Related papers: Property Testing of Computational Networks

The primary problem in property testing is to decide whether a given function satisfies a certain property, or is far from any function satisfying it. This crucially requires a notion of distance between functions. The most prevalent notion…

Network data is a major object data type that has been widely collected or derived from common sources such as brain imaging. Such data contains numeric, topological, and geometrical information, and may be necessarily considered in certain…

Pruning the weights of randomly initialized neural networks plays an important role in the context of lottery ticket hypothesis. Ramanujan et al. (2020) empirically showed that only pruning the weights can achieve remarkable performance…

Deep neural networks, particularly those employing Rectified Linear Units (ReLU), are often perceived as complex, high-dimensional, non-linear systems. This complexity poses a significant challenge to understanding their internal learning…

Complex functional brain networks are large networks of brain regions and functional brain connections. Statistical characterizations of these networks aim to quantify global and local properties of brain activity with a small number of…

Approximation and learning of classifiers of large data sets by neural networks in terms of high-dimensional geometry and statistical learning theory are investigated. The influence of the VC dimension of sets of input-output functions of…

In this paper, we consider a problem in which distributively extracted features are used for performing inference in wireless networks. We elaborate on our proposed architecture, which we herein refer to as "in-network learning", provide a…

We introduce a probability distribution, combined with an efficient sampling algorithm, for weights and biases of fully-connected neural networks. In a supervised learning context, no iterative optimization or gradient computations of…

A general Bayesian framework for model selection on random network models regarding their features is considered. The goal is to develop a principle Bayesian model selection approach to compare different fittable, not necessarily nested,…

We investigate the expressive power of depth-2 bandlimited random neural networks. A random net is a neural network where the hidden layer parameters are frozen with random assignment, and only the output layer parameters are trained by…

Accurately analyzing graph properties of social networks is a challenging task because of access limitations to the graph data. To address this challenge, several algorithms to obtain unbiased estimates of properties from few samples via a…

While it is well-known that neural networks enjoy excellent approximation capabilities, it remains a big challenge to compute such approximations from point samples. Based on tools from Information-based complexity, recent work by Grohs and…

Deep Neural Networks (DNNs) have emerged as a powerful mechanism and are being increasingly deployed in real-world safety-critical domains. Despite the widespread success, their complex architecture makes proving any formal guarantees about…

Characterizing quantum nonlocality in networks is a challenging, but important problem. Using quantum sources one can achieve distributions which are unattainable classically. A key point in investigations is to decide whether an observed…

Recently, deep learning has been widely applied in functional data analysis (FDA) with notable empirical success. However, the infinite dimensionality of functional data necessitates an effective dimension reduction approach for functional…

A distance estimator for a graph property $\mathcal{P}$ is an algorithm that given $G$ and $\alpha, \varepsilon >0$ distinguishes between the case that $G$ is $(\alpha-\varepsilon)$-close to $\mathcal{P}$ and the case that $G$ is…

While deep learning is successful in a number of applications, it is not yet well understood theoretically. A satisfactory theoretical characterization of deep learning however, is beginning to emerge. It covers the following questions: 1)…

Scale-free networks play a fundamental role in the study of complex networks and various applied fields due to their ability to model a wide range of real-world systems. A key characteristic of these networks is their degree distribution,…

We study the relative-error property testing model for Boolean functions that was recently introduced in the work of Chen et al. (SODA 2025). In relative-error testing, the testing algorithm gets uniform random satisfying assignments as…

Neural networks often operate in the overparameterized regime, in which there are far more parameters than training samples, allowing the training data to be fit perfectly. That is, training the network effectively learns an interpolating…