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The assumption of independence between observations (units) in a dataset is prevalent across various methodologies for learning causal graphical models. However, this assumption often finds itself in conflict with real-world data, posing…

In the ongoing quest for hybridizing discrete reasoning with neural nets, there is an increasing interest in neural architectures that can learn how to solve discrete reasoning or optimization problems from natural inputs. In this paper, we…

Existing studies have shown that Message-Passing Graph Neural Networks (MPNNs) are highly susceptible to adversarial attacks. In contrast, despite the increasing importance of Graph Transformers (GTs), their robustness properties are…

Extremal optimization is a new general-purpose method for approximating solutions to hard optimization problems. We study the method in detail by way of the NP-hard graph partitioning problem. We discuss the scaling behavior of extremal…

Graph neural networks (GNNs) have received massive attention in the field of machine learning on graphs. Inspired by the success of neural networks, a line of research has been conducted to train GNNs to deal with various tasks, such as…

We consider the robustness of computational hardness of problems whose input is obtained by applying independent random deletions to worst-case instances. For some classical $NP$-hard problems on graphs, such as Coloring, Vertex-Cover, and…

Inferring missing links or detecting spurious ones based on observed graphs, known as link prediction, is a long-standing challenge in graph data analysis. With the recent advances in deep learning, graph neural networks have been used for…

There are good arguments to support the claim that deep neural networks (DNNs) capture better feature representations than the previous hand-crafted feature engineering, which leads to a significant performance improvement. In this paper,…

Encoder-decoder architectures are prominent building blocks of state-of-the-art solutions for tasks across multiple fields where deep learning (DL) or foundation models play a key role. Although there is a growing community working on the…

We consider a generalization of the Hopfield model, where the entries of patterns are Gaussian and diluted. We focus on the high-storage regime and we investigate analytically the topological properties of the emergent network, as well as…

We consider a general linear program in standard form whose right-hand side constraint vector is subject to random perturbations. This defines a stochastic linear program for which, under general conditions, we characterize the fluctuations…

In this paper we propose a solution to the problem of parameter estimation of nonlinearly parameterized regressions--continuous or discrete time--and apply it for system identification and adaptive control. We restrict our attention to…

Differentially private algorithms allow large-scale data analytics while preserving user privacy. Designing such algorithms for graph data is gaining importance with the growth of large networks that model various (sensitive) relationships…

Despite their impressive performance, deep neural networks exhibit striking failures on out-of-distribution inputs. One core idea of adversarial example research is to reveal neural network errors under such distribution shifts. We…

We study the classical Node-Disjoint Paths (NDP) problem: given an $n$-vertex graph $G$ and a collection $M=\{(s_1,t_1),\ldots,(s_k,t_k)\}$ of pairs of vertices of $G$ called demand pairs, find a maximum-cardinality set of node-disjoint…

This work analyzes Graph Neural Networks, a generalization of Fully-Connected Deep Neural Nets on Graph structured data, when their width, that is the number of nodes in each fullyconnected layer is increasing to infinity. Infinite Width…

Neural networks have been very successful in many applications; we often, however, lack a theoretical understanding of what the neural networks are actually learning. This problem emerges when trying to generalise to new data sets. The…

Recent research shows that when Gradient Descent (GD) is applied to neural networks, the loss almost never decreases monotonically. Instead, the loss oscillates as gradient descent converges to its ''Edge of Stability'' (EoS). Here, we find…

Reconstructing the states of the nodes of a dynamical network is a problem of fundamental importance in the study of neuronal and genetic networks. An underlying related problem is that of observability, i.e., identifying the conditions…

Neural networks are known to be highly sensitive to adversarial examples. These may arise due to different factors, such as random initialization, or spurious correlations in the learning problem. To better understand these factors, we…