Related papers: Physical limits of inference
In this paper we investigate the potential for persuasion linked to the quantum indeterminacy of beliefs. We first formulate the persuasion problem in the context of quantum-like beliefs. We provide an economic example of belief…
Bayesian inference provides a uniquely rigorous approach to obtain principled justification for uncertainty in predictions, yet it is difficult to articulate suitably general prior belief in the machine learning context, where computational…
For each Turing machine T, we construct an algebra A'(T) such that the variety generated by A'(T) has definable principal subcongruences if and only if T halts, thus proving that the property of having definable principal subcongruences is…
A key challenge in causal inference from observational studies is the identification and estimation of causal effects in the presence of unmeasured confounding. In this paper, we introduce a novel approach for causal inference that…
Physical theories that depend on many parameters or are tested against data from many different experiments pose unique challenges to statistical inference. Many models in particle physics, astrophysics and cosmology fall into one or both…
This work explores the connection between logical independence and the algebraic structure of quantum mechanics. Building on results by Brukner et al., it introduces the notion of \textit{onto-epistemic ignorance}: situations in which the…
Taking the view that computation is after all physical, we argue that physics, particularly quantum physics, could help extend the notion of computability. Here, we list the important and unique features of quantum mechanics and then…
We show the existence of rigid combinatorial objects which previously were not known to exist. Specifically, for a wide range of the underlying parameters, we show the existence of non-trivial orthogonal arrays, $t$-designs, and $t$-wise…
For infinite machines which are free from the classical Thompson's lamp paradox we show that they are not free from its inverted version. We provide a program for infinite machines and an infinite mechanism which simulate this paradox.…
Models of computation operating over the real numbers and computing a larger class of functions compared to the class of general recursive functions invariably introduce a non-finite element of infinite information encoded in an arbitrary…
Incompleteness theorems of Godel, Turing, Chaitin, and Algorithmic Information Theory have profound epistemological implications. Incompleteness limits our ability to ever understand every observable phenomenon in the universe.…
The study of entanglement in systems composed of identical particles raises interesting challenges with far-reaching implications in both, our fundamental understanding of the physics of composite quantum systems, and our capability of…
We establish three impossibility results regarding our knowledge of the quantum state of the universe. Suppose the universal quantum state is a typical unit vector in a high-dimensional subspace $\mathscr{H}_0$ of Hilbert space…
The range of a quantum measurement is the set of outcome probability distributions that can be produced by varying the input state. We introduce data-driven inference as a protocol that, given a set of experimental data as a collection of…
The Turing Machine has two implicit properties that depend on its underlying notion of computing: the format is fully determinate and computations are information preserving. Distributed representations lack these properties and cannot be…
We report an inconsistency found in probability theory (also referred to as measure-theoretic probability). For probability measures induced by real-valued random variables, we deduce an "equality" such that one side of the "equality" is a…
In the paper we present results to develop an irreducible theory of complex systems in terms of self-organization processes of prime integer relations. Based on the integers and controlled by arithmetic only the self-organization processes…
Within psychology, neuroscience and artificial intelligence, there has been increasing interest in the proposal that the brain builds probabilistic models of sensory and linguistic input: that is, to infer a probabilistic model from a…
Quantum theory makes the most accurate empirical predictions and yet it lacks simple, comprehensible physical principles from which the theory can be uniquely derived. A broad class of probabilistic theories exist which all share some…
In this paper, a unified framework for representing uncertain information based on the notion of an interval structure is proposed. It is shown that the lower and upper approximations of the rough-set model, the lower and upper bounds of…