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Given a small random sample of $n$-bit strings labeled by an unknown Boolean function, which properties of this function can be tested computationally efficiently? We show an equivalence between properties that are efficiently testable from…
We study property testing in the context of distributed computing, under the classical CONGEST model. It is known that testing whether a graph is triangle-free can be done in a constant number of rounds, where the constant depends on how…
The Gaussian graphical model is routinely employed to model the joint distribution of multiple random variables. The graph it induces is not only useful for describing the relationship between random variables but also critical for…
Algebraic geometry, although little explored in signal processing, provides tools that are very convenient for investigating generic properties in a wide range of applications. Generic properties are properties that hold "almost…
Robert Griffiths has recently addressed, within the framework of a 'consistent quantum theory' that he has developed, the issue of whether, as is often claimed, quantum mechanics entails a need for faster-than-light transfers of information…
\emph{Group Testing} (GT) addresses the problem of identifying a small subset of defective items from a large population, by grouping items into as few test pools as possible. In \emph{Adaptive GT} (AGT), outcomes of previous tests can…
For any integers $d,q\ge 3$, we consider the $q$-state ferromagnetic Potts model with an external field on a sequence of expander graphs that converges to the $d$-regular tree $\mathtt{T}_d$ in the Benjamini-Schramm sense. We show that…
We characterize the set of properties of Boolean-valued functions on a finite domain $\mathcal{X}$ that are testable with a constant number of samples. Specifically, we show that a property $\mathcal{P}$ is testable with a constant number…
In Graph Neural Networks (GNNs), hierarchical pooling operators generate local summaries of the data by coarsening the graph structure and the vertex features. While considerable attention has been devoted to analyzing the expressive power…
Context: This work is based on property-based testing (PBT). PBT is an increasingly important form of software testing. Furthermore, it serves as a concrete gateway into the abstract area of formal methods. Specifically, we focus on…
We examine the extent to which sublinear-sample property testing and estimation apply to settings where samples are independently but not identically distributed. Specifically, we consider the following distributional property testing…
A graph is probe diamond-free if its vertex set admits a partition into probes and nonprobes, where the set of nonprobes is independent, such that adding edges only between pairs of nonprobes yields a diamond-free graph. Although this class…
Federated Learning (FL) on graphs enables collaborative model training to enhance performance without compromising the privacy of each client. However, existing methods often overlook the mutable nature of graph data, which frequently…
Local certification is a topic originating from distributed computing, where a prover tries to convince the vertices of a graph $G$ that $G$ satisfies some property $\mathcal{P}$. To convince the vertices, the prover gives a small piece of…
We consider the multiple hypothesis testing (MHT) problem over the joint domain formed by a graph and a measure space. On each sample point of this joint domain, we assign a hypothesis test and a corresponding $p$-value. The goal is to make…
This work focuses on training graph foundation models (GFMs) that have strong generalization ability in graph-level tasks such as graph classification. Effective GFM training requires capturing information consistent across different…
We investigate the parameterized complexity of finding subgraphs with hereditary properties on graphs belonging to a hereditary graph class. Given a graph $G$, a non-trivial hereditary property $\Pi$ and an integer parameter $k$, the…
We discuss a graph-based approach for testing spatial point patterns. This approach falls under the category of data-random graphs, which have been introduced and used for statistical pattern recognition in recent years. Our goal is to test…
Graph Attention Networks (GATs) are designed to provide flexible neighborhood aggregation that assigns weights to neighbors according to their importance. In practice, however, GATs are often unable to switch off task-irrelevant…
We initiate the study of property testing in arbitrary planar graphs. We prove that bipartiteness can be tested in constant time, improving on the previous bound of $\tilde{O}(\sqrt{n})$ for graphs on $n$ vertices. The constant-time…