Related papers: Stability of Graph Scattering Transforms

This paper aims to provide a novel design of a multiscale framelet convolution for spectral graph neural networks (GNNs). While current spectral methods excel in various graph learning tasks, they often lack the flexibility to adapt to…

The classification of high-dimensional data defined on graphs is particularly difficult when the graph geometry is unknown. We introduce a Haar scattering transform on graphs, which computes invariant signal descriptors. It is implemented…

Despite their impressive performance, contemporary neural networks often lack structural safeguards that promote stable learning and interpretable behavior. In this work, we introduce a reformulation of layer-level transformations that…

Recently, transformer architectures for graphs emerged as an alternative to established techniques for machine learning with graphs, such as (message-passing) graph neural networks. So far, they have shown promising empirical results, e.g.,…

We argue that Transformers are essentially graph-to-graph models, with sequences just being a special case. Attention weights are functionally equivalent to graph edges. Our Graph-to-Graph Transformer architecture makes this ability…

Graph convolutional neural network provides good solutions for node classification and other tasks with non-Euclidean data. There are several graph convolutional models that attempt to develop deep networks but do not cause serious…

Graph neural networks (GNNs) are learning architectures that rely on knowledge of the graph structure to generate meaningful representations of large-scale network data. GNN stability is thus important as in real-world scenarios there are…

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,…

Over the last few years, we have witnessed the availability of an increasing data generated from non-Euclidean domains, which are usually represented as graphs with complex relationships, and Graph Neural Networks (GNN) have gained a high…

Mapping complex input data into suitable lower dimensional manifolds is a common procedure in machine learning. This step is beneficial mainly for two reasons: (1) it reduces the data dimensionality and (2) it provides a new data…

The scattering transform is a wavelet-based model of Convolutional Neural Networks originally introduced by S. Mallat. Mallat's analysis shows that this network has desirable stability and invariance guarantees and therefore helps explain…

Graph neural networks have shown significant success in the field of graph representation learning. Graph convolutions perform neighborhood aggregation and represent one of the most important graph operations. Nevertheless, one layer of…

We live in a world increasingly dominated by networks -- communications, social, information, biological etc. A central attribute of many of these networks is that they are dynamic, that is, they exhibit structural changes over time. While…

Convolutional neural networks (CNNs) have been shown to both extract more information than the traditional two-point statistics from cosmological fields, and marginalise over astrophysical effects extremely well. However, CNNs require large…

In this work, we present a generalization of extended persistent homology to filtrations of graded sub-groups by defining relative homology in this setting. Our work provides a more comprehensive and flexible approach to get an algebraic…

In reliable decision-making systems based on machine learning, models have to be robust to distributional shifts or provide the uncertainty of their predictions. In node-level problems of graph learning, distributional shifts can be…

Transformers have recently emerged as powerful neural networks for graph learning, showcasing state-of-the-art performance on several graph property prediction tasks. However, these results have been limited to small-scale graphs, where the…

In this paper, we present a novel convolution theorem which encompasses the well known convolution theorem in (graph) signal processing as well as the one related to time-varying filters. Specifically, we show how a node-wise convolution…

A powerful framework for studying graphs is to consider them as geometric graphs: nodes are randomly sampled from an underlying metric space, and any pair of nodes is connected if their distance is less than a specified neighborhood radius.…

This work introduces a wavelet neural network to learn a filter-bank specialized to fit non-stationary signals and improve interpretability and performance for digital signal processing. The network uses a wavelet transform as the first…