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Directed acyclic graphs are a fundamental class of networks that includes citation networks, food webs, and family trees, among others. Here we define a random graph model for directed acyclic graphs and give solutions for a number of the…
We study the approximation of functions which are invariant with respect to certain permutations of the input indices using flow maps of dynamical systems. Such invariant functions includes the much studied translation-invariant ones…
Precise knowledge of causal directed acyclic graphs (DAGs) is assumed for standard approaches towards valid adjustment set selection for unbiased estimation, but in practice, the DAG is often inferred from data or expert knowledge,…
Graph Neural Networks (GNNs) have made significant advances on several fundamental inference tasks. As a result, there is a surge of interest in using these models for making potentially important decisions in high-regret applications.…
Directed acyclic graphs (DAGs) can be characterised as directed graphs whose strongly connected components are isolated vertices. Using this restriction on the strong components, we discover that when $m = cn$, where $m$ is the number of…
Mechanics-related problems often present unique challenges in achieving accurate geometric and physical representations, particularly for non-uniform structures. Graph neural networks (GNNs) have emerged as a promising tool to tackle these…
We theoretically discuss why deep neural networks (DNNs) performs better than other models in some cases by investigating statistical properties of DNNs for non-smooth functions. While DNNs have empirically shown higher performance than…
Graph neural networks (GNNs) are the predominant approach for graph-based machine learning. While neural networks have shown great performance at learning useful representations, they are often criticized for their limited high-level…
The geometry of a graph is encoded in dynamical processes on the graph. Many graph neural network (GNN) architectures are inspired by such dynamical systems, typically based on the graph Laplacian. Here, we introduce Dirac--Bianconi GNNs…
Graphs play an important role in many applications. Recently, Graph Neural Networks (GNNs) have achieved promising results in graph analysis tasks. Some state-of-the-art GNN models have been proposed, e.g., Graph Convolutional Networks…
Not only are Deep Neural Networks (DNNs) black box models, but also we frequently conceptualize them as such. We lack good interpretations of the mechanisms linking inputs to outputs. Therefore, we find it difficult to analyze in…
This work addresses the problem of learning directed acyclic graphs (DAGs) from nodal observations generated by a linear structural equation model. DAG learning is a central task in signal processing, machine learning, and causal inference,…
Directed acyclic graphs (DAGs) serve as crucial data representations in domains such as hardware synthesis and compiler/program optimization for computing systems. DAG generative models facilitate the creation of synthetic DAGs, which can…
Assuming a directed acyclic graph (DAG) that represents prior knowledge of causal relationships between variables is a common starting point for cause-effect estimation. Existing literature typically invokes hypothetical domain expert…
A fundamental challenge in understanding graph neural networks (GNNs) lies in characterizing their optimization dynamics and loss landscape geometry, critical for improving interpretability and robustness. While mode connectivity, a lens…
Graph neural networks (GNNs) have been shown to replicate convolutional neural networks' (CNNs) superior performance in many problems involving graphs. By replacing regular convolutions with linear shift-invariant graph filters (LSI-GFs),…
Graph neural networks (GNNs) have emerged as a fundamental tool for learning from graph-structured data, achieving strong performance across a wide range of applications. However, understanding their generalization capabilities remains…
We present a systematic comparison between neural network (NN) architectures for inference of AC-OPF solutions. Using fully connected NNs as a baseline we demonstrate the efficacy of leveraging network topology in the models by constructing…
Graph neural networks (GNNs) are naturally distributed architectures for learning representations from network data. This renders them suitable candidates for decentralized tasks. In these scenarios, the underlying graph often changes with…
Graph neural networks (GNN) are very popular methods in machine learning and have been applied very successfully to the prediction of the properties of molecules and materials. First-order GNNs are well known to be incomplete, i.e., there…