{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,12]],"date-time":"2026-05-12T22:23:37Z","timestamp":1778624617798,"version":"3.51.4"},"reference-count":40,"publisher":"The Royal Society","issue":"1791","license":[{"start":{"date-parts":[[2019,12,16]],"date-time":"2019-12-16T00:00:00Z","timestamp":1576454400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/royalsociety.org\/journals\/ethics-policies\/data-sharing-mining\/"}],"funder":[{"DOI":"10.13039\/501100003246","name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek","doi-asserted-by":"crossref","award":["016.Vidi.188.029"],"award-info":[{"award-number":["016.Vidi.188.029"]}],"id":[{"id":"10.13039\/501100003246","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["royalsocietypublishing.org"],"crossmark-restriction":true},"short-container-title":["Phil. Trans. R. Soc. B"],"published-print":{"date-parts":[[2020,2,3]]},"abstract":"<jats:p>\n                    Neither neurobiological nor process models of meaning composition specify the operator through which constituent parts are bound together into compositional structures. In this paper, we argue that a neurophysiological computation system cannot achieve the compositionality exhibited in human thought and language if it were to rely on a multiplicative operator to perform binding, as the tensor product (TP)-based systems that have been widely adopted in cognitive science, neuroscience and artificial intelligence do. We show via simulation and two behavioural experiments that TPs violate variable-value independence, but human behaviour does not. Specifically, TPs fail to capture that in the statements\n                    <jats:italic>fuzzy cactus<\/jats:italic>\n                    and\n                    <jats:italic>fuzzy penguin<\/jats:italic>\n                    , both cactus and penguin are predicated by\n                    <jats:italic>fuzzy<\/jats:italic>\n                    (x) and belong to the set of fuzzy things, rendering these arguments similar to each other. Consistent with that thesis, people judged arguments that shared the same role to be similar, even when those arguments themselves (e.g., cacti and penguins) were judged to be dissimilar when in isolation. By contrast, the similarity of the TPs representing\n                    <jats:italic>fuzzy<\/jats:italic>\n                    (cactus) and\n                    <jats:italic>fuzzy<\/jats:italic>\n                    (penguin) was determined by the similarity of the arguments, which in this case approaches zero. Based on these results, we argue that neural systems that use TPs for binding cannot approximate how the human mind and brain represent compositional information during processing. We describe a contrasting binding mechanism that any physiological or artificial neural system could use to maintain independence between a role and its argument, a prerequisite for compositionality and, thus, for instantiating the expressive power of human thought and language in a neural system.\n                  <\/jats:p>\n                  <jats:p>This article is part of the theme issue \u2018Towards mechanistic models of meaning composition\u2019.<\/jats:p>","DOI":"10.1098\/rstb.2019.0306","type":"journal-article","created":{"date-parts":[[2019,12,16]],"date-time":"2019-12-16T06:06:28Z","timestamp":1576476388000},"page":"20190306","update-policy":"https:\/\/doi.org\/10.1098\/crossmark-policy","source":"Crossref","is-referenced-by-count":24,"title":["Tensors and compositionality in neural systems"],"prefix":"10.1098","volume":"375","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3395-7234","authenticated-orcid":true,"given":"Andrea E.","family":"Martin","sequence":"first","affiliation":[{"name":"Max Planck Institute for Psycholinguistics, Wundtlaan 1, 6525 XD Nijmegen, The Netherlands"},{"name":"Donders Center for Cognitive Neuroimaging, Radboud University, 6525 EN Nijmegen, The Netherlands"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Leonidas A. A.","family":"Doumas","sequence":"additional","affiliation":[{"name":"School of Philosophy, Psychology, and Language Sciences, The University of Edinburgh, 7 George Square, EH8 9JZ, Edinburgh, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"175","published-online":{"date-parts":[[2019,12,16]]},"reference":[{"key":"e_1_3_8_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/bs.plm.2018.10.002"},{"key":"e_1_3_8_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/0010-0277(88)90031-5"},{"key":"e_1_3_8_4_2","doi-asserted-by":"publisher","DOI":"10.1080\/09540091.2011.569880"},{"key":"e_1_3_8_5_2","doi-asserted-by":"publisher","DOI":"10.3389\/fpsyg.2016.00120"},{"key":"e_1_3_8_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cobeha.2019.04.008"},{"key":"e_1_3_8_7_2","doi-asserted-by":"publisher","DOI":"10.7551\/mitpress\/11265.001.0001"},{"key":"e_1_3_8_8_2","doi-asserted-by":"publisher","DOI":"10.1093\/acprof:oso\/9780198270126.001.0001"},{"key":"e_1_3_8_9_2","doi-asserted-by":"publisher","DOI":"10.1098\/rstb.2019.0303"},{"key":"e_1_3_8_10_2","unstructured":"Coecke B Sadrzadeh M Clark S. 2010 Mathematical foundations for a compositional distributional model of meaning. arXiv preprint arXiv:1003. 4394."