Related papers: A Noise Sensitivity Theorem for Schreier Graphs

Connected networks are a fundamental structure of neurobiology. Understanding these networks will help us elucidate the neural mechanisms of computation. Mathematically speaking these networks are `graphs' - structures containing objects…

The notion of local weak convergence, or Benjamini--Schramm convergence, was introduced by Benjamini and Schramm. The local weak limit of sparse Erd\H os--R\'enyi graphs is the Galton--Watson measure with Poisson offspring almost surely.…

We introduce and study the planted directed polymer, in which the path of a random walker is inferred from noisy 'images' accumulated at each timestep. Formulated as a nonlinear problem of Bayesian inference for a hidden Markov model, this…

Traditionally, statistical and causal inference on human subjects rely on the assumption that individuals are independently affected by treatments or exposures. However, recently there has been increasing interest in settings, such as…

Efficient and robust online processing technique of irregularly structured data is crucial in the current era of data abundance. In this paper, we propose a graph/network version of the classical adaptive Sign algorithm for online graph…

Graph neural networks (GNNs) are an emerging model for learning graph embeddings and making predictions on graph structured data. However, robustness of graph neural networks is not yet well-understood. In this work, we focus on node…

Recently the study of noise sensitivity and noise stability of Boolean functions has received considerable attention. The purpose of this paper is to extend these notions in a natural way to a different class of perturbations, namely those…

We consider classification in the presence of class-dependent asymmetric label noise with unknown noise probabilities. In this setting, identifiability conditions are known, but additional assumptions were shown to be required for finite…

Deducing the structure of neural circuits is one of the central problems of modern neuroscience. Recently-introduced calcium fluorescent imaging methods permit experimentalists to observe network activity in large populations of neurons,…

In today's world, modern infrastructures are being equipped with information and communication technologies to create large IoT networks. It is essential to monitor these networks to ensure smooth operations by detecting and correcting link…

In this paper we study networks of nodes characterised by binary traits that change both endogenously and through nearest-neighbour interaction. Our analytical results show that those traits can be ranked according to the noisiness of their…

We consider the model of random interlacements on transient graphs, which was first introduced by Sznitman [Ann. of Math. (2) (2010) 171 2039-2087] for the special case of ${\mathbb{Z}}^d$ (with $d\geq3$). In Sznitman [Ann. of Math. (2)…

To a subshift over a finite alphabet, one can naturally associate an infinite family of finite graphs, called its Rauzy graphs. We show that for a subshift of subexponential complexity the Rauzy graphs converge to the line $\mathbf{Z}$ in…

Background: Imagine a paper with n nodes on it where each pair undergoes a coin toss experiment; if heads we connect the pair with an undirected link, while tails maintain the disconnection. This procedure yields a random graph. Now…

We study continuous time Markov processes on graphs. The notion of frequency is introduced, which serves well as a scaling factor between any Markov time of a continuous time Markov process and that of its jump chain. As an application, we…

Graph embedding has recently gained momentum in the research community, in particular after the introduction of random walk and neural network based approaches. However, most of the embedding approaches focus on representing the local…

A first step is taken towards understanding often observed non-robustness phenomena of deep neural net (DNN) classifiers. This is done from the perspective of Boolean functions by asking if certain sequences of Boolean functions represented…

Graph attention networks (GATs) are widely used and often appear robust to noise in node covariates and edges, yet rigorous statistical guarantees demonstrating a provable advantage of GATs over non-attention graph neural networks~(GNNs)…

The chain graph model admits both undirected and directed edges in one graph, where symmetric conditional dependencies are encoded via undirected edges and asymmetric causal relations are encoded via directed edges. Though frequently…

We investigate how the graph topology influences the robustness to noise in undirected linear consensus networks. We measure the structural robustness by using the smallest possible value of steady state population variance of states under…