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We show that every finite semilattice can be represented as an atomized semilattice, an algebraic structure with additional elements (atoms) that extend the semilattice's partial order. Each atom maps to one subdirectly irreducible…
This manuscript bridges nonparametric smoothness-based and shape-restricted estimation, which may appear as two disjoint paradigms in the field. The proposed approach is motivated by a conceptually simple observation: every Lipschitz…
We address the problem of complementing higher-order patterns without repetitions of existential variables. Differently from the first-order case, the complement of a pattern cannot, in general, be described by a pattern, or even by a…
Given a finite and non-empty set $X$ and randomly selected specific functions and relations on $X$, we investigate the existence and non-existence of fixed points and reflexive points, respectively. First, we consider the class of…
A new technique for approximating the entire solution set for a nonlinear system of relations (nonlinear equations, inequalities, etc. involving algebraic, smooth, or even continuous functions) is presented. The technique is to first plot…
Neighborhood regression has been a successful approach in graphical and structural equation modeling, with applications to learning undirected and directed graphical models. We extend these ideas by defining and studying an algebraic…
Definite descriptions are first-order expressions that denote unique objects. In this paper, we propose a second-order counterpart, designed to refer to unique relations between objects. We investigate this notion within the framework of…
We study the problem of deciding universal termination of linear and affine loops over the reals in the bit-model of real computation. We show that both problems are as close to decidable as one can expect them to be: there exist sound…
Language models are defined over a finite set of inputs, which creates a vocabulary bottleneck when we attempt to scale the number of supported languages. Tackling this bottleneck results in a trade-off between what can be represented in…
Recently, image captioning has aroused great interest in both academic and industrial worlds. Most existing systems are built upon large-scale datasets consisting of image-sentence pairs, which, however, are time-consuming to construct. In…
Introducing explicit constraints on the structural predictions has been an effective way to improve the performance of semantic segmentation models. Existing methods are mainly based on insufficient hand-crafted rules that only partially…
As a pioneering work we construct explicit real algebraic functions which may have both compact and non-compact preimages. The author has obtained explicit real algebraic functions with preimages satisfying some nice conditions. More…
Existing methods for pixel-wise labelling tasks generally disregard the underlying structure of labellings, often leading to predictions that are visually implausible. While incorporating structure into the model should improve prediction…
Graphs and hypergraphs combine expressive modeling power with algorithmic efficiency for a wide range of applications. Hedgegraphs generalize hypergraphs further by grouping hyperedges under a color/hedge. This allows hedgegraphs to model…
This article presents a survey of work on lifted graphical models. We review a general form for a lifted graphical model, a par-factor graph, and show how a number of existing statistical relational representations map to this formalism. We…
While the embedding of words has revolutionized the field of Natural Language Processing, the embedding of concepts has received much less attention so far. A dense and meaningful representation of concepts, however, could prove useful for…
Hypergraphs allow one to encode higher-order relationships in data and are thus a very flexible modeling tool. Current learning methods are either based on approximations of the hypergraphs via graphs or on tensor methods which are only…
The past years have seen a drastic rise in studies devoted to the investigation of colexification patterns in individual languages families in particular and the languages of the world in specific. Specifically computational studies have…
New partial results are obtained related to the following old problem of Erd\"os: for any infinite set $X$ of real numbers to show that there is always a measurable (or, equivalently, closed) subset of reals of positive Lebesgue measure…
Pre-trained models have revolutionized natural language understanding. However, researchers have found they can encode artifacts undesired in many applications, such as professions correlating with one gender more than another. We explore…