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.
Survey on GNNs' power and limitations.
problem Theoretical limitations of GNNs.
method Comprehensive overview of GNNs and their variants.
result Provably powerful variants of GNNs.
GNNs are powerful but limited in their ability to distinguish certain graph structures.
problem Limited understanding of GNNs' representational properties and limitations.
method Theoretical framework and analysis of GNN expressive power, development of a provably most expressive GNN architecture.
result GNNs cannot learn to distinguish certain simple graph structures, but a new architecture can.
Enhances GCNs to resist graph attacks.
problem Vulnerability of GCNs to topological attacks.
method Introduces a new robust convolution operator and training paradigm.
result Improves adversarial robustness and performance.
We study the evolution of convex complete non-compact graphs by positive powers of Gauss curvature. We show that if the initial complete graph has a local uniform convexity, then the graph evolves by any positive power of Gauss curvature for all time. In particular, the initial graph is not necessarily differentiable.
DeepGDL models create realistic power grids from confidential data.
problem Creating realistic power grids from confidential data.
method Graph distribution learning (GDL) with a deep nonlinear recurrent structure.
result DeepGDL models accurately create synthetic power grids.
Graph isomorphism can be tested using GNNs, proving their expressive power.
problem Testing graph isomorphism using Graph Neural Networks (GNNs).
method Equivalence between GNNs' function approximation and graph isomorphism testing, using sigma-algebra.
result Equivalence between graph isomorphism testing and GNN function approximation.
Method segments graphs to estimate network models using power graph fused lasso.
problem Estimating non-parametric network models from noisy data.
method Power graph fused lasso (PGFL) for graph segmentation.
result PGFL achieves optimal error rate for graphon estimation under subGaussian noise.
A new graph signature invariant to graph automorphisms.
problem Graph symmetry and feature generation.
method Power spectrum signature derived from squared graph Fourier transform.
result Power spectrum signature is stable under graph perturbations.
New method clusters signed graphs using matrix power means.
problem Clustering signed graphs with positive and negative relations.
method Signed Power Mean Laplacian, defined as matrix power mean of normalized standard and signless Laplacians.
result Signed power mean Laplacian captures ground truth clusters under reasonable settings.
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.
Introduces a new method for clustering multilayer graphs.
problem How to merge information from different layers in multilayer graphs.
method Introduces a one-parameter family of matrix power means for merging Laplacians from different layers.
result The method allows for accurate recovery of ground truth clusters under various settings.
A hierarchy of GNNs based on learnable local features is proposed.
problem Limited understanding of GNN architectures and their systematic construction.
method A hierarchy of GNNs based on aggregation regions is derived, and theoretical results are provided.
result Simple GNN architecture exceeds Weisfeiler-Lehman graph isomorphism test.
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.
Graph Neural Networks outperform the Weisfeiler-Lehman algorithm in representation power.
problem Limited representation power of Graph Neural Networks compared to the Weisfeiler-Lehman algorithm.
method Algebraic analysis using eigenvalue decomposition of graph operators.
result Graph Neural Networks produce more discriminative representations than the Weisfeiler-Lehman algorithm.
Graph machine learning lacks a balanced theory, focusing on expressive power and optimization.
problem Insufficient theoretical understanding of GNNs' generalization behavior.
method Develop a balanced theory focusing on expressive power, generalization, and optimization.
result Theoretical advancements need to align with practical success in graph machine learning.
Graph Neural Tangent Kernels combine GNNs and GKs for better graph classification.
problem Limited expressive power of graph kernels and difficulties in training graph neural networks.
method Graph Neural Tangent Kernels (GNTKs) are infinitely wide multi-layer GNNs trained by gradient descent.
result GNTKs achieve strong performance on graph classification datasets.
edGNN improves graph embeddings for directed labeled graphs.
problem Improving node and graph embeddings for directed labeled graphs.
method edGNN is a GNN designed for directed labeled graphs, leveraging both topology and labels.
result edGNN is as powerful as the Weisfeiler-Lehman algorithm for graph isomorphism.
