Related papers: Categories of Empirical Models
In addition to the important role of contextuality in foundations of quantum theory, this intrinsically quantum property has been identified as a potential resource for quantum advantage in different tasks. It is thus of fundamental…
Despite the empirical success of foundation models, we do not have a systematic characterization of the representations that these models learn. In this paper, we establish the contexture theory. It shows that a large class of…
We consider the contextual fraction as a quantitative measure of contextuality of empirical models, i.e. tables of probabilities of measurement outcomes in an experimental scenario. It provides a general way to compare the degree of…
Different analytic notions of contextuality fall into two major groups: probabilistic and strong notions of contextuality. Kochen and Specker's Theorem~0 is a demarcation criterion for differentiating between those groups. Whereas…
We aim to counter the tendency for specialization in science by advancing a language that can facilitate the translation of ideas and methods between disparate contexts. The focus is on questions of "resource-theoretic nature". In a…
Models for categorical sequences typically assume exchangeable or first-order dependent sequence elements. These are common assumptions, for example, in models of computer malware traces and protein sequences. Although such simplifying…
We introduce a notion of contextuality for transformations in sequential contexts, distinct from the Bell-Kochen-Specker and Spekkens notions of contextuality. Within a transformation-based model for quantum computation we show that strong…
Contextuality is a feature of quantum correlations. It is crucial from a foundational perspective as a nonclassical phenomenon, and from an applied perspective as a resource for quantum advantage. It is commonly defined in terms of hidden…
Recent work by Abramsky and Brandenburger used sheaf theory to give a mathematical formulation of non-locality and contextuality. By adopting this viewpoint, it has been possible to define cohomological obstructions to the existence of…
In quantum mechanics, not everything that can be observed can be observed simultaneously. Observational data exhibits \emph{contextuality} -- a generalisation of nonlocality -- if the result of an observation is necessarily dependent on…
We present a formal theory of contextuality for a set of random variables grouped into different subsets (contexts) corresponding to different, mutually incompatible conditions. Within each context the random variables are jointly…
Contextuality describes the nontrivial dependence of measurement outcomes on particular choices of jointly measurable observables. In this work we review and generalize the bundle diagram representation introduced in [S. Abramsky et al.,…
Contextuality is one way of capturing the non-classicality of quantum theory. The contextual nature of a theory is often witnessed via the violation of non-contextuality inequalities---certain linear inequalities involving probabilities of…
Quantum coherence, nonlocality, and contextuality are key resources for quantum advantage in metrology, communication, and computation. We introduce a graph-based approach to derive classicality inequalities that bound local,…
Graphical models can represent a multivariate distribution in a convenient and accessible form as a graph. Causal models can be viewed as a special class of graphical models that not only represent the distribution of the observed system…
Generalisation in machine learning often relies on the ability to encode structures present in data into an inductive bias of the model class. To understand the power of quantum machine learning, it is therefore crucial to identify the…
The data of a physical experiment can be represented as a presheaf of probability distributions. A striking feature of quantum theory is that those probability distributions obtained in quantum mechanical experiments do not always admit a…
Contextuality is the failure of "local" probabilistic models to become global ones. In this paper we introduce the notions of \emph{measurable fibre bundles}, \emph{probability fibre bundles}, and \emph{sample fibre bundle} which capture…
In this work we present a hierarchy of generalized contextuality. It refines the traditional binary distinction between contextual and noncontextual theories, and facilitates their comparison based on how contextual they are. Our approach…
Causal Models are like Dependency Graphs and Belief Nets in that they provide a structure and a set of assumptions from which a joint distribution can, in principle, be computed. Unlike Dependency Graphs, Causal Models are models of…