Related papers: Computably Enumerable Equivalence Relations
The TTE approach to Computable Analysis is the study of so-called representations (encodings for continuous objects such as reals, functions, and sets) with respect to the notions of computability they induce. A rich variety of such…
In recent years, much work in descriptive set theory has been focused on the Borel complexity of naturally occurring classification problems, in particular, the study of countable Borel equivalence relations and their structure under the…
A relationally exchangeable structure is a random combinatorial structure whose law is invariant with respect to relabeling its relations, as opposed to its elements. Aside from exchangeable random partitions, examples include edge…
Discourse relations bind smaller linguistic elements into coherent texts. However, automatically identifying discourse relations is difficult, because it requires understanding the semantics of the linked sentences. A more subtle challenge…
Counterfactual explanations (CEs) are a practical tool for demonstrating why machine learning classifiers make particular decisions. For CEs to be useful, it is important that they are easy for users to interpret. Existing methods for…
In recent years, methods from network science are gaining rapidly interest in economics and finance. A reason for this is that in a globalized world the interconnectedness among economic and financial entities are crucial to understand and…
Structural Equation Modeling (SEM) or Covariance Structure Analysis (CSA) is a versatile and powerful method in the social and behavioral sciences, providing a framework for modeling complex relationships, testing mediation, accounting for…
The past decade has seen a significant interest in learning tractable probabilistic representations. Arithmetic circuits (ACs) were among the first proposed tractable representations, with some subsequent representations being instances of…
We study Borel equivalence relations induced by Borel actions of tsi Polish groups on standard Borel spaces. We characterize when such an equivalence relation admits classification by countable structures using a variant of the $\mathbb…
In this survey, we study the relations between amenability (resp. amenability at infinity) of C*-dynamical systems and equality or nuclearity (resp. exactness) of the corresponding crossed products.
A combinatorial characterization of measurable filters on a countable set is found. We apply it to the problem of measurability of the intersection of nonmeasurable filters.
In machine learning, it is common to obtain multiple equally performing models for the same prediction task, e.g., when training neural networks with different random seeds. Model multiplicity (MM) is the situation which arises when these…
We present Relational Sentence Embedding (RSE), a new paradigm to further discover the potential of sentence embeddings. Prior work mainly models the similarity between sentences based on their embedding distance. Because of the complex…
We show that for both the unary relation of transcendence and the finitary relation of algebraic independence on a field, the degree spectra of these relations may consist of any single computably enumerable Turing degree, or of those c.e.…
The Connes Embedding Problem (CEP) asks whether every separable II_1 factor embeds into an ultrapower of the hyperfinite II_1 factor. We show that the CEP is equivalent to the computability of the universal theory of every type II_1 von…
Identifying latent representations or causal structures is important for good generalization and downstream task performance. However, both fields have been developed rather independently. We observe that several methods in both…
A $\lambda$-calculus is introduced in which all programs can be evaluated in probabilistic polynomial time and in which there is sufficient structure to represent sequential cryptographic constructions and adversaries for them, even when…
In this paper we give a robust logical and computational characterisation of peer-to-peer database systems. We first define a pre- cise model-theoretic semantics of a peer-to-peer system, which allows for local inconsistency handling. We…
We propose a definition of quantum computable functions as mappings between superpositions of natural numbers to probability distributions of natural numbers. Each function is obtained as a limit of an infinite computation of a quantum…
These lecture notes are an informal introduction to the theory of computational complexity and its links to quantum computing and statistical mechanics.