Related papers: Simplicial Neural Networks
Graph neural networks (GNNs) are powerful graph-based deep-learning models that have gained significant attention and demonstrated remarkable performance in various domains, including natural language processing, drug discovery, and…
It is increasingly common for data to possess intricate structure, necessitating new models and analytical tools. Graphs, a prominent type of structure, can encode the relationships between any two entities (nodes). However, graphs neither…
Graph neural networks (GNNs) have recently grown in popularity in the field of artificial intelligence (AI) due to their unique ability to ingest relatively unstructured data types as input data. Although some elements of the GNN…
Topological neural networks (TNNs) are information processing architectures that model representations from data lying over topological spaces (e.g., simplicial or cell complexes) and allow for decentralized implementation through localized…
Graph Convolutional Neural Networks (GCNNs) are generalizations of CNNs to graph-structured data, in which convolution is guided by the graph topology. In many cases where graphs are unavailable, existing methods manually construct graphs…
Graph Neural Networks (GNNs) extend convolutional neural networks to operate on graphs. Despite their impressive performances in various graph learning tasks, the theoretical understanding of their generalization capability is still…
Neural networks are fundamental tools of modern machine learning. The standard paradigm assumes binary interactions (across feedforward linear passes) between inter-tangled units, organized in sequential layers. Generalized architectures…
Graph learning is currently dominated by graph kernels, which, while powerful, suffer some significant limitations. Convolutional Neural Networks (CNNs) offer a very appealing alternative, but processing graphs with CNNs is not trivial. To…
Tensor networks (TNs) and neural networks (NNs) are two fundamental data modeling approaches. TNs were introduced to solve the curse of dimensionality in large-scale tensors by converting an exponential number of dimensions to polynomial…
Two architectures that generalize convolutional neural networks (CNNs) for the processing of signals supported on graphs are introduced. We start with the selection graph neural network (GNN), which replaces linear time invariant filters…
A Sheaf Neural Network (SNN) is a type of Graph Neural Network (GNN) that operates on a sheaf, an object that equips a graph with vector spaces over its nodes and edges and linear maps between these spaces. SNNs have been shown to have…
Geometric deep learning extends deep learning to incorporate information about the geometry and topology data, especially in complex domains like graphs. Despite the popularity of message passing in this field, it has limitations such as…
Graph Neural Networks (GNN) have emerged as a popular and standard approach for learning from graph-structured data. The literature on GNN highlights the potential of this evolving research area and its widespread adoption in real-life…
Classical graph algorithms work well for combinatorial problems that can be thoroughly formalized and abstracted. Once the algorithm is derived, it generalizes to instances of any size. However, developing an algorithm that handles complex…
We explore the use of graph neural networks (GNNs) to model spatial processes in which there is no a priori graphical structure. Similar to finite element analysis, we assign nodes of a GNN to spatial locations and use a computational…
Graph data often contain noisy and spurious correlations that mask the true causal relationships, which are essential for enabling graph models to make predictions based on the underlying causal structure of the data. Dependence on spurious…
Graphs are naturally used to describe the structures of various real-world systems in biology, society, computer science etc., where subgraphs or motifs as basic blocks play an important role in function expression and information…
We introduce Group equivariant Convolutional Neural Networks (G-CNNs), a natural generalization of convolutional neural networks that reduces sample complexity by exploiting symmetries. G-CNNs use G-convolutions, a new type of layer that…
Graph neural networks (GNNs) rely on graph convolutions to extract local features from network data. These graph convolutions combine information from adjacent nodes using coefficients that are shared across all nodes. Since these…
We generalize the scattering transform to graphs and consequently construct a convolutional neural network on graphs. We show that under certain conditions, any feature generated by such a network is approximately invariant to permutations…