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In the present article, real number representations, that are generalizations of classical positive and alternating representations of numbers, are introduced and investigated. The main metric relation, properties of cylinder sets are…

Number Theory · Mathematics 2021-01-05 Symon Serbenyuk

There has been a lot of recent interest in mining patterns from graphs. Often, the exact structure of the patterns of interest is not known. This happens, for example, when molecular structures are mined to discover fragments useful as…

Data Structures and Algorithms · Computer Science 2007-05-23 Pavel Dmitriev , Carl Lagoze

In many applications involving multi-media data, the definition of similarity between items is integral to several key tasks, e.g., nearest-neighbor retrieval, classification, and recommendation. Data in such regimes typically exhibits…

Artificial Intelligence · Computer Science 2010-09-01 Brian McFee , Gert Lanckriet

In the paper the main attention is paid to conditions on algebras from a given variety which provide coincidence of their algebraic geometries. The main part here play the notions mentioned in the title of the paper.

General Mathematics · Mathematics 2007-05-23 B. Plotkin

Learning representations that generalize to novel compositions of known concepts is crucial for bridging the gap between human and machine perception. One prominent effort is learning object-centric representations, which are widely…

Machine Learning · Computer Science 2024-11-13 Thaddäus Wiedemer , Jack Brady , Alexander Panfilov , Attila Juhos , Matthias Bethge , Wieland Brendel

Complexity of patterns is a key information for human brain to differ objects of about the same size and shape. Like other innate human senses, the complexity perception cannot be easily quantified. We propose a transparent and universal…

Pattern Formation and Solitons · Physics 2020-12-30 Andrey A. Bagrov , Ilia A. Iakovlev , Askar A. Iliasov , Mikhail I. Katsnelson , Vladimir V. Mazurenko

To operate intelligently in domestic environments, robots require the ability to understand arbitrary spatial relations between objects and to generalize them to objects of varying sizes and shapes. In this work, we present a novel…

Robotics · Computer Science 2019-07-02 Philipp Jund , Andreas Eitel , Nichola Abdo , Wolfram Burgard

The goal of this paper is to retrieve an image based on instance, attribute and category similarity notions. Different from existing works, which usually address only one of these entities in isolation, we introduce a cooperative embedding…

Computer Vision and Pattern Recognition · Computer Science 2019-04-03 William Thong , Cees G. M. Snoek , Arnold W. M. Smeulders

Similarity query is the family of queries based on some similarity metrics. Unlike the traditional database queries which are mostly based on value equality, similarity queries aim to find targets "similar enough to" the given data objects,…

Databases · Computer Science 2022-04-19 Yifan Wang

Both algebraic and computational approaches for dealing with similarity spaces are well known in generalized rough set theory. However, these studies may be said to have been confined to particular perspectives of distinguishability in the…

Logic · Mathematics 2009-05-14 A. Mani

Capturing the similarities between human language units is crucial for explaining how humans associate different objects, and therefore its computation has received extensive attention, research, and applications. With the ever-increasing…

Computation and Language · Computer Science 2025-09-04 Wenchuan Mu

The words of a language reflect the structure of the human mind, allowing us to transmit thoughts between individuals. However, language can represent only a subset of our rich and detailed cognitive architecture. Here, we ask what kinds of…

Computation and Language · Computer Science 2018-03-07 Gabriel Grand , Idan Asher Blank , Francisco Pereira , Evelina Fedorenko

We consider object detection using a generic model for natural shapes. A common approach for object recognition involves matching object models directly to images. Another approach involves building intermediate representations via a…

Computer Vision and Pattern Recognition · Computer Science 2014-12-23 Pedro F. Felzenszwalb

We present a technique for estimating the similarity between objects such as movies or foods whose proper representation depends on human perception. Our technique combines a modest number of human similarity assessments to infer a pairwise…

Artificial Intelligence · Computer Science 2018-02-19 Jesse Anderton , Pavel Metrikov , Virgil Pavlu , Javed Aslam

Principles of analogical reasoning have recently been applied in the context of machine learning, for example to develop new methods for classification and preference learning. In this paper, we argue that, while analogical reasoning is…

Machine Learning · Computer Science 2020-05-27 Eyke Hüllermeier

Correspondence identifies relationships among objects via similarities among their components; it is ubiquitous in the analysis of spatial datasets, including images, weather maps, and computational simulations. This paper develops a novel…

Artificial Intelligence · Computer Science 2007-05-23 Chris Bailey-Kellogg , Naren Ramakrishnan

Generalization in generative modeling is defined as the ability to learn an underlying distribution from a finite dataset and produce novel samples, with evaluation largely driven by held-out performance and perceived sample quality. In…

Machine Learning · Computer Science 2026-03-05 Jerome Garnier-Brun , Luca Biggio , Davide Beltrame , Marc Mézard , Luca Saglietti

We present a notion of generalized entanglement which goes beyond the conventional definition based on quantum subsystems. This is accomplished by directly defining entanglement as a property of quantum states relative to a distinguished…

Quantum Physics · Physics 2007-05-23 Lorenza Viola , Howard Barnum , Emanuel Knill , Gerardo Ortiz , Rolando Somma

Recognizing elementary underlying concepts from observations (disentanglement) and generating novel combinations of these concepts (compositional generalization) are fundamental abilities for humans to support rapid knowledge learning and…

Computer Vision and Pattern Recognition · Computer Science 2023-05-30 Tao Yang , Yuwang Wang , Cuiling Lan , Yan Lu , Nanning Zheng

Motivated by applications in databases, this paper considers various fragments of the calculus of binary relations. The fragments are obtained by leaving out, or keeping in, some of the standard operators, along with some derived operators…

Logic in Computer Science · Computer Science 2014-03-31 George H. L. Fletcher , Marc Gyssens , Dirk Leinders , Jan Van den Bussche , Dirk Van Gucht , Stijn Vansummeren