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Quantum theory is indeterministic, but not completely so. When a system is in a pure state there are properties it possesses with certainty, known as actual properties. The actual properties of a quantum system (in a pure state) fully…
A new method of deriving comparative statics information using generalized compensated derivatives is presented which yields constraint-free semidefiniteness results for any differentiable, constrained optimization problem. More generally,…
This work unifies the analysis of various randomized methods for solving linear and nonlinear inverse problems by framing the problem in a stochastic optimization setting. By doing so, we show that many randomized methods are variants of a…
Generalised Probabilistic Theories (GPTs) provide a unifying framework encompassing classical theories, quantum theories, as well as hypothetical alternatives. We investigate the problem of extending a system with a finite set of…
We show how any PAC learning algorithm that works under the uniform distribution can be transformed, in a blackbox fashion, into one that works under an arbitrary and unknown distribution $\mathcal{D}$. The efficiency of our transformation…
A quantum probability model is introduced and used to explain human probability judgment errors including the conjunction, disjunction, inverse, and conditional fallacies, as well as unpacking effects and partitioning effects. Quantum…
Duality theorems play a fundamental role in convex optimization. Recently, it was shown how duality theorems for countable probability distributions and finite-dimensional quantum states can be leveraged for building relatively complete…
Linearizability is a standard correctness criterion for concurrent algorithms, typically proved by establishing the algorithms' linearization points. However, relying on linearization points leads to proofs that are…
It is not fully understood why adversarial examples can deceive neural networks and transfer between different networks. To elucidate this, several studies have hypothesized that adversarial perturbations, while appearing as noises, contain…
Generalization is a central concept in machine learning theory, yet for quantum models, it is predominantly analyzed through uniform bounds that depend on a model's overall capacity rather than the specific function learned. These…
Inspired by connections to two dimensional quantum theory, we define several models of computation based on permuting distinguishable particles (which we call balls), and characterize their computational complexity. In the quantum setting,…
We present a so-called universal convergence theorem for inexact primal-dual penalty and augmented Lagrangian methods that can be applied to a large number of such methods and reduces their convergence analysis to verification of some…
We discuss conditionalisation for Accept-Desirability models in an abstract decision-making framework, where uncertain rewards live in a general linear space, and events are special projection operators on that linear space. This abstract…
Density modelling is the task of learning an unknown probability density function from samples, and is one of the central problems of unsupervised machine learning. In this work, we show that there exists a density modelling problem for…
Dempster-Shafer evidence theory has been widely used in various fields of applications, because of the flexibility and effectiveness in modeling uncertainties without prior information. Besides, it has been proven that the quantum theory…
QBism is an interpretation of quantum theory which views quantum mechanics as standard probability theory supplemented with a few extra normative constraints. The fundamental gambit is to represent states and measurements, as well as time…
Solomonoff unified Occam's razor and Epicurus' principle of multiple explanations to one elegant, formal, universal theory of inductive inference, which initiated the field of algorithmic information theory. His central result is that the…
Certain quantization problems are equivalent to the construction of morphisms from "quantum" to "classical" props. Once such a morphism is constructed, Hensel's lemma shows that it is in fact an isomorphism. This gives a new, simple proof…
Conformal predictors provide set or functional predictions that are valid under the assumption of randomness, i.e., under the assumption of independent and identically distributed data. The question asked in this paper is whether there are…
Uniform proofs are sequent calculus proofs with the following characteristic: the last step in the derivation of a complex formula at any stage in the proof is always the introduction of the top-level logical symbol of that formula. We…