Related papers: Global and Local Uncertainty Principles for Signal…
Heisenberg's uncertainty principle, coherence and Bell nonlocality have been individually examined through many experiments. In this Letter, we systematically characterize all of this quantumness in a unified manner. We first construct…
The interdependence between nodes in graphs is key to improve class predictions on nodes and utilized in approaches like Label Propagation (LP) or in Graph Neural Networks (GNN). Nonetheless, uncertainty estimation for non-independent…
Graph transformation that predicts graph transition from one mode to another is an important and common problem. Despite much progress in developing advanced graph transformation techniques in recent years, the fundamental assumption…
Heisenberg's uncertainty principle has been understood to set a limitation on measurements; however, the long-standing mathematical formulation established by Heisenberg, Kennard, and Robertson does not allow such an interpretation.…
We consider statistical graph signal processing (GSP) in a generalized framework where each vertex of a graph is associated with an element from a Hilbert space. This general model encompasses various signals such as the traditional…
Graph neural networks (GNNs) emerge as a powerful family of representation learning models on graphs. To derive node representations, they utilize a global model that recursively aggregates information from the neighboring nodes. However,…
The goal of this paper is to review the main trends in the domain of uncertainty principles and localization, emphasize their mutual connections and investigate practical consequences. The discussion is strongly oriented towards, and…
While heterophily has been widely studied in node-level tasks, its impact on graph-level tasks remains unclear. We present the first analysis of heterophily in graph-level learning, combining theoretical insights with empirical validation.…
Heisenberg's uncertainty principle, which imposes intrinsic restrictions on our ability to predict the outcomes of incompatible quantum measurements to arbitrary precision, demonstrates one of the key differences between classical and…
This paper proposes a unified framework to quantify local and global inferential uncertainty for high dimensional nonparanormal graphical models. In particular, we consider the problems of testing the presence of a single edge and…
In this article, we derive Stein's method for approximating a spatial random graph by a generalised random geometric graph, which has vertices given by a finite Gibbs point process and edges based on a general connection function. Our main…
The majority of popular graph kernels is based on the concept of Haussler's $\mathcal{R}$-convolution kernel and defines graph similarities in terms of mutual substructures. In this work, we enrich these similarity measures by considering…
As irregularly structured data representations, graphs have received a large amount of attention in recent years and have been widely applied to various real-world scenarios such as social, traffic, and energy settings. Compared to…
Local convergence has emerged as a fundamental tool for analyzing sparse random graph models. We introduce a new notion of local convergence, color convergence, based on the Weisfeiler-Leman algorithm. Color convergence fully characterizes…
Heisenberg's uncertainty principle is formulated for a set of generalized measurements within the framework of majorization theory, resulting in a partial uncertainty order on probability vectors that is stronger than those based on…
Recent advancements in Large Language Models (LLMs) have significantly improved text generation capabilities, but these systems are still known to hallucinate, and granular uncertainty estimation for long-form LLM generations remains…
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…
Existence of minimal length is suggested in any quantum theory of gravity such as string theory, double special relativity and black hole physics. One way to impose minimal length is deforming Heisenberg algebra in phase space which is…
A recent paper, ``A Graphon-Signal Analysis of Graph Neural Networks'', by Levie, analyzed message passing graph neural networks (MPNNs) by embedding the input space of MPNNs, i.e., attributed graphs (graph-signals), to a space of…
For many random graph models, the analysis of a related birth process suggests local sampling algorithms for the size of, e.g., the giant connected component, the $k$-core, the size and probability of an epidemic outbreak, etc. In this…