Related papers: On the resolution of the sensitivity conjecture

Since the seminal paper by Tversky and Kahneman, the conjunction fallacy has been the subject of multiple debates and become a fundamental challenge for cognitive theories in decision-making. In this article, we take a rather uncommon…

Decision circuits have been developed to perform efficient evaluation of influence diagrams [Bhattacharjya and Shachter, 2007], building on the advances in arithmetic circuits for belief network inference [Darwiche,2003]. In the process of…

Analyzing how human beings resolve syntactic ambiguity has long been an issue of interest in the field of linguistics. It is, at the same time, one of the most challenging issues for spoken language understanding (SLU) systems as well. As…

In this paper we obtain the average sensitivity of the laced Boolean functions. This confirms a conjecture of Shparlinski. We also compute the weights of the laced Boolean functions and show that they are almost balanced.

Neural networks with ReLU activation play a key role in modern machine learning. Understanding the functions represented by ReLU networks is a major topic in current research as this enables a better interpretability of learning processes.…

Error detectable and error correctable coding in Hamming space was researched to discover possible fault tolerant coding constellations, which can implement Boolean logic with fault tolerant property. Basic logic operators of the Boolean…

A sensitivity analysis in an observational study assesses the robustness of significant findings to unmeasured confounding. While sensitivity analyses in matched observational studies have been well addressed when there is a single outcome…

Query evaluation over probabilistic databases is known to be intractable in many cases, even in data complexity, i.e., when the query is fixed. Although some restrictions of the queries [19] and instances [4] have been proposed to lower the…

We live in a world full of complex systems which we need to improve our understanding of. To accomplish this, purely probabilistic investigations are often not enough. They are only the first step and must be followed by learning the…

Neural networks demonstrate inherent vulnerability to small, non-random perturbations, emerging as adversarial attacks. Such attacks, born from the gradient of the loss function relative to the input, are discerned as input conjugates,…

With fast developments in computational power and algorithms, deep learning has made breakthroughs and been applied in many fields. However, generalization remains to be a critical challenge, and the limited generalization capability…

Uncertainty quantification is at the core of the reliability and robustness of machine learning. In this paper, we provide a theoretical framework to dissect the uncertainty, especially the \textit{epistemic} component, in deep learning…

This paper addresses the controversy between Mayers, Lo and Chau on one side, and Yuen on the opposite side, on whether there exist or not unconditionally secure protocols. For such purpose, a complete classification of all possible bit…

The usual figure of merit characterizing the performance of neural networks applied to problems in the quantum domain is their accuracy, being the probability of a correct answer on a previously unseen input. Here we append this parameter…

Sensitivity analysis measures the influence of a Bayesian network's parameters on a quantity of interest defined by the network, such as the probability of a variable taking a specific value. Various sensitivity measures have been defined…

There exist many methods for sensitivity analysis readily available to the practitioner. While each seeks to help the modeler answer the same general question -- How do sources of uncertainty or changes in the model inputs relate to…

We establish a precise relationship between spherical harmonics and Fourier basis functions over a hypercube randomly embedded in the sphere. In particular, we give a bound on the expected Boolean noise sensitivity of a randomly rotated…

In decision-making problems under uncertainty, probabilistic constraints are a valuable tool to express safety of decisions. They result from taking the probability measure of a given set of random inequalities depending on the decision…

The adaptation and use of Machine Learning (ML) in our daily lives has led to concerns in lack of transparency, privacy, reliability, among others. As a result, we are seeing research in niche areas such as interpretability, causality, bias…

Most real world applications require dealing with stochasticity like sensor noise or predictive uncertainty, where formal specifications of desired behavior are inherently probabilistic. Despite the promise of formal verification in…