive than the Weisfeiler-Leman (WL) test and can disambiguate even hard graph isomorphism instances.
π-GNN learns soft permutations for graph representations, improving graph classification and regression.
problem Limitations of MPNNs in graph neural networks.
method Proposes π-GNN, which learns a soft permutation matrix for each graph, projecting graphs into a common vector space.
result π-GNN achieves performance competitive with state-of-the-art models on graph classification and regression tasks.