Optimizes wireless power control using graph neural networks and counterfactual optimization.
problem Mitigating interference in wireless networks with multiple transmitter-receiver pairs.
method Graph neural network architecture combined with unsupervised primal-dual counterfactual optimization.
result Guarantees a minimum rate constraint that adapts to network size, balancing user rates.
Graph NNs lose predictive power exponentially with more layers.
problem Graph Neural Networks (graph NNs) lose predictive power exponentially with more layers.
method Generalized the forward propagation of a Graph Convolutional Network (GCN) as a dynamical system and analyzed its asymptotic behaviors.
result GCNs' output exponentially approaches signals related to node degrees and connected components, leading to 'information loss' in the limit of infinite layers.
We study convex entire graphs evolving with normal velocity equal to a positive power of the mean curvature. Under mild assumptions we prove longtime existence.
GCNs struggle with learning graph moments, but modular designs improve their performance.
problem GCNs' limitations in learning graph moments.
method Investigated through graph moments, analyzed expressiveness, designed modular GCNs.
result Modular GCNs using different propagation rules can distinguish graphs from various models.
This work characterizes topological descriptors of graph products and their expressive power.
problem Capturing multiscale structural information in graph products using topological descriptors.
method Analysis of various filtrations on graph products, including Euler characteristic and persistent homology.
result Persistent homology of graph products contains more information than individual graphs.
CW Networks leverage cell complexes to enhance GNNs, achieving state-of-the-art results on molecular datasets.
problem Graph Neural Networks struggle with long-range interactions and lack principled ways to model higher-order structures.
method CW Networks use cell complexes to decouple computational and input graph structures, enabling flexible hierarchical message passing.
result CW Networks achieve state-of-the-art results on molecular datasets.
Graph Attention Networks predict power outage durations from natural disasters.
problem Accurately predicting power outage durations from geospatial and weather data.
method Graph Attention Networks (GAT) for semi-supervised learning.
result GAT model outperforms existing methods by 2% - 15% in accuracy.
Adding random features to GNNs improves their performance.
problem Limitations of GNNs in distinguishing graphs and learning efficient algorithms.
method Adding random features to each node in GNNs.
result Random features enable GNNs to learn optimal algorithms for graph problems.
We present a model for random simple graphs with a degree distribution that obeys a power law (i.e., is heavy-tailed). To attain this behavior, the edge probabilities in the graph are constructed from Bertoin-Fujita-Roynette-Yor (BFRY) random variables, which have been recently utilized in Bayesian statistics for the c…
OmniMatch algorithm perfectly matches graphs without edge correlation.
problem Graph matching in the absence of edge correlation.
method OmniMatch algorithm for seeded multiple graph matching.
result OmniMatch aligns O(sα) unseeded vertices across multiple networks efficiently and perfectly. 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.
This study compares GNNs and GA-MLPs, finding GA-MLPs can distinguish graphs but not count walks.
problem Comparing expressive power and graph isomorphism testing capabilities of GNNs and GA-MLPs.
method GA-MLPs augment node features with multi-hop operators and apply MLPs node-wise; GNNs are compared as a baseline.
result GA-MLPs can distinguish almost all non-isomorphic graphs but cannot count attributed walks, unlike GNNs.
Graph Neural Networks struggle on random graphs without node identifiers.
problem Graph Neural Networks' limitations on random graphs without node identifiers.
method Study of Graph Neural Networks and Structural Graph Neural Networks convergence on large random graphs.
result Structural Graph Neural Networks are more powerful and universal than Graph Neural Networks on random graphs.
Study compares different levels of supervision for training graph embeddings in wireless networks.
problem Improving power control in wireless interference networks.
method Training graph neural networks (GNNs) with different levels of supervision (supervised, unsupervised, self-supervised).
result Different levels of supervision impact system-level throughput, convergence, and generalization.
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.
