Related papers: Noise sensitivity of critical random graphs

Let G_n be a sequence of finite transitive graphs with vertex degree d=d(n) and |G_n|=n. Denote by p^t(v,v) the return probability after t steps of the non-backtracking random walk on G_n. We show that if p^t(v,v) has quasi-random…

Let $0 < \epsilon < 1/2$ be a noise parameter, and let $T_{\epsilon}$ be the noise operator acting on functions on the boolean cube $\{0,1\}^n$. Let $f$ be a nonnegative function on $\{0,1\}^n$. We upper bound the entropy of $T_{\epsilon}…

Machine learning classifiers have been demonstrated, both empirically and theoretically, to be robust to label noise under certain conditions -- notably the typical assumption is that label noise is independent of the features given the…

Network analysis is an important tool in understanding the behavior of complex systems of interacting entities. However, due to the limitations of data gathering technologies, some interactions might be missing from the network model. This…

Several recent works have shown that state-of-the-art classifiers are vulnerable to worst-case (i.e., adversarial) perturbations of the datapoints. On the other hand, it has been empirically observed that these same classifiers are…

Let $\mathcal{H}$ denote a collection of subsets of $\{1,2,\ldots,n\}$, and assign independent random variables uniformly distributed over $[0,1]$ to the $n$ elements. Declare an element $p$-present if its corresponding value is at most…

The time over threshold is a widely used quantity to describe signals from various detectors in particle physics. Its electronics implementation is straightforward and in this paper we present the studies of its behavior in the presence of…

In real-world applications, node features in graphs often contain noise from various sources, leading to significant performance degradation in GNNs. Although several methods have been developed to enhance robustness, they rely on the…

Recent research on the dynamics of certain fluid dynamical instabilities shows that when there is a slow invariant manifold subject to fast timescale instability the dynamics are extremely sensitive to noise. The behaviour of such systems…

We study the sensitivity to noise of |permanent(X)|^2 for random real and complex n x n Gaussian matrices X, and show that asymptotically the correlation between the noisy and noiseless outcomes tends to zero when the noise level is…

How can we find meaningful clusters in a graph robustly against noise edges? Graph clustering (i.e., dividing nodes into groups of similar ones) is a fundamental problem in graph analysis with applications in various fields. Recent studies…

We prove for an infinite array of globally coupled overdamped anharmonic oscillators subject to additive Gaussian white noise the existence of a well-behaved critical manifold in the parameter space which separates a symmetric phase from a…

The three-state majority-vote model with noise on Erdos-Renyi's random graphs has been studied. Using Monte Carlo simulations we obtain the phase diagram, along with the critical exponents. Exact results for limiting cases are presented,…

We consider a graph-structured change point problem in which we observe a random vector with piecewise constant but unknown mean and whose independent, sub-Gaussian coordinates correspond to the $n$ nodes of a fixed graph. We are interested…

We provide tight upper and lower bounds on the noise resilience of interactive communication over noisy channels with feedback. In this setting, we show that the maximal fraction of noise that any robust protocol can resist is 1/3.…

We consider the complete graph $\cK_n$ on $n$ vertices with exponential mean $n$ edge lengths. Writing $C_{ij}$ for the weight of the smallest-weight path between vertex $i,j\in [n]$, Janson showed that $\max_{i,j\in [n]} C_{ij}/\log{n}$…

Many real-world systems undergo abrupt changes in dynamics as they move across critical points, often with dramatic consequences. Much existing theory on identifying the time-series signatures of nearby critical points -- such as increased…

We study the susceptibility, i.e., the mean cluster size, in random graphs with given vertex degrees. We show, under weak assumptions, that the susceptibility converges to the expected cluster size in the corresponding branching process. In…

Graph neural networks based on message-passing mechanisms have achieved advanced results in graph classification tasks. However, their generalization performance degrades when noisy labels are present in the training data. Most existing…

We study the problem of estimating vector-valued variables from noisy "relative" measurements. This problem arises in several sensor network applications. The measurement model can be expressed in terms of a graph, whose nodes correspond to…