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Lipschitz continuity of algorithms, introduced by Kumabe and Yoshida (FOCS'23), measures the stability of an algorithm against small input perturbations. Algorithms with small Lipschitz continuity are desirable, as they ensure reliable…
We demonstrate that locally linear embedding (LLE) inherently admits some unwanted results when no regularization is used, even for cases in which regularization is not supposed to be needed in the original algorithm. The existence of one…
A theory of modules over posets is developed to define computationally feasible, topologically interpretable data structures, in terms of birth and death of homology classes, for persistent homology with multiple real parameters. To replace…
When reasoning about formal objects whose structures involve binding, it is often necessary to analyze expressions relative to a context that associates types, values, and other related attributes with variables that appear free in the…
The use of attention models for automated image captioning has enabled many systems to produce accurate and meaningful descriptions for images. Over the years, many novel approaches have been proposed to enhance the attention process using…
Sentence embeddings can be decoded to give approximations of the original texts used to create them. We explore this effect in the context of text simplification, demonstrating that reconstructed text embeddings preserve complexity levels.…
Piecewise constant image approximations of sequential number of segments or clusters of disconnected pixels are treated. The method of majorizing of optimal approximation sequence by hierarchical sequence of image approximations is…
Image captioning models are becoming increasingly successful at describing the content of images in restricted domains. However, if these models are to function in the wild - for example, as assistants for people with impaired vision - a…
This paper aims to provide an unsupervised modelling approach that allows for a more flexible representation of text embeddings. It jointly encodes the words and the paragraphs as individual matrices of arbitrary column dimension with unit…
An order theoretic and algebraic framework for the extended real numbers is established which includes extensions of the usual difference to expressions involving $-\infty$ and/or $+\infty$, so-called residuations. Based on this,…
We consider bipartite graphs definable in o-minimal structures, in which the edge relation $G$ is a finite union of graphs of certain measure-preserving maps. We establish a fact on the existence of definable matchings with few short…
Finite mixtures are a flexible modeling tool for irregularly shaped densities and samples from heterogeneous populations. When modeling with mixtures using an exchangeable prior on the component features, the component labels are arbitrary…
We investigate the definability (reducts) lattice of the order of integers and describe a sublattice generated by relations 'between', 'cycle', 'separation', 'neighbor', '1-codirection', 'order' and equality'. Some open questions are…
Despite recent successes in language models, their ability to represent numbers is insufficient. Humans conceptualize numbers based on their magnitudes, effectively projecting them on a number line; whereas subword tokenization fails to…
Assuming 0# does not exist, we present a combinatorial approach to Jensen's method of coding by a real. The forcing uses combinatorial consequences of fine structure (including the Covering Lemma, in various guises), but makes no direct…
Labeling explicit discourse relations is one of the most challenging sub-tasks of the shallow discourse parsing where the goal is to identify the discourse connectives and the boundaries of their arguments. The state-of-the-art models…
In previous publications dressed coordinates and dressed states has been introduced. Specifically, a system composed by a harmonic oscillator interacting linearly with an infinity set of other oscillators has been treated. In this paper we…
Discrete tomography is concerned with the reconstruction of images that are defined on a discrete set of lattice points from their projections in several directions. The range of values that can be assigned to each lattice point is…
We seek a practical method for establishing dense correspondences between two images with similar content, but possibly different 3D scenes. One of the challenges in designing such a system is the local scale differences of objects…
Some of the simplest, yet most frequently used predictors in statistics and machine learning use weighted linear combinations of features. Such linear predictors can model non-linear relationships between features by adding interaction…