Related papers: Self-embeddings of models of arithmetic; fixed poi…

Model counting ($\#\text{SAT}$) is a fundamental yet $\#\text{P}$-complete problem central to probabilistic reasoning. In this work, we address \textit{incremental model counting}, where sequences of structurally similar formulas must be…

For a given measure space $(X,{\mathscr B},\mu)$ we construct all measure spaces $(Y,{\mathscr C},\lambda)$ in which $(X,{\mathscr B},\mu)$ is embeddable. The construction is modeled on the ultrafilter construction of the Stone--\v{C}ech…

The best-performing approaches for scholarly document quality prediction are based on embedding models. In addition to their performance when used in classifiers, embedding models can also provide predictions even for words that were not…

The advancement of deep learning technologies is bringing new models every day, motivating the study of scalable model selection. An ideal model selection scheme should minimally support two operations efficiently over a large pool of…

In this paper we consider a fragment of the first-order theory of the real numbers that includes systems of equations of continuous functions in bounded domains, and for which all functions are computable in the sense that it is possible to…

Neural network models often face challenges when processing very small or very large numbers due to issues such as overflow, underflow, and unstable output variations. To mitigate these problems, we propose using embedding vectors for…

We propose a unified framework for establishing existence of nonparametric M-estimators, computing the corresponding estimates, and proving their strong consistency when the class of functions is exceptionally rich. In particular, the…

The Intrinsic Dimension (ID) is a key concept in unsupervised learning and feature selection, as it is a lower bound to the number of variables which are necessary to describe a system. However, in almost any real-world dataset the ID…

Single Index Models (SIMs) are simple yet flexible semi-parametric models for machine learning, where the response variable is modeled as a monotonic function of a linear combination of features. Estimation in this context requires learning…

We introduce a weak asymptotic version of nonlinear contraction, termed \emph{asymptotic pointwise contraction}. For a mapping on a metric space, this notion requires the existence of a sequence of functions that dominate the distances…

In several familiar subcategories of the category ${\mathbb T}$ of topological spaces and continuous maps, embeddings are not pushout-stable. But, an interesting feature, capturable in many categories, namely in categories $\mathcal{B}$ of…

In this paper we consider the problem of prescribing the nodal set of low-energy eigenfunctions of the Laplacian. Our main result is that, given any separating closed hypersurface \Sigma in a compact n-manifold M, there is a Riemannian…

We consider the model selection consistency or sparsistency of a broad set of $\ell_1$-regularized $M$-estimators for linear and non-linear statistical models in a unified fashion. For this purpose, we propose the local structured…

Low-dimensional embedding, manifold learning, clustering, classification, and anomaly detection are among the most important problems in machine learning. The existing methods usually consider the case when each instance has a fixed,…

Let $X$ be a weakly pseudoconvex manifold and $L\longrightarrow X$ be a holomorphic line bundle with a singular positive Hermitian metric $h$. In this article, we provide a points separation theorem and an embedding for the adjoint linear…

Model robustness indicates a model's capability to generalize well on unforeseen distributional shifts, including data corruptions and adversarial attacks. Data augmentation is one of the most prevalent and effective ways to enhance…

Conventional word embeddings represent words with fixed vectors, which are usually trained based on co-occurrence patterns among words. In doing so, however, the power of such representations is limited, where the same word might be…

The planar embedding conjecture asserts that any planar metric admits an embedding into L_1 with constant distortion. This is a well-known open problem with important algorithmic implications, and has received a lot of attention over the…

Frechet's classical isometric embedding argument has evolved to become a major tool in the study of metric spaces. An important example of a Frechet embedding is Bourgain's embedding. The authors have recently shown that for every e>0 any…

In this paper, we examine some properties of the fixed point set of a digitally continuous function. The digital setting requires new methods that are not analogous to those of classical topological fixed point theory, and we obtain results…