Unified framework for analyzing graph neural operators converging to graph limits.
problem Analyzing convergence of graph neural operators to graph limits.
method Develops a unified spectral framework for graph neural operators under various graphon assumptions.
result Unified framework enables direct comparison of convergence rates and tradeoffs.
Finslerian graph neural networks recover nonlinear diffusion geometry
problem Graph neural networks on point clouds
method Estimates of the Finsler Laplacian
result Recovery of Finsler geometry
Graph Neural Networks (GNNs), which generalize deep neural networks to graph-structured data, have drawn considerable attention and achieved state-of-the-art performance in numerous graph related tasks. However, existing GNN models mainly focus on designing graph convolution operations. The graph pooling (or downsampli…
New centrality-based graph shift operators improve graph neural networks.
problem Improving graph neural networks by enhancing graph shift operators.
method Proposed Centrality Graph Shift Operators (CGSOs) using global centrality metrics.
result CGSOs lead to improved performance in graph neural networks on real-world datasets.
Graph convolutional networks adapt the architecture of convolutional neural networks to learn rich representations of data supported on arbitrary graphs by replacing the convolution operations of convolutional neural networks with graph-dependent linear operations. However, these graph-dependent linear operations are d…
GATES improves neural architecture search by modeling operations as information transformation.
problem Improving predictor-based neural architecture search efficiency.
method GATES models operations as information transformation, covering both node and edge cell search spaces.
result GATES boosts sample efficiency and improves predictor performance.
NTKs explain GNNs' alignment for graph prediction.
problem Understanding GNNs' alignment for graph prediction.
method Analyzing NTKs and alignment in GNNs, focusing on cross-covariance.
result Optimizing alignment in GNNs optimizes graph representation.
This work extends GNNs to handle multiple graphs with non-commuting operators, proving transferability.
problem Handling multiple graphs with non-commuting operators in graph neural networks.
method Developed a mathematical theory for graph-tuple neural networks (GtNNs) with non-commuting non-expansive operators.
result Proved universal transferability of GtNNs, ensuring no non-transferable energy under convergence.
Graph neural network predicts optimal coarse-grained mapping operators.
problem Optimal coarse-grained mapping operators selection for molecular dynamics simulations.
method Graph Neural Network (DSGPM) trained on expert-annotated data.
result DSGPM outperforms state-of-the-art methods in graph segmentation.
Paper revisits graph-CNNs using Laplace-Beltrami spectral filters and polynomials.
problem Improving spectral graph convolutional neural networks (graph-CNNs).
method Developed Laplace-Beltrami CNN (LB-CNN) by replacing graph Laplacian with LB operator and approximating spectral filters using Chebyshev, Laguerre, and Hermite polynomials.
result Classification accuracy of LB-CNN is not dependent on the type of polynomials or operators.
Recently, graph neural networks have been adopted in a wide variety of applications ranging from relational representations to modeling irregular data domains such as point clouds and social graphs. However, the space of graph neural network architectures remains highly fragmented impeding the development of optimized …
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.
Unified view of GNNs as graph signal denoising.
problem Understanding and improving GNNs for graph data.
method Established GNNs as graph denoising problems with smoothness assumptions.
result Unified framework UGNN for adaptive smoothness graphs.
New approach to deeper graph neural networks to avoid performance degradation.
problem Performance degradation of graph neural networks when going deeper.
method Decoupling representation transformation and propagation in graph convolution operations.
result Deeper graph neural networks can be used to learn graph node representations from larger receptive fields.
Novel parametrized graph shift operators improve graph neural network performance.
problem Improving graph neural network performance on various datasets.
method Proposed a novel parametrized graph shift operator (PGSO) that optimizes parameters during training.
result PGSO improves accuracy in node and graph classification tasks on real-world datasets.
New methods for clustering graphs using spectral analysis.
problem Graph clustering for complex systems.
method Transfer operators and spectral properties.
result Spectral clustering can be interpreted using Koopman operators.
Paper introduces a new metric to select optimal Graph Shift Operator for GNNs.
problem Empirical selection of Graph Shift Operator remains challenging.
method Introduces a novel alignment gain metric connecting geometric distortion to generalization bounds via spectral proxy.
result Provides a principled, computation-efficient criterion to rank and select optimal GSO.
