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Neural network parameterizations exhibit inherent symmetries that yield multiple equivalent minima within the loss landscape. Scale Graph Metanetworks (ScaleGMNs) explicitly leverage these symmetries by proposing an architecture equivariant…

Graph Neural Networks (GNNs) are the subject of intense focus by the machine learning community for problems involving relational reasoning. GNNs can be broadly divided into spatial and spectral approaches. Spatial approaches use a form of…

Graph convolutional networks (GCNs) and its variants are designed for unsigned graphs containing only positive links. Many existing GCNs have been derived from the spectral domain analysis of signals lying over (unsigned) graphs and in each…

We present the Topology Transformation Equivariant Representation learning, a general paradigm of self-supervised learning for node representations of graph data to enable the wide applicability of Graph Convolutional Neural Networks…

Recent advances in Graph Convolutional Neural Networks (GCNNs) have shown their efficiency for non-Euclidean data on graphs, which often require a large amount of labeled data with high cost. It it thus critical to learn graph feature…

Graph neural networks (GNN) have shown great advantages in many graph-based learning tasks but often fail to predict accurately for a task-based on sets of nodes such as link/motif prediction and so on. Many works have recently proposed to…

Many applications in traffic, civil engineering, or electrical engineering revolve around edge-level signals. Such signals can be categorized as inherently directed, for example, the water flow in a pipe network, and undirected, like the…

We present enumeration results on the number of connected graphs up to 10 vertices for which there is at least one other graph with the same spectrum (a cospectral mate), or at least one other graph with the same Smith normal form…

We address the problem of identifying a graph structure from the observation of signals defined on its nodes. Fundamentally, the unknown graph encodes direct relationships between signal elements, which we aim to recover from observable…

The structural properties of graphs are usually characterized in terms of invariants, which are functions of graphs that do not depend on the labeling of the nodes. In this paper we study convex graph invariants, which are graph invariants…

In this study, we investigate whether the representations learned by neural networks possess a privileged and convergent basis. Specifically, we examine the significance of feature directions represented by individual neurons. First, we…

Alignment between non-rigid stretchable structures is one of the most challenging tasks in computer vision, as the invariant properties are hard to define, and there is no labeled data for real datasets. We present unsupervised neural…

Effectively predicting molecular interactions has the potential to accelerate molecular dynamics by multiple orders of magnitude and thus revolutionize chemical simulations. Graph neural networks (GNNs) have recently shown great successes…

Graph representation learning has recently been applied to a broad spectrum of problems ranging from computer graphics and chemistry to high energy physics and social media. The popularity of graph neural networks has sparked interest, both…

Graph Transformers have emerged as a powerful alternative to Message-Passing Graph Neural Networks (MP-GNNs) to address limitations such as over-squashing of information exchange. However, incorporating graph inductive bias into transformer…

Graph machine learning architectures are typically tailored to specific tasks on specific datasets, which hinders their broader applicability. This has led to a new quest in graph machine learning: how to build graph foundation models…

Invariant learning demonstrates substantial potential for enhancing the generalization of graph neural networks (GNNs) with out-of-distribution (OOD) data. It aims to recognize stable features in graph data for classification, based on the…

Spectral graph convolutional networks are generalizations of standard convolutional networks for graph-structured data using the Laplacian operator. A common misconception is the instability of spectral filters, i.e. the impossibility to…

Message-passing neural networks (MPNNs) are the leading architecture for deep learning on graph-structured data, in large part due to their simplicity and scalability. Unfortunately, it was shown that these architectures are limited in…

Graph alignment, the problem of identifying corresponding nodes across multiple graphs, is fundamental to numerous applications. Most existing unsupervised methods embed node features into latent representations to enable cross-graph…