Related papers: Exponential Decay of Sensitivity in Graph-Structur…
A wide array of graphical models can be parametrised to have atomic probabilities represented by monomial functions. Such monomial structure has proven very useful when studying robustness under the assumption of a multilinear model where…
We investigate the vulnerabilities of consensus-based distributed optimization protocols to nodes that deviate from the prescribed update rule (e.g., due to failures or adversarial attacks). We first characterize certain fundamental…
Graph convolutional neural networks (GCNNs) are nonlinear processing tools to learn representations from network data. A key property of GCNNs is their stability to graph perturbations. Current analysis considers deterministic perturbations…
Effective resistances are ubiquitous in graph algorithms and network analysis. In this work, we study sublinear time algorithms to approximate the effective resistance of an adjacent pair $s$ and $t$. We consider the classical adjacency…
Graph neural networks (GNNs) have become increasingly popular for classification tasks on graph-structured data. Yet, the interplay between graph topology and feature evolution in GNNs is not well understood. In this paper, we focus on…
Graph Neural Networks (GNNs) have emerged as highly successful tools for graph-related tasks. However, real-world problems involve very large graphs, and the compute resources needed to fit GNNs to those problems grow rapidly. Moreover, the…
This paper shows that the implicit bias of gradient descent on linearly separable data is exactly characterized by the optimal solution of a dual optimization problem given by a smoothed margin, even for general losses. This is in contrast…
Termination analyses investigate the termination behavior of programs, intending to detect nontermination, which is known to cause a variety of program bugs (e.g. hanging programs, denial-of-service vulnerabilities). Beyond formal…
In this paper we study numerical approximations of the evolution problem for the nonlocal $p$-Laplacian with homogeneous Neumann boundary conditions. First, we derive a bound on the distance between two continuous-in-time trajectories…
Modern Natural Language Processing (NLP) models are known to be sensitive to input perturbations and their performance can decrease when applied to real-world, noisy data. However, it is still unclear why models are less robust to some…
We study how neural networks trained by gradient descent extrapolate, i.e., what they learn outside the support of the training distribution. Previous works report mixed empirical results when extrapolating with neural networks: while…
Message Passing Neural Networks (MPNNs) hold a key position in machine learning on graphs, but they struggle with unintended behaviors, such as over-smoothing and over-squashing, due to irregular data structures. The observation and…
A common theoretical approach to understanding neural networks is to take an infinite-width limit, at which point the outputs become Gaussian process (GP) distributed. This is known as a neural network Gaussian process (NNGP). However, the…
The accuracy of probability distributions inferred using machine-learning algorithms heavily depends on data availability and quality. In practical applications it is therefore fundamental to investigate the robustness of a statistical…
We consider the problem of learning a graph from a finite set of noisy graph signal observations, the goal of which is to find a smooth representation of the graph signal. Such a problem is motivated by the desire to infer relational…
We consider a nonlinear parabolic equation with an exponential nonlinearity which is critical with respect to the growth of the nonlinearity and the regularity of the initial data. After showing the equivalence of the notions of weak and…
Primal-dual methods for solving convex optimization problems with functional constraints often exhibit a distinct two-stage behavior. Initially, they converge towards a solution at a sublinear rate. Then, after a certain point, the method…
While promising, graph reasoners based on Large Language Models (LLMs) lack built-in invariance to symmetries in graph representations. Operating on sequential graph serializations, LLMs can produce different outputs under node reindexing,…
Large Language Models (LLMs) have demonstrated remarkable performance across various natural language processing tasks. Recently, several LLMs-based pipelines have been developed to enhance learning on graphs with text attributes,…
A quadratic approximation of neural network loss landscapes has been extensively used to study the optimization process of these networks. Though, it usually holds in a very small neighborhood of the minimum, it cannot explain many…