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Found 28 papers, 4 papers with code
Reply to 'Comments on Graphon Signal Processing' [arXiv:2310.14683]
This technical note addresses an issue [arXiv:2310. 14683] with the proof (but not the statement) of [arXiv:2003. 05030, Proposition 4].
A Poincaré Inequality and Consistency Results for Signal Sampling on Large Graphs
We prove a Poincar\'e inequality for graphon signals and show that complements of node subsets satisfying this inequality are unique sampling sets for Paley-Wiener spaces of graphon signals.
A Local Graph Limits Perspective on Sampling-Based GNNs
We propose a theoretical framework for training Graph Neural Networks (GNNs) on large input graphs via training on small, fixed-size sampled subgraphs.
Geometric Graph Filters and Neural Networks: Limit Properties and Discriminability Trade-offs
This paper studies the relationship between a graph neural network (GNN) and a manifold neural network (MNN) when the graph is constructed from a set of points sampled from the manifold, thus encoding geometric information.
Graph Neural Tangent Kernel: Convergence on Large Graphs
We use graphons to define limit objects -- graphon NNs for GNNs, and graphon NTKs for GNTKs -- , and prove that, on a sequence of graphs, the GNTKs converge to the graphon NTK.
Convolutional Filtering on Sampled Manifolds
The increasing availability of geometric data has motivated the need for information processing over non-Euclidean domains modeled as manifolds.
A Spectral Analysis of Graph Neural Networks on Dense and Sparse Graphs
In this work we propose a random graph model that can produce graphs at different levels of sparsity.
Training Graph Neural Networks on Growing Stochastic Graphs
In this paper, we propose to learn GNNs on very large graphs by leveraging the limit object of a sequence of growing graphs, the graphon.
Convolutional Neural Networks on Manifolds: From Graphs and Back
Deep neural network architectures have been proved as a powerful technique to solve problems based on these data residing on the manifold.
Transferability Properties of Graph Neural Networks
In this paper, we study the problem of training GNNs on graphs of moderate size and transferring them to large-scale graphs.
Stability of Neural Networks on Manifolds to Relative Perturbations
Hence, in this paper, we analyze the stability properties of convolutional neural networks on manifolds to understand the stability of GNNs on large graphs.
Stable and Transferable Wireless Resource Allocation Policies via Manifold Neural Networks
We consider the problem of resource allocation in large scale wireless networks.
Iterative Decoding for Compositional Generalization in Transformers
Deep learning models generalize well to in-distribution data but struggle to generalize compositionally, i. e., to combine a set of learned primitives to solve more complex tasks.
Training Stable Graph Neural Networks Through Constrained Learning
Graph Neural Networks (GNN) rely on graph convolutions to learn features from network data.
Stability to Deformations of Manifold Filters and Manifold Neural Networks
The most important practical consequence of this analysis is to shed light on the behavior of graph filters and GNNs in large-scale graphs.
Learning by Transference: Training Graph Neural Networks on Growing Graphs
Graph neural networks (GNNs) use graph convolutions to exploit network invariances and learn meaningful feature representations from network data.
Stability of Neural Networks on Riemannian Manifolds
We further construct a manifold neural network architecture with these filters.
Nonlinear State-Space Generalizations of Graph Convolutional Neural Networks
In this work, we approach GCNNs from a state-space perspective revealing that the graph convolutional module is a minimalistic linear state-space model, in which the state update matrix is the graph shift operator.
Graph and graphon neural network stability
We then extend this analysis by interpreting the graphon neural network as a generating model for GNNs on deterministic and stochastic graphs instantiated from the original and perturbed graphons.
Graph-Adaptive Activation Functions for Graph Neural Networks
Activation functions are crucial in graph neural networks (GNNs) as they allow defining a nonlinear family of functions to capture the relationship between the input graph data and their representations.
Graph Neural Networks: Architectures, Stability and Transferability
They are presented here as generalizations of convolutional neural networks (CNNs) in which individual layers contain banks of graph convolutional filters instead of banks of classical convolutional filters.
Graphon Neural Networks and the Transferability of Graph Neural Networks
These graph convolutions combine information from adjacent nodes using coefficients that are shared across all nodes.
Graphon Signal Processing
Graphons are infinite-dimensional objects that represent the limit of convergent sequences of graphs as their number of nodes goes to infinity.
Graphon Pooling in Graph Neural Networks
In this work, we propose a new strategy for pooling and sampling on GNNs using graphons which preserves the spectral properties of the graph.
Gated Graph Recurrent Neural Networks
Graph processes exhibit a temporal structure determined by the sequence index and and a spatial structure determined by the graph support.
Invariance-Preserving Localized Activation Functions for Graph Neural Networks
Graph neural networks (GNNs) are information processing architectures tailored to these graph signals and made of stacked layers that compose graph convolutional filters with nonlinear activation functions.
Gated Graph Convolutional Recurrent Neural Networks
Graph processes model a number of important problems such as identifying the epicenter of an earthquake or predicting weather.
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Median activation functions for graph neural networks
Graph neural networks (GNNs) have been shown to replicate convolutional neural networks' (CNNs) superior performance in many problems involving graphs.
