Related papers: On the resolution of the sensitivity conjecture
The strong coupling limit of a quantum system is in general quite complicated, but in some cases a great simplification occurs: the strongly coupled limit is equivalent to the weakly coupled limit of some other system. In string theory…
In this paper, we study the tedious link between the properties of sensibility and approximability of models of untyped {\lambda}-calculus. Approximability is known to be a slightly, but strictly stronger property that sensibility. However,…
A conjecture is given that, if true, could lead to an algorithm for computing definite sums of rational functions.
We define a measure for the complexity of Boolean functions related to their implementation in neural networks, and in particular close related to the generalization ability that could be obtained through the learning process. The measure…
Formal explainability guarantees the rigor of computed explanations, and so it is paramount in domains where rigor is critical, including those deemed high-risk. Unfortunately, since its inception formal explainability has been hampered by…
In this paper, we consider the problem of making distributionally robust, skeptical inferences for the multi-label problem, or more generally for Boolean vectors. By distributionally robust, we mean that we consider a set of possible…
Bayesian inference is often utilized for uncertainty quantification tasks. A recent analysis by Xu and Raginsky 2022 rigorously decomposed the predictive uncertainty in Bayesian inference into two uncertainties, called aleatoric and…
A recently introduced measure of Boolean functions complexity--disjunc\-tive complexity (DC)--is compared with other complexity measures: the space complexity of streaming algorithms and the complexity of nondeterministic branching programs…
In their classical 1993 paper [CV93] Chaudhuri and Vardi notice that some fundamental database theory results and techniques fail to survive when we try to see query answers as bags (multisets) of tuples rather than as sets of tuples. But…
A quantum-like description of human decision process is developed, and a heuristic argument supporting the theory as sound phenomenology is given. It is shown to be capable of quantitatively explaining the conjunction fallacy in the same…
The unwavering success of deep learning in the past decade led to the increasing prevalence of deep learning methods in various application fields. However, the downsides of deep learning, most prominently its lack of trustworthiness, may…
Computational models typically assume that operations are applied in a fixed sequential order. In recent years several works have looked at relaxing this assumption, considering computations without any fixed causal structure and showing…
Neural networks are becoming increasingly prevalent in software, and it is therefore important to be able to verify their behavior. Because verifying the correctness of neural networks is extremely challenging, it is common to focus on the…
Unmeasured confounding remains a critical challenge in causal inference for the social sciences. This paper proposes a sensitivity analysis framework to systematically evaluate how unmeasured confounders influence statistical inference in…
A relational database is said to be uncertain if primary key constraints can possibly be violated. A repair (or possible world) of an uncertain database is obtained by selecting a maximal number of tuples without ever selecting two distinct…
A decision procedure implemented over a computational trust mechanism aims to allow for decisions to be made regarding whether some entity or information should be trusted. As recognised in the literature, trust is contextual, and we…
The classical PCP theorem is arguably the most important achievement of classical complexity theory in the past quarter century. In recent years, researchers in quantum computational complexity have tried to identify approaches and develop…
Sensitivity methods for the analysis of the outputs of discrete Bayesian networks have been extensively studied and implemented in different software packages. These methods usually focus on the study of sensitivity functions and on the…
The subject of this textbook is the analysis of Boolean functions. Roughly speaking, this refers to studying Boolean functions $f : \{0,1\}^n \to \{0,1\}$ via their Fourier expansion and other analytic means. Boolean functions are perhaps…
We develop a sensitivity function for the design of electron optics using an adjoint approach based on a form of reciprocity implicit in Hamilton's equations of motion. The sensitivity function, which is computed with a small number of…