Related papers: Data efficiency in graph networks through equivari…

Recent advances in Graph Neural Networks (GNNs) have explored the potential of random noise as an input feature to enhance expressivity across diverse tasks. However, naively incorporating noise can degrade performance, while architectures…

Equivariance w.r.t. geometric transformations in neural networks improves data efficiency, parameter efficiency and robustness to out-of-domain perspective shifts. When equivariance is not designed into a neural network, the network can…

To improve our understanding of connected systems, different tools derived from statistics, signal processing, information theory and statistical physics have been developed in the last decade. Here, we will focus on the graph comparison…

We address the efficiency issue for the construction of a deep graph neural network (GNN). The approach exploits the idea of representing each input graph as a fixed point of a dynamical system (implemented through a recurrent neural…

We investigate the optimization of neural networks on symmetric data, and compare the strategy of constraining the architecture to be equivariant to that of using data augmentation. Our analysis reveals that that the relative geometry of…

Equivariant networks are specifically designed to ensure consistent behavior with respect to a set of input transformations, leading to higher sample efficiency and more accurate and robust predictions. However, redesigning each component…

Graph embedding aims to transfer a graph into vectors to facilitate subsequent graph analytics tasks like link prediction and graph clustering. Most approaches on graph embedding focus on preserving the graph structure or minimizing the…

Structural network embedding is a crucial step in enabling effective downstream tasks for complex systems that aims to project a network into a lower-dimensional space while preserving similarities among nodes. We introduce a simple and…

We present a novel framework to overcome the limitations of equivariant architectures in learning functions with group symmetries. In contrary to equivariant architectures, we use an arbitrary base model such as an MLP or a transformer and…

Many successful deep learning architectures are equivariant to certain transformations in order to conserve parameters and improve generalization: most famously, convolution layers are equivariant to shifts of the input. This approach only…

In graph signal processing, data samples are associated to vertices on a graph, while edge weights represent similarities between those samples. We propose a convex optimization problem to learn sparse well connected graphs from data. We…

Equivariant machine learning is an approach for designing deep learning models that respect the symmetries of the problem, with the aim of reducing model complexity and improving generalization. In this paper, we focus on an extension of…

Recent research has shown that incorporating equivariance into neural network architectures is very helpful, and there have been some works investigating the equivariance of networks under group actions. However, as digital images and…

We consider the problem of embedding the nodes of a hypergraph into Euclidean space under the assumption that the interactions arose through closeness to unknown hyperedge centres. In this way, we tackle the inverse problem associated with…

Recent advances in neural networks have solved common graph problems such as link prediction, node classification, node clustering, node recommendation by developing embeddings of entities and relations into vector spaces. Graph embeddings…

Many scientific problems require to process data in the form of geometric graphs. Unlike generic graph data, geometric graphs exhibit symmetries of translations, rotations, and/or reflections. Researchers have leveraged such inductive bias…

Many machine learning tasks involve learning functions that are known to be invariant or equivariant to certain symmetries of the input data. However, it is often challenging to design neural network architectures that respect these…

The set of functions parameterized by a linear fully-connected neural network is a determinantal variety. We investigate the subvariety of functions that are equivariant or invariant under the action of a permutation group. Examples of such…

Machine learning frameworks such as graph neural networks typically rely on a given, fixed graph to exploit relational inductive biases and thus effectively learn from network data. However, when said graphs are (partially) unobserved,…

Message-passing has proved to be an effective way to design graph neural networks, as it is able to leverage both permutation equivariance and an inductive bias towards learning local structures in order to achieve good generalization.…