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The work motivates embeddings from psychometric and cognitive foundations, grounding vector representations in semantic similarity derived from word association tasks. It proposes a theoretical framework that treats word embedding recovery as metric recovery, unifying existing algorithms via co-occurrence counts from Markov random walks on graphs and manifolds, and introducing a direct metric-recovery algorithm.",{"@graph":69,"@context":123},[70,84,106],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/word-graph-and-manifold-embedding-from-markov-processes/267063/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/word-graph-and-manifold-embedding-from-markov-processes/267063.png","ImageObject",300,407,{"name":92,"@type":93},"Gloria","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-28","2026-09-14",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",11,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"Why do the authors connect word embeddings to analogical reasoning?","Question",{"text":113,"@type":114},"They argue that analogy performance can be explained as similarity judgments in semantic spaces, where vector relations correspond to operations in metric embeddings.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"What is the proposed theoretical framework for word embeddings?",{"text":118,"@type":114},"The authors propose interpreting word embeddings as manifold learning and focusing on metric recovery as the central object of study.",{"name":120,"@type":111,"acceptedAnswer":121},"How do Markov random walks and co-occurrence counts fit into the method?",{"text":122,"@type":114},"They unify existing embedding algorithms as consistent metric recovery methods based on co-occurrence counts obtained from simple Markov random walks over graphs and manifolds.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},267063,1789414363,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":29,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":130,"read_time":144,"preview_page_count":4},2336474459895,"https://ap-avatar.wpscdn.com/avatar/22000baeef7a5ed0655?x-image-process=image/resize,m_fixed,w_180,h_180&k=1786071322749376916","Word, graph and manifold embedding from Markov processes  \nTatsunori B. Hashimoto  \nMIT CSAIL  \n[thashim@csail.mit.edu](thashim@csail.mit.edu)  \nDavid Alvarez-Melis  \nMIT CSAIL  \n[davidam@csail.mit.edu](davidam@csail.mit.edu)  \nTommi S. Jaakkola  \nMIT CSAIL  \n[tommi@mit.edu](tommi@mit.edu)  \nThis is an extended abstract of a preprint [6] containing full technical details.  \n1 Introduction  \nContinuous space models of words, objects, and signals have proven to be powerful tools for learning expressive representations of data, and been adopted across areas, from natural language processing to computer vision. Recently, there has been particular interest in word embeddings, largely due to their intriguing semantic properties [12] and their successful use as features for downstream NLP tasks [22, 19] . Embedding methods based on neural networks [3, 14, 12] have been at the forefront of this trend thanks to their simplicity, scalability and semantically-rich embeddings, but other nonparametric embedding methods have proven to share similar properties [9] .  \nDespite their empirical success, understanding of word embeddings has lagged behind. Recent work has started to fill this gap, seeking better understanding of these representations, their properties, and associated algorithms [9, 4, 10, 1] . Yet, some questions are not fully answered yet. For example, it has been widely demonstrated that word embeddings can be used to solve analogy tasks. What remains to be explained is why: how is it that analytical reasoning, a complex cognitive process, can be replicated with simple operations on vector representations of words? We attempt to provide an explanation for this, by drawing a connection between the cognitive perspective of analogical reasoning, semantic similarities and the embedding of cooccurrence counts.  \nIn this work we extend both the conceptual and theoretical understanding of word embeddings. First, we motivate them by examining the psychometric and cognitive basis for embeddings. In particular, we ground embeddings in semantic spaces, and revisit word vector representations derived from word association tasks, which were shown to be have similar linear structure as those shown by modern methods. Second, we propose a new theoretical framework for understanding word embeddings as a type of manifold learning. In contrast to prior work [1], we take metric recovery as the key object of study, unifying existing algorithms as consistent metric recovery methods based on co-occurrence counts from simple Markov random walks over graphs and manifolds, and propose anew algorithm which directly recovers an underlying metric.  \n2 Word vectors and semantic spaces  \nThe conceptual motivation of most current word embedding relies largely on the distributional hypothesis [5]: words appearing in similar contexts tend to have similar meanings. Hence, word co-occurrence counts lie at the heart of all these approaches. But besides linguistics, word cooccurrences and their relationship with semantics also play a central role in psychometrics and cognitive science, where semantic similarity has long been studied [18, 20], often by means of free word association tasks and semantic spaces, i.e., vector spaces where semantically related words are close to each other. Yet, this rich literature seems to have been largely overlooked by recent work on word embeddings.  \nAnalogy  \n\n| B\u003Cbr>\u003Cbr>| I\u003Cbr> D1\u003Cbr>|  |\n| --- | --- | --- |\n| A | \u003Cbr>C |  D3\u003Cbr>|\n\nD2  \nD4  \nSeries Completion  \nClassi􀀌cation  \n\n| A\u003Cbr>\u003Cbr>I  | C\u003Cbr>| \u003Cbr> D3 |\n| --- | --- | --- |\n|  | \u003Cbr> D1 | D2 |\n| \u003Cbr>B |  |  |\n\nD4  \nFigure 1: Sternberg's model for inductive reasoning in semantic space. A, B, C are given, I is the ideal point and D are the choices. The correct answer is shaded green. Adapted from [20] .  \nSemantic spaces such as those used in the psychometrics literature provide a natural conceptual framework for continuous word representations. For one, the intriguing observa","cbCaikTdsraFMFSA","https://ap.wps.com/l/cbCaikTdsraFMFSA","pdf",1061003,"English","# Introduction\n## Word embeddings and semantic properties\n## Motivation from cognitive/psychometric perspectives\n# Word vectors and semantic spaces\n## Distributional hypothesis and co-occurrence counts\n## Semantic spaces and analogy reasoning","[{\"question\":\"Why do the authors connect word embeddings to analogical reasoning?\",\"answer\":\"They argue that analogy performance can be explained as similarity judgments in semantic spaces, where vector relations correspond to operations in metric embeddings.\"},{\"question\":\"What is the proposed theoretical framework for word embeddings?\",\"answer\":\"The authors propose interpreting word embeddings as manifold learning and focusing on metric recovery as the central object of study.\"},{\"question\":\"How do Markov random walks and co-occurrence counts fit into the method?\",\"answer\":\"They unify existing embedding algorithms as consistent metric recovery methods based on co-occurrence counts obtained from simple Markov random walks over graphs and manifolds.\"}]","Word, graph and manifold embedding from Markov processes | PDF",15]