Geometry and Meaning

By Dominic Widdows. Computational Linguistics, 2004

325 citations recorded by the source corpus.

From Pythagoras's harmonic sequence to Einstein's theory of relativity, geometric models of position, proximity, ratio, and the underlying properties of physical space have provided us with powerful ideas and accurate scientific tools. Currently, similar geometric models are being applied to another type of space the conceptual space of information and meaning, where the contributions of Pythagoras and Einstein are a part of the landscape itself. The rich geometry of conceptual space can be glimpsed, for instance, in internet documents: while the documents themselves define a structure of visual layouts and point-to-point links, search engines create an additional structure by matching keywords to nearby documents in a spatial arrangement of content. What the "Geometry of Meaning" provides is a much-needed exploration of computational techniques to represent meaning and of the conceptual spaces on which these representations are founded."

Subfields: Theoretical Computer Science

View Paper: https://www.semanticscholar.org/paper/36eff99a7f23cec395e4efc80ff7f937934c7be6

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In Theoretical Computer Science

Citations in the corpus

Semantic Vector Products: Some Initial Investigations (2008, methodology): “…they were performed using vectors from large empirical semantic vector spaces built using the 100 million word British National Corpus 1 and the Infomap NLP soft- ware 2 , which uses singular value decomposition to create a reduced wordspace from a large cooccurrence matrix (Widdows 2004, Ch 6).”
Quantum Models of Cognition and Decision (2012, methodology): “Viewing concepts from a geometric perspective opens the door to modelling via a quantum-theoretic approach (Gabora & Aerts, 2002; Aerts & Czachor, 2004; Widdows, 2004; Aerts & Gabora, 2005; Bruza & Cole, 2005; Gabora et al., 2008).”
Distributional Memory: A General Framework for Corpus-Based Semantics (2010, unknown): “…research areas such as neural systems (Smolensky 1990; Smolensky and Legendre 2006), quantum information (Widdows and Peters 2003; Aerts and Czachor 2004; Widdows 2004; Van Rijsbergen 2004; Bruza and Cole 2005; Hou and Song 2009), holographic models of memory (Jones and Mewhort 2007), and so on.”
What Does It Mean to Span Cultural Boundaries? Variety and Atypicality in Cultural Consumption (2016, methodology): “We address this question by building on a geometric model of conceptual space (Gärdenfors 2004; Kovács and Hannan 2015; Pontikes and Hannan 2014; Widdows 2004).”
Vector Space Models of Lexical Meaning (2015, background): “There is some preliminary work in this direction, e.g. (Preller & Sadrzadeh, 2009; Clarke, 2008; Widdows, 2004 ), and the question is creating substantial interest in the computational linguistics community; see e.g. the 2013 workshop Towards a Formal Distributional Semantics, attached to the 10th…”
Category-theoretic quantitative compositional distributional models of natural language semantics (2013, unknown): “used for this branch of physics and those potentially useful for linguistic modelling has been noted by several sources, such as [86, 54, 83].”
An ecology of social categories. (2014, background): “…a familiar example of producers actively playing both roles, as researchers frequently alternate between author and reviewer roles. sociological science | www.sociologicalscience.com 313 August 2014 | Volume 1 ations of what Gärdenfors (2004) calls conceptual spaces (see also Widdows 2004).”
Combining Symbolic and Distributional Models of Meaning (2007, background): “Some limited kind of compositionality has perhaps been demonstrated by (Widdows 2004) who showed that a kind of negation on word senses could be defined in vector space drinks John beer quickly strong eats Mary potatoes big green subj obj adv adj subj obj adj adj Figure 1: Example dependency trees…”
From Frequency to Meaning: Vector Space Models of Semantics (2010, background): “Widdows (2004) gives a gentle introduction to vectors from the perspective of semantics.”
Symbol Interdependency in Symbolic and Embodied Cognition (2011, methodology): “Keywords: Symbolic; Embodied; Amodal; Modal; Perceptual simulations; Symbol interdependency; LSA; Semantic knowledge”
Quantum Structure in Cognition (2008, methodology): “Quantum mechanics has also been used in the domain of information retrieval (Widdows, 2003, 2006; Widdows & Peters, 2003; Van Rijsbergen, 2004), and here it is more specifically the quantum logic structure underlying quantum mechanics that has proved effective in producing theoretical models for…”
Experimental Support for a Categorical Compositional Distributional Model of Meaning (2011, background): “This setting offers geometric means to reason about semantic similarity ( e.g. via cosine measure or k -means clustering), as discussed in Widdows (2005).”