ParPIC clusters directed graphs using random walks and diffusion operators.
problem Challenges in vertex-level clustering for directed graphs due to edge directionality.
method Parametrized Power-Iteration Clustering (ParPIC) based on reversible random walks and diffusion operators.
result ParPIC achieves competitive clustering accuracy with improved scalability compared to spectral and teleportation-based methods.
Enhances graph neural networks with Relational Pooling for better graph classification.
problem Improving graph neural networks for better graph classification.
method Relational Pooling (RP) based on finite partial exchangeability theory.
result Improved performance on graph classification tasks.
Graphs can't learn certain tasks due to depth vs width limitations.
problem Understanding limitations of graph neural networks in learning specific tasks.
method Analyzing expressive power of GNNmp under depth, width, and node attributes.
result GNNmp can lose significant power when depth and width are restricted.
Correlation matrices of foreign exchange rate time series are investigated for 60 world currencies. Minimal Spanning Tree (MST) graphs for the gold, silver and platinum are presented. Inverse power like scaling is discussed for these graphs as well as for four distinct currency groups (major, liquid, less liquid and no…
New method segments power grids in real time for easier control.
problem Segmenting large-scale power grids for real-time control.
method Guided machine learning approach with Influence Graph and community detection.
result Promising and original interpretable results on various grids.
New graph neural networks can distinguish graphs better than previous models.
problem Graph isomorphism tests limit the expressive power of GNNs.
method Developed k-order invariant and equivariant graph neural networks, and a reduced 2-order network.
result A reduced 2-order network with a single quadratic operation has 3-WL expressiveness, surpassing message passing models.
Paper compares expressive power of GNNs, proving approximation guarantees for practical architectures.
problem Understanding the expressive power of Graph Neural Networks (GNNs).
method Theoretical framework comparing invariant and equivariant GNNs, proving approximation guarantees for practical architectures.
result Folklore Graph Neural Networks (FGNN) are the most expressive architectures for a given tensor order.
Paper explores how GNNs can learn graph biconnectivity, finding ESAN is the only known expressive framework.
problem Understanding the expressive power of GNNs beyond the WL test.
method Introduces a novel class of expressivity metrics via graph biconnectivity and develops the GD-WL approach.
result GD-WL consistently outperforms prior GNN architectures in learning biconnectivity metrics.
Graph neural networks benefit from a new initialization method that improves node learning.
problem Poor initialization in GNNs leads to slower convergence and increased training instability.
method Integrates a statistically grounded one-hot graph encoder embedding (GEE) into standard GNNs.
result GG framework provides consistent and substantial performance gains in node classification.
New method explains GNNs using power iteration clustering.
problem Mysterious mechanism of message passing in GNNs.
method Subspace power iteration clustering (SPIC) models.
result Message passing in GNNs can be understood through power iteration.
New probabilistic graph models for efficient power system simulation.
problem Complexity of modern power grids and challenges in physics-based models.
method Data-driven probabilistic graphs with custom non-linear models.
result Accurate and scalable models for large-scale power systems.
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. DE improves GNNs by distinguishing graph substructures, enhancing accuracy.
problem Limited expressive power of GNNs in representing graph substructures.
method Introduces Distance Encoding (DE) to assist GNNs in distinguishing graph substructures.
result DE distinguishes graph substructures that traditional GNNs cannot, improving accuracy.
Paper compares GCNs and MPNNs, finding GCNs are one step ahead of WL algorithm.
problem Comparing graph convolutional networks (GCNs) and message-passing neural networks (MPNNs).
method Casts GCNs and MPNNs as MPNNs, studies distinguishing power of different architectures.
result GCNs are one step ahead of the Weisfeiler-Lehman (WL) algorithm in distinguishing power.
The paper uses g-adic representations to connect number theory and graph theory.
problem Relating metric properties of Cayley graphs to additive number theory problems.
method Using g-adic representations to study Cayley graphs of integers with various generating sets. result Explicit formulas for the smallest positive integer of a given length and bounds on Cayley graph diameter.