Prevalence and recoverability of syntactic parameters in sparse distributed memories

Park, Jeong Joon; Boettcher, Ronnel; Zhao, Andrew; Mun, Alex; Yuh, K.A.; Kumar, Vibhor; Marcolli, Matilde

doi:10.48550/arxiv.1510.06342

Cited by 2 publications

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“…The fact that different syntactic parameters have very different frequencies of occurrence among world languages certainly suggests otherwise. We will return to this point in §6 and suggest a possible approach, based on the results of [26], to correct, at least in part, for this problem.…”

Section: Phylogenetic Algebraic Geometrymentioning

confidence: 99%

“…How detectable are relations between syntactic parameters computationally? Recently, a mathematical approach to these questions was proposed in [22], [26], [29], [32].…”

Section: Dependencies and Geometrymentioning

confidence: 99%

“…In [26], it was shown that, to some extent, the presence of dependencies between the syntactic parameters listed in the SSWL database can be detected using Kanerva networks. The latter were introduced in [16] as sparse distributed memories aimed at modeling associative memory in neuroscience.…”

Section: Dependencies and Geometrymentioning

confidence: 99%

“…A main open problems in the parameteric approach for comparative generative grammar is understanding the space of syntactic parameters, identifying dependence relations between parameters and possibly identifying a fundamental set of such variables that would represent a good system of coordinates for the space of languages. Recently, the use of mathematical methods for the study of the space of syntactic parameters of world languages was proposed in [26], [29], [32].…”

Section: Introductionmentioning

confidence: 99%

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Syntactic Phylogenetic Trees

Shu

Aziz

Huynh

et al. 2018

Foundations of Mathematics and Physics One Century After Hilbert

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In light of recent controversies surrounding the use of computational methods for the reconstruction of phylogenetic trees of language families (especially the Indo-European family), a possible approach based on syntactic information, complementing other linguistic methods, appeared as a promising possibility, largely developed in recent years in Longobardi's Parametric Comparison Method. In this paper we identify several serious problems that arise in the use of syntactic data from the SSWL database for the purpose of computational phylogenetic reconstruction. We show that the most naive approach fails to produce reliable linguistic phylogenetic trees. We identify some of the sources of the observed problems and we discuss how they may be, at least partly, corrected by using additional information, such as prior subdivision into language families and subfamilies, and a better use of the information about ancient languages. We also describe how the use of phylogenetic algebraic geometry can help in estimating to what extent the probability distribution at the leaves of the phylogenetic tree obtained from the SSWL data can be considered reliable, by testing it on phylogenetic trees established by other forms of linguistic analysis. In simple examples, we find that, after restricting to smaller language subfamilies and considering only those SSWL parameters that are fully mapped for the whole subfamily, the SSWL data match extremely well reliable phylogenetic trees, according to the evaluation of phylogenetic invariants. This is a promising sign for the use of SSWL data for linguistic phylogenetics. We also argue how dependencies and nontrivial geometry/topology in the space of syntactic parameters would have to be taken into consideration in phylogenetic reconstructions based on syntactic data. A more detailed analysis of syntactic phylogenetic trees and their algebro-geometric invariants will appear elsewhere.

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Section: Phylogenetic Algebraic Geometrymentioning

confidence: 99%

“…How detectable are relations between syntactic parameters computationally? Recently, a mathematical approach to these questions was proposed in [22], [26], [29], [32].…”

Section: Dependencies and Geometrymentioning

confidence: 99%

Section: Dependencies and Geometrymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Syntactic Phylogenetic Trees

Shu

Aziz

Huynh

et al. 2018

Foundations of Mathematics and Physics One Century After Hilbert

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“…In the case of syntactic parameters behaving as independent variables, in the low temperature regime (see [17] for a discussion of the interpretation of the temperature parameter in this model) the dynamics converges rapidly towards an equilibrium state where all the spin variables corresponding to a given syntactic feature for the various languages align to the value most prevalent in the initial configuration. The SSWL database does not record relations between parameters, although it can be shown by other approaches that interesting relations are present, see [14], [15]. Using syntactic data from [6], [7], which record explicit entailment relation between different parameter, it was shown in [17], for small graph examples, that in the presence of relations the dynamics settles on equilibrium states that are not necessarily given by completely aligned spins.…”

Section: Dynamics In the Space Of Code Parametersmentioning

confidence: 99%

Syntactic Structures and Code Parameters

Shu

Marcolli

2017

Math.Comput.Sci.

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Abstract. We assign binary and ternary error-correcting codes to the data of syntactic structures of world languages and we study the distribution of code points in the space of code parameters. We show that, while most codes populate the lower region approximating a superposition of Thomae functions, there is a substantial presence of codes above the Gilbert-Varshamov bound and even above the asymptotic bound and the Plotkin bound. We investigate the dynamics induced on the space of code parameters by spin glass models of language change, and show that, in the presence of entailment relations between syntactic parameters the dynamics can sometimes improve the code. For large sets of languages and syntactic data, one can gain information on the spin glass dynamics from the induced dynamics in the space of code parameters.

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Prevalence and recoverability of syntactic parameters in sparse distributed memories

Cited by 2 publications

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Syntactic Phylogenetic Trees

Syntactic Phylogenetic Trees

Syntactic Structures and Code Parameters

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