},{"key":"e_1_3_8_11_2","first-page":"73","volume-title":"The Cambridge handbook of thinking and reasoning","author":"Doumas LA","year":"2005"},{"key":"e_1_3_8_12_2","doi-asserted-by":"publisher","DOI":"10.1111\/j.1747-9991.2009.00228.x"},{"key":"e_1_3_8_13_2","doi-asserted-by":"publisher","DOI":"10.1075\/sihols.82"},{"key":"e_1_3_8_14_2","volume-title":"An investigation of the laws of thought: on which are founded the mathematical theories of logic and probabilities","author":"Boole G","year":"1854"},{"key":"e_1_3_8_15_2","volume-title":"Die Grundlagen der Arithmetik: eine logisch mathematische Untersuchung \u00fcber den begriff der zahl","author":"Frege G","year":"1884"},{"key":"e_1_3_8_16_2","volume-title":"Plato's sophist","author":"Plato","year":"1990"},{"key":"e_1_3_8_17_2","volume-title":"Tractatus logico-philosophicus","author":"Wittgenstein L","year":"1922"},{"key":"e_1_3_8_18_2","volume-title":"Semantics in generative grammar","author":"Kratzer A","year":"1998"},{"key":"e_1_3_8_19_2","first-page":"203","article-title":"Montague grammar and transformational grammar","volume":"6","author":"Partee B","year":"1975","journal-title":"Linguistic inquiry"},{"key":"e_1_3_8_20_2","first-page":"541","volume-title":"Quantification in natural languages","author":"Partee BH","year":"1995"},{"key":"e_1_3_8_21_2","doi-asserted-by":"publisher","DOI":"10.1515\/9783112316009"},{"key":"e_1_3_8_22_2","unstructured":"von Humboldt WF. 1836 Uber die Verschiedenheit desmenschlichen Sprachbaues und ihren Einfluss auf die geistige Entwickelung des Menschengeschlechts. (Lettre \u00e0 M. Jacquet sur les alphabets de la Polyn\u00e9sie Asiatique. ). Bonn Germany: F. D\u00fcmmler. See https:\/\/archive.org\/details\/berdieverschied00humbgoog\/page\/n15."},{"key":"e_1_3_8_23_2","volume-title":"The big book of concepts","author":"Murphy G","year":"2004"},{"key":"e_1_3_8_24_2","doi-asserted-by":"publisher","DOI":"10.1080\/09540098908915629"},{"key":"e_1_3_8_25_2","unstructured":"Plate TA. 1991 Holographic reduced representations: convolution algebra for compositional distributed representations. Technical Report. CRG-TR-91-1 University of Toronto."},{"key":"e_1_3_8_26_2","doi-asserted-by":"publisher","DOI":"10.1016\/0004-3702(90)90007-M"},{"key":"e_1_3_8_27_2","volume-title":"The harmonic mind: from neural computation to optimality-theoretic grammar (cognitive architecture)","author":"Smolensky P","year":"2006"},{"key":"e_1_3_8_28_2","doi-asserted-by":"publisher","DOI":"10.1016\/0010-0277(90)90014-B"},{"key":"e_1_3_8_29_2","first-page":"229","volume-title":"Cognitive dynamics: conceptual and representational change in humans and machines","author":"Holyoak KJ","year":"2000"},{"key":"e_1_3_8_30_2","doi-asserted-by":"crossref","first-page":"52","DOI":"10.1093\/oxfordhb\/9780199734689.013.0005","volume-title":"Oxford handbook of thinking and reasoning","author":"Doumas LAA","year":"2012"},{"key":"e_1_3_8_31_2","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pbio.2000663"},{"key":"e_1_3_8_32_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0896-6273(00)80821-1"},{"key":"e_1_3_8_33_2","doi-asserted-by":"publisher","DOI":"10.1016\/0959-4388(95)80014-X"},{"key":"e_1_3_8_34_2","doi-asserted-by":"publisher","DOI":"10.1037\/0033-295X.115.1.1"},{"key":"e_1_3_8_35_2","doi-asserted-by":"publisher","DOI":"10.1037\/0033-295X.104.3.427"},{"key":"e_1_3_8_36_2","doi-asserted-by":"publisher","DOI":"10.1037\/0033-295X.110.2.220"},{"key":"e_1_3_8_37_2","doi-asserted-by":"publisher","DOI":"10.1109\/72.377968"},{"key":"e_1_3_8_38_2","article-title":"Distributed representations of words and phrases and their compositionality)","author":"Mikolov T","year":"2013","journal-title":"arXiv preprint"},{"key":"e_1_3_8_39_2","doi-asserted-by":"crossref","first-page":"195","DOI":"10.7551\/mitpress\/4117.001.0001","volume-title":"Language in mind: advances in the study of language and thought","author":"Gentner D","year":"2003"},{"key":"e_1_3_8_40_2","volume-title":"The foundations of mind: origins of conceptual thought","author":"Mandler JM","year":"2004"},{"key":"e_1_3_8_41_2","doi-asserted-by":"publisher","DOI":"10.1093\/acprof:oso\/9780195301069.001.0001"}],"container-title":["Philosophical Transactions of the Royal Society B: Biological Sciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/royalsocietypublishing.org\/doi\/pdf\/10.1098\/rstb.2019.0306","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/royalsocietypublishing.org\/doi\/full-xml\/10.1098\/rstb.2019.0306","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/royalsocietypublishing.org\/doi\/pdf\/10.1098\/rstb.2019.0306","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,12]],"date-time":"2026-05-12T21:26:16Z","timestamp":1778621176000},"score":1,"resource":{"primary":{"URL":"http:\/\/royalsocietypublishing.org\/rstb\/article\/23718"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,12,16]]},"references-count":40,"journal-issue":{"issue":"1791","published-print":{"date-parts":[[2020,2,3]]}},"alternative-id":["10.1098\/rstb.2019.0306"],"URL":"https:\/\/doi.org\/10.1098\/rstb.2019.0306","relation":{},"ISSN":["0962-8436","1471-2970"],"issn-type":[{"value":"0962-8436","type":"print"},{"value":"1471-2970","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,12,16]]},"assertion":[{"value":"2019-07-02","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2019-12-16","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}