Related papers: Sign and Basis Invariant Networks for Spectral Gra…
Spectral embedding is a powerful graph embedding technique that has received a lot of attention recently due to its effectiveness on Graph Transformers. However, from a theoretical perspective, the universal expressive power of spectral…
We present a simple proof for the universality of invariant and equivariant tensorized graph neural networks. Our approach considers a restricted intermediate hypothetical model named Graph Homomorphism Model to reach the universality…
Given a signed social graph, how can we learn appropriate node representations to infer the signs of missing edges? Signed social graphs have received considerable attention to model trust relationships. Learning node representations is…
In certain situations, neural networks are trained upon data that obey underlying symmetries. However, the predictions do not respect the symmetries exactly unless embedded in the network structure. In this work, we introduce architectures…
We introduce a set of novel multiscale basis transforms for signals on graphs that utilize their "dual" domains by incorporating the "natural" distances between graph Laplacian eigenvectors, rather than simply using the eigenvalue ordering.…
Exploiting symmetries and invariance in data is a powerful, yet not fully exploited, way to achieve better generalisation with more efficiency. In this paper, we introduce two graph network architectures that are equivariant to several…
Graph Representation Learning (GRL) has become essential for modern graph data mining and learning tasks. GRL aims to capture the graph's structural information and exploit it in combination with node and edge attributes to compute…
Training a Convolutional Neural Network (CNN) to be robust against rotation has mostly been done with data augmentation. In this paper, another progressive vision of research direction is highlighted to encourage less dependence on data…
We propose a learning paradigm for numerical approximation of differential invariants of planar curves. Deep neural-networks' (DNNs) universal approximation properties are utilized to estimate geometric measures. The proposed framework is…
The spectra of signed matrices have played a fundamental role in social sciences, graph theory, and control theory. In this work, we investigate the computational problems of identifying symmetric signings of matrices with natural spectral…
We propose a generalization of transformer neural network architecture for arbitrary graphs. The original transformer was designed for Natural Language Processing (NLP), which operates on fully connected graphs representing all connections…
Equivariant neural networks provide a principled framework for incorporating symmetry into learning architectures and have been extensively analyzed through the lens of their separation power, that is, the ability to distinguish inputs…
Most existing neural networks for learning graphs address permutation invariance by conceiving of the network as a message passing scheme, where each node sums the feature vectors coming from its neighbors. We argue that this imposes a…
This paper proposes a family of permutation-invariant graph embeddings, generalizing the Skew Spectrum of graphs of Kondor & Borgwardt (2008). Grounded in group theory and harmonic analysis, our method introduces a new class of graph…
We propose a novel approach for visual representation learning called Signature-Graph Neural Networks (SGN). SGN learns latent global structures that augment the feature representation of Convolutional Neural Networks (CNN). SGN constructs…
Message-passing neural networks (MPNNs) are a powerful framework for learning representations of graph-structured domains. However, weights in MPNNs act on features only, limiting their ability to capture structural patterns. We introduce a…
Graph Neural Networks (GNNs) have advanced relational data analysis but lack invariance learning techniques common in image classification. In node classification with GNNs, it is actually the ego-graph of the center node that is…
This paper introduces a new model to learn graph neural networks equivariant to rotations, translations, reflections and permutations called E(n)-Equivariant Graph Neural Networks (EGNNs). In contrast with existing methods, our work does…
A large body of work has investigated the properties of graph neural networks and identified several limitations, particularly pertaining to their expressive power. Their inability to count certain patterns (e.g., cycles) in a graph lies at…
Recent successes in word embedding and document embedding have motivated researchers to explore similar representations for networks and to use such representations for tasks such as edge prediction, node label prediction, and community…