Lucas BechbergerUniversität Osnabrück | UOS · Institute of Cognitive Science
Lucas Bechberger
Master of Science
About
23
Publications
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Introduction
AI Researcher, PhD student.
Background in Machine Learning, Artificial Intelligence, Computer Science, and Natural Language Processing.
Currently pursuing a PhD in Cognitive Science on the topic of "Conceptual Spaces for Artificial Intelligence".
Learn more about my research on my personal website https://www.lucas-bechberger.de or by following me on Twitter @LucasBechberger.
Publications
Publications (23)
Shape information is crucial for human perception and cognition, and should therefore also play a role in cognitive AI systems. We employ the interdisciplinary framework of conceptual spaces, which proposes a geometric representation of conceptual knowledge through low-dimensional interpretable similarity spaces. These similarity spaces are often b...
Shape information is crucial for human perception and cognition, and should therefore also play a role in cognitive AI systems. We employ the interdisciplinary framework of conceptual spaces, which proposes a geometric representation of conceptual knowledge through low-dimensional interpretable similarity spaces. These similarity spaces are often b...
The highly influential framework of conceptual spaces provides a geometric way of representing knowledge. Instances are represented by points in a high-dimensional space and concepts are represented by regions in this space. In this article, we extend our recent mathematical formalization of this framework by providing quantitative mathematical def...
This open access book is a timely contribution in presenting recent issues, approaches, and results that are not only central to the highly interdisciplinary field of concept research but also particularly important to newly emergent paradigms and challenges. The contributors present a unique, holistic picture for the understanding and use of conce...
Numerical concepts are an integral part of everyday conversation and communication. Expressions relating to numbers in natural language can have precise or imprecise interpretations. While the precise interpretation most prominently appears in mathematical contexts, the imprecise interpretation seems to arise when numbers (as quantities) are applie...
It is impossible to talk about human cognition without talking about concepts—there simply is no human cognition without concepts. Concepts form an abstraction of reality that is central to the functioning of the human mind. Conceptual knowledge (of e.g., APPLE, LOVE and BEFORE) is crucial for us to categorize, understand, and reason about the worl...
The cognitive framework of conceptual spaces proposes to represent concepts as regions in psychological similarity spaces. These similarity spaces are typically obtained through multidimensional scaling (MDS), which converts human dissimilarity ratings for a fixed set of stimuli into a spatial representation. One can distinguish metric MDS (which a...
This open access book is a timely contribution in presenting recent issues, approaches, and results that are not only central to the highly interdisciplinary field of concept research but also particularly important to newly emergent paradigms and challenges. The contributors present a unique, holistic picture for the understanding and use of conce...
The cognitive framework of conceptual spaces [3] proposes to represent concepts and properties such as apple and round as convex regions in perception-based similarity spaces.
The cognitive framework of conceptual spaces proposes to represent concepts as regions in psychological similarity spaces. These similarity spaces are typically obtained through multidimensional scaling (MDS), which converts human dissimilarity ratings for a fixed set of stimuli into a spatial representation. One can distinguish metric MDS (which a...
The highly influential framework of conceptual spaces provides a geometric way of representing knowledge. Instances are represented by points in a similarity space and concepts are represented by convex regions in this space. After pointing out a problem with the convexity requirement, we propose a formalization of conceptual spaces based on fuzzy...
The cognitive framework of conceptual spaces bridges the gap between symbolic and subsymbolic AI by proposing an intermediate conceptual layer where knowledge is represented geometrically. There are two main approaches for obtaining the dimensions of this conceptual similarity space: using similarity ratings from psychological experiments and using...
The highly influential framework of conceptual spaces provides a geometric way of representing knowledge. Instances are represented by points in a similarity space and concepts are represented by convex regions in this space. After pointing out a problem with the convexity requirement, we propose a formalization of conceptual spaces based on fuzzy...
The highly influential framework of conceptual spaces provides a geometric way of representing knowledge. Instances are represented by points in a high-dimensional space and concepts are represented by regions in this space. Our recent mathematical formalization of this framework is capable of representing correlations between different domains in...
The highly influential framework of conceptual spaces provides a geometric way of representing knowledge. Instances are represented by points in a high-dimensional space and concepts are represented by regions in this space. Our recent mathematical formalization of this framework is capable of representing correlations between different domains in...
The highly influential framework of conceptual spaces provides a geometric way of representing knowledge. Instances are represented by points and concepts are represented by regions in a high-dimensional space. Based on our recent formalization, we present a general-purpose implementation of the conceptual spaces framework that is not only capable...
The highly influential framework of conceptual spaces provides a geometric way of representing knowledge. Instances are represented by points in a high-dimensional space and concepts are represented by convex regions in this space. After pointing out a problem with the convexity requirement, we propose a formalization of conceptual spaces based on...
The highly influential framework of conceptual spaces provides a geometric way of representing knowledge. Instances are represented by points in a high-dimensional space and concepts are represented by convex regions in this space. After pointing out a problem with the convexity requirement, we propose a formalization of conceptual spaces based on...
The highly influential framework of conceptual spaces provides a geometric way of representing knowledge. It aims at bridging the gap between symbolic and subsymbolic processing. Instances are represented by points in a high-dimensional space and concepts are represented by convex regions in this space. In this paper, we present our approach toward...
The cognitive framework of conceptual spaces [3] provides geometric means for representing knowledge. A conceptual space is a high-dimensional space whose dimensions are partitioned into so-called domains. Within each domain, the Euclidean metric is used to compute distances. Distances in the overall space are computed by applying the Manhattan met...
The cognitive framework of conceptual spaces [1] attempts to bridge the gap between symbolic and subsymbolic AI by proposing an intermediate conceptual layer based on geometric representations. A conceptual space is a high-dimensional space spanned by a number of quality dimensions representing interpretable features. Convex regions in this space c...
One common criticism of symbolic AI approaches is that the symbols on which these approaches operate do not contain any meaning: for the system, they are just arbitrary tokens that can be manipulated in some way. These tokens can only receive meaning though their interpretation by a human. This lack of inherent meaning in abstract symbols is descri...
This paper presents the NewsTeller system which retrieves a news event based on a user query and the user's general interests. It can be used by a social dialog system to initiate news-related small talk. The NewsTeller system is implemented as a pipeline with four stages: After collecting a large set of potentially relevant news events, a classifi...
Questions
Question (1)
In my artificial intelligence application, I am working in a high-dimensional space with the following metric: The set of dimensions is partitioned into domains and the distance between two points is computed by measuring the Euclidean distance with respect to each of these domains and then summing up these group-wise distances. This is basically a combination of the Euclidean (within-domain) and the Manhattan (between-domains) distances.
For my application, I need to compute the hypervolume of a hyperball in this space (i.e., the set of all points with a distance of less than r to the origin). I managed to find a formula for this hypervolume and also a mathematical proof for it. As I spent quite some time on developing this, I would like to publish my findings somewhere.
The problem is that the proof itself is not really related to artificial intelligence any more, so I highly doubt that any of the typical AI venues would publish this. It seems that this is more of a mathematical problem than anything else, but I don't know what could be an appropriate journal/conference/workshop for something like this.
If anyone can point me towards something, that would be greatly appreciated. Please let me also know if I need to elaborate more. Thanks in advance!