We introduce Graph Neural Processes (GNP), inspired by the recent work in conditional and latent neural processes. A Graph Neural Process is defined as a Conditional Neural Process that operates on arbitrary graph data. It takes features of sparsely observed context points as input, and outputs a distribution over targ…
Graph neural networks have become increasingly popular in recent years due to their ability to naturally encode relational input data and their ability to scale to large graphs by operating on a sparse representation of graph adjacency matrices. As we look to scale up these models using custom hardware, a natural assum…
Graph data augmentation improves GNN performance in node classification.
problem Improving generalizability of graph neural networks (GNNs) in semi-supervised node classification.
method Introduces GAug framework for graph data augmentation using neural edge predictors.
result GAug framework improves GNN-based node classification performance across various architectures and datasets.
New graph coarsening method preserves GNN message-passing signals.
problem Preserving GNN message-passing on coarsened graphs.
method Proposed a new oriented message-passing operation for coarsened graphs.
result Improved node classification results compared to naive methods.
Paper analyzes GCNN sensitivity to probabilistic graph perturbations.
problem Investigating how GCNNs handle probabilistic graph errors.
method Establishes error bounds and linear relationships between GSO perturbations and GCNN outputs.
result GCNNs maintain stability under graph edge perturbations if GSO errors are bounded.
PiNet improves graph classification efficiency and accuracy.
problem Graph level classification challenges.
method Attention-based pooling mechanism for graph convolution operations.
result Superior performance and high sample efficiency.
Graph Neural Networks (GNNs) have boosted the performance of many graph related tasks such as node classification and graph classification. Recent researches show that graph neural networks are vulnerable to adversarial attacks, which deliberately add carefully created unnoticeable perturbation to the graph structure. …
Graph neural networks, which generalize deep neural network models to graph structured data, have attracted increasing attention in recent years. They usually learn node representations by transforming, propagating and aggregating node features and have been proven to improve the performance of many graph related tasks…
Graph neural networks improve AMG convergence for sparse systems.
problem Efficiently constructing algebraic multigrid prolongation operators for sparse linear systems.
method Train a graph neural network to learn prolongation operators from matrix classes, using an unsupervised loss function.
result Improved convergence rates compared to classical AMG methods.
VEGN uses graph neural networks to predict disease-causing mutations from genetic variants.
problem Identifying disease-causing mutations from millions of genetic variants.
method VEGN employs a graph neural network on a heterogeneous graph of genes and variants, learning gene-gene interactions.
result VEGN outperforms existing state-of-the-art models in variant effect prediction.
This paper explores vulnerabilities in hierarchical graph pooling neural networks for graph classification.
problem Vulnerability of hierarchical graph pooling neural networks in graph classification tasks.
method Proposes an adversarial attack framework using a surrogate model to generate adversarial samples.
result Adversarial samples can fool hierarchical GNN-based graph classification models, demonstrating their vulnerability.
A new graph neural network framework captures long-range interactions efficiently.
problem Efficiently modeling long-range interactions in graph neural networks for PDEs.
method Proposes a multi-level graph neural network framework using multipole methods.
result Captures interaction at all ranges with only linear complexity, learning discretization-invariant solution operators.
Most of the successful deep neural network architectures are structured, often consisting of elements like convolutional neural networks and gated recurrent neural networks. Recently, graph neural networks have been successfully applied to graph structured data such as point cloud and molecular data. These networks oft…
New equivariant filters improve graph classification.
problem Designing deep learning models for graph symmetries.
method Nonlinear spectral filters (NLSFs) that are equivariant to graph functional shifts.
result NLSFs outperform existing spectral GNNs in graph classification.
The paper explores how different patterns of heterophily affect Graph Neural Networks.
problem Understanding the impact of heterophily on Graph Neural Networks.
method Theoretical analysis and experiments with Heterophilous Stochastic Block Models (HSBM).
result The impact of heterophily on classification depends on the Euclidean distance of neighborhood distributions and the averaged node degree.
