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A weak value is an effective description of the influence of a pre and post-selected 'principal' system on another 'meter' system to which it is weakly coupled. Weak values can describe anomalously large deflections of the meter, and…
The assumption of normality in data has been considered in the field of statistical analysis for a long time. However, in many practical situations, this assumption is clearly unrealistic. It has recently been suggested that the use of…
We analyze the average of weak values over statistical ensembles of pre- and post-selected states. The protocol of weak values, proposed by Aharonov et al., is the result of a weak measurement conditional on the outcome of a subsequent…
Statistical system models provide the basis for the examination of various sorts of distributions. Classification distributions are a very common and versatile form of statistics in e.g. real economic, social, and IT systems. The…
We say that a function is rare-case hard against a given class of algorithms (the adversary) if all algorithms in the class can compute the function only on an $o(1)$-fraction of instances of size $n$ for large enough $n$. Starting from any…
A regularity lemma for polynomials provides a decomposition in terms of a bounded number of approximately independent polynomials. Such regularity lemmas play an important role in numerous results, yet suffer from the familiar shortcoming…
Quantum measurement is one of the most fascinating and discussed phenomena in quantum physics, due to the impact on the system of the measurement action and the resulting interpretation issues. Scholars proposed weak measurements to amplify…
Randomness is fundamental in quantum theory, with many philosophical and practical implications. In this paper we discuss the concept of algorithmic randomness, which provides a quantitative method to assess the Borel normality of a given…
In this paper we demonstrate that the class of basic feasible functionals has recursion theoretic properties which naturally generalize the corresponding properties of the class of feasible functions. We also improve the Kapron - Cook…
We study the problem of selecting limited features to observe such that models trained on them can perform well simultaneously across multiple subpopulations. This problem has applications in settings where collecting each feature is…
In this paper we study the almost sure conditional central limit theorem in its functional form for a class of random variables satisfying a projective criterion. Applications to strongly mixing processes and non irreducible Markov chains…
This paper considers deep neural networks for learning weakly dependent processes in a general framework that includes, for instance, regression estimation, time series prediction, time series classification. The $\psi$-weak dependence…
We propose a general formalism of iterated random functions with semigroup property, under which exact and approximate Bayesian posterior updates can be viewed as specific instances. A convergence theory for iterated random functions is…
The weak-to-strong generalization phenomenon is the driver for important machine learning applications including highly data-efficient learning and, most recently, performing superalignment. While decades of research have resulted in…
The Wigner function of quantum systems is an effective instrument to construct the approximate classical description of the systems for which the classical approximation is possible. During the last time, the Wigner function formalism is…
We show how the success of deep learning could depend not only on mathematics but also on physics: although well-known mathematical theorems guarantee that neural networks can approximate arbitrary functions well, the class of functions of…
We study Martin-L\"{o}f random (ML-random) points on computable probability measures on sample and parameter spaces (Bayes models). We consider variants of conditional randomness defined by ML-randomness on Bayes models and those of…
We study the weak values of a quantum observable from the point of view of the Wigner formalism. The main actor is here the cross-Wigner transform of two functions, which is in disguise the cross-ambiguity function familiar from radar…
We introduce weak exceptional sequence of modules which can be viewed as another modification of the standard case, different than the works of Igusa-Todorov \cite{Igusa-Todorov} and Buan-Marsh \cite{Buan-Marsh}. For hereditary algebras it…
Reduction is shown to be a possible consequence of the basic principles of quantum mechanics, involving no branching of the quantum state of the universe. The key feature of a measurement is attributed to the creation of macroscopic germs…