相关论文: Decreasing verification radius in local certificat…

Certified defenses promise provable robustness guarantees. We study the malicious exploitation of probabilistic certification frameworks to better understand the limits of guarantee provisions. Now, the objective is to not only mislead a…

A proper vertex-colouring of a graph G is said to be locally identifying if for any pair u,v of adjacent vertices with distinct closed neighbourhoods, the sets of colours in the closed neighbourhoods of u and v are different. We show that…

Barrier certificates play an important role in verifying the safety of continuous-time systems, including autonomous driving, robotic manipulators and other critical applications. Recently, ReLU neural barrier certificates -- barrier…

A local algorithm is a distributed algorithm where each node must operate solely based on the information that was available at system startup within a constant-size neighbourhood of the node. We study the applicability of local algorithms…

Local search is a powerful heuristic in optimization and computer science, the complexity of which has been studied in the white box and black box models. In the black box model, we are given a graph $G = (V,E)$ and oracle access to a…

An undirected graph consists of a set of vertices and a set of undirected edges between vertices. Such a graph may contain an abundant number of cycles, then a feedback vertex set (FVS) is a set of vertices intersecting with each of these…

Deep neural networks are increasingly being used as controllers for safety-critical systems. Because neural networks are opaque, certifying their correctness is a significant challenge. To address this issue, several neural network…

We investigate the statistical properties of cut sizes generated by heuristic algorithms which solve approximately the graph bisection problem. On an ensemble of sparse random graphs, we find empirically that the distribution of the cut…

We analyze the query complexity of finding a local minimum in $t$ rounds on general graphs. More precisely, given a graph $G = (V,E)$ and oracle access to an unknown function $f : V \to \mathbb{R}$, the goal is to find a local minimum--a…

Despite the exploding interest in graph neural networks there has been little effort to verify and improve their robustness. This is even more alarming given recent findings showing that they are extremely vulnerable to adversarial attacks…

In this work we introduce the graph-theoretic notion of mendability: for each locally checkable graph problem we can define its mending radius, which captures the idea of how far one needs to modify a partial solution in order to "patch a…

As state-of-the-art neural networks are deployed on reasoning and algorithmic tasks, exactness guarantees become increasingly important. However, high average-case accuracy can still mask inconsistent behaviors. This motivates exact…

The problem of finding code distance has been long studied for the generic ensembles of linear codes and led to several algorithms that substantially reduce exponential complexity of this task. However, no asymptotic complexity bounds are…

Formal verification techniques are widely used for detecting design flaws in software systems. Formal verification can be done by transforming an already implemented source code to a formal model and attempting to prove certain properties…

The graph edit distance is used for comparing graphs in various domains. Due to its high computational complexity it is primarily approximated. Widely-used heuristics search for an optimal assignment of vertices based on the distance…

In tasks like node classification, image segmentation, and named-entity recognition we have a classifier that simultaneously outputs multiple predictions (a vector of labels) based on a single input, i.e. a single graph, image, or document…

In this work we study local computation with advice: the goal is to solve a graph problem $\Pi$ with a distributed algorithm in $T(\Delta)$ communication rounds, for some function $T$ that only depends on the maximum degree $\Delta$ of the…

Characterizing increasingly complex quantum systems is a central task in quantum information science, yet experimental costs often scale prohibitively with system size. Certifying key properties using simple local measurements is highly…

Consider a distributed coding for computing problem with constant decoding locality, i.e., with a vanishing error probability, any single sample of the function can be approximately recovered by probing only constant number of compressed…

This paper is concerned with the local reducibility properties of linear realizations of codes on finite graphs. Trimness and properness are dual properties of constraint codes. A linear realization is locally reducible if any constraint…