In graph neural networks (GNNs), pooling operators compute local summaries of input graphs to capture their global properties, and they are fundamental for building deep GNNs that learn hierarchical representations. In this work, we propose the Node Decimation Pooling (NDP), a pooling operator for GNNs that generates c…
We present graph attention networks (GATs), novel neural network architectures that operate on graph-structured data, leveraging masked self-attentional layers to address the shortcomings of prior methods based on graph convolutions or their approximations. By stacking layers in which nodes are able to attend over thei…
Generalizes neural networks for infinite-dimensional mappings, including PDE solutions.
problem Learning mappings between infinite-dimensional spaces and finite-dimensional approximations.
method Graph kernel network architecture with message passing for kernel integration.
result Competitive performance compared to state-of-the-art solvers for PDEs.
Framework predicts Navier-Stokes solutions on 2D domains using graph neural networks.
problem Predicting stationary Navier-Stokes solutions in non-parametrized 2D geometries.
method Graph-based multi-fidelity learning framework combining reduced-order models, Transformers, and Mamba architectures.
result Mamba architecture reduces computational cost while maintaining performance.
We propose a novel graph pooling operation using cliques as the unit pool. As this approach is purely topological, rather than featural, it is more readily interpretable, a better analogue to image coarsening than filtering or pruning techniques, and entirely nonparametric. The operation is implemented within graph con…
Graph Neural Simulators improve data efficiency for PDE surrogates.
problem Lack of data efficiency in neural operators for PDE systems.
method Graph Neural Simulators (GNS) leverage message-passing and numerical time-stepping to learn PDE dynamics efficiently.
result GNS achieves less than 1% relative L2 error using only 3% of available trajectories.
Node Masking improves GNNs' scalability and generalization.
problem Improving GNNs' ability to handle arbitrary graphs.
method Introducing Node Masking to enhance GNNs' performance.
result Node Masking enables GNNs to generalize and scale better.
Develops a smooth operator framework for analyzing neural network representations.
problem Analyzing the geometry of feedforward neural network representations.
method Introduces a smooth operator-theoretic approach based on diffusion Markov operators derived from feature clouds.
result Establishes a stable operator-geometric framework for tracking training, width, and perturbation stability.
EvoNUDGE uses graph neural networks to improve genetic programming performance.
problem Efficiency in evolutionary computation for problem solving.
method Graph neural network to elicit additional knowledge from symbolic regression problems.
result EvoNUDGE significantly outperforms conventional and neural genetic programming methods.
SpeqNets improve graph neural networks by scaling and adapting to graph sparsity.
problem Graph neural networks struggle with permutation-equivariant functions and scalability to large graphs.
method Introducing sparsity-aware, permutation-equivariant graph networks with heuristics for graph isomorphism.
result Significantly improved predictive performance and reduced computation times compared to existing methods.
Proposes SimPool for graph pooling using structural similarity features.
problem Challenges in graph pooling due to lack of spatial locality.
method Integrates structural similarity features with a revised pooling layer to propose SimPool.
result SimPool produces node cluster assignments resembling CNN's locality preserving pooling.
Spektral simplifies graph neural networks with TensorFlow and Keras.
problem Building graph neural networks efficiently.
method Open-source library implementing various graph neural network methods.
result Performance of implemented methods in node, graph, and graph regression tasks.
With the advent of data science, the analysis of network or graph data has become a very timely research problem. A variety of recent works have been proposed to generalize neural networks to graphs, either from a spectral graph theory or a spatial perspective. The majority of these works however focus on adapting the …
Develops GIN for fMRI sex classification, explaining results.
problem Difficulty in explaining GNN classification results in neuroscientific terms.
method Develops Graph Isomorphism Network (GIN) for fMRI data, leveraging CNN saliency maps.
result GIN enables visualization of brain regions important for sex classification.
MCNO learns PDE solution operators using Monte Carlo sampling.
problem Learning solution operators for PDEs efficiently and flexibly.
method Directly learns kernel function using Monte Carlo sampling of input-output pairs.
result Competitive accuracy with efficient computational cost on 1D PDE benchmarks.
Efficient memory layer improves graph neural networks for graph classification and regression.
problem Efficiently learning node representations and graph coarsening for arbitrary graph topology.
method Introduces a memory layer for GNNs that learns node representations and graph coarsening, and two new networks: MemGNN and GMN.
result Proposed models achieve state-of-the-art results in graph classification and regression benchmarks.