Related papers: Contextuality and bundle diagrams
The contextual fraction introduced by Abramsky and Brandenburger defines a quantitative measure of contextuality associated with empirical models, i.e. tables of probabilities of measurement outcomes in experimental scenarios. In this paper…
An operational definition of contextuality is introduced which generalizes the standard notion in three ways: (1) it applies to arbitrary operational theories rather than just quantum theory, (2) it applies to arbitrary experimental…
A notion of morphism that is suitable for the sheaf-theoretic approach to contextuality is developed, resulting in a resource theory for contextuality. The key features involve using an underlying relation rather than a function between…
The amount of contextuality is quantified in terms of the probability of the necessary violations of noncontextual assignments to counterfactual elements of physical reality.
The relevance and importance of contextualizing data analytics is described. Qualitative characteristics might form the context of quantitative analysis. Topics that are at issue include: contrast, baselining, secondary data sources,…
Persistence diagram (PD) bundles, a generalization of vineyards, were introduced as a way to study the persistent homology of a set of filtrations parameterized by a topological space $B$. In this paper, we present an algorithm for…
A pedagogical but concise overview of fiber bundles and their connections is provided, in the context of gauge theories in physics. The emphasis is on defining and visualizing concepts and relationships between them, as well as listing…
Contextuality is a fundamental property of quantum theory and a critical resource for quantum computation. Here, we experimentally observe the arguably cleanest form of contextuality in quantum theory [A. Cabello \emph{et al.}, Phys. Rev.…
Ontological theories of quantum mechanics provide a realistic description of single systems by means of well-defined quantities conditioning the measurement outcomes. In order to be complete, they should also fulfil the minimal condition of…
Real-world problems, for example in climate applications, often require causal reasoning on spatially gridded time series data or data with comparable structure. While the underlying system is often believed to behave similarly at different…
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 introduce a new framework for contextuality based on simplicial sets, combinatorial models of topological spaces that play a prominent role in modern homotopy theory. Our approach extends measurement scenarios to consist of spaces…
The neural architectures of language models are becoming increasingly complex, especially that of Transformers, based on the attention mechanism. Although their application to numerous natural language processing tasks has proven to be very…
This short paper examines diagrams describing neural network systems in academic conference proceedings. Many aspects of scholarly communication are controlled, particularly with relation to text and formatting, but often diagrams are not…
We introduce a preparation-dual notion of contextuality, formulated as an obstruction to stochastic extension. In parallel with the sheaf-theoretic formulation of measurement contextuality, preparation contextuality arises when locally…
Quantum theory features several phenomena which can be considered as resources for information processing tasks. Some of these effects, such as entanglement, arise in a nonlocal scenario, where a quantum state is distributed between…
We study the relationship between assumptions of state separability and both preparation and measurement contextuality, and the relationship of both of these to the frame problem, the problem of predicting what does not change in…
Categorical bundles provide a natural framework for gauge theories involving multiple gauge groups. Unlike the case of traditional bundles there are distinct notions of triviality, and hence also of local triviality, for categorical…
Purpose - This paper presents a methodology for defining and modeling context-awareness and describing efficiently the interactions between systems, applications and their context. Also the relation of modern context-aware systems with…
I assess various proposals for the source of the intuition that there is something problematic about contextuality, ultimately concluding that contextuality is best thought of in terms of fine-tuning. I then argue that as with other…