{"id":811033,"date":"2022-01-11T14:20:50","date_gmt":"2022-01-11T22:20:50","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/?post_type=msr-project&#038;p=811033"},"modified":"2022-01-11T14:21:10","modified_gmt":"2022-01-11T22:21:10","slug":"rm-roles","status":"publish","type":"msr-project","link":"https:\/\/www.microsoft.com\/en-us\/research\/project\/rm-roles\/","title":{"rendered":"RM Roles"},"content":{"rendered":"<section class=\"mb-3 moray-highlight\">\n\t<div class=\"card-img-overlay mx-lg-0\">\n\t\t<div class=\"card-background bg-gray-200 has-background- card-background--full-bleed\">\n\t\t\t\t\t<\/div>\n\t\t<!-- Foreground -->\n\t\t<div class=\"card-foreground d-flex mt-md-n5 my-lg-5 px-g px-lg-0\">\n\t\t\t<!-- Container -->\n\t\t\t<div class=\"container d-flex mt-md-n5 my-lg-5 align-self-center\">\n\t\t\t\t<!-- Card wrapper -->\n\t\t\t\t<div class=\"w-100 w-lg-col-5\">\n\t\t\t\t\t<!-- Card -->\n\t\t\t\t\t<div class=\"card material-md-card py-5 px-md-5\">\n\t\t\t\t\t\t<div class=\"card-body \">\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\n<h1 id=\"rm-roles\">RM Roles<\/h1>\n\n\n\n<p> Can we encode tree structures into Tensor Product Representations (TPR&#8217;s) where the rank of the TPR doesn&#8217;t grow with the depth of the tree? <\/p>\n\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/div>\n\t<\/div>\n<\/section>\n\n\n\n\n\n<p>Can we encode tree structures into Tensor Product Representations (TPR&#8217;s) where the rank of the TPR doesn&#8217;t grow with the depth of the tree?\u00a0 This project develops a new technique called Recursive Matrix Roles to generate child roles from a given parent role (and with the same dimensionality as the parent role).\u00a0 After allocating a fixed set of roles for the first level children, this technique allows the remaining child roles of a tree to be dynamically allocated in a predictable (and learnable) way.\u00a0 Two proof-of-concept examples are developed using the technique: beta reduction and tree adjoining.<\/p>\n\n\n","protected":false},"excerpt":{"rendered":"<p>Can we encode tree structures into Tensor Product Representations (TPR&#8217;s) where the rank of the TPR doesn&#8217;t grow with the depth of the tree? Can we encode tree structures into Tensor Product Representations (TPR&#8217;s) where the rank of the TPR doesn&#8217;t grow with the depth of the tree?\u00a0 This project develops a new technique called [&hellip;]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","footnotes":""},"research-area":[13556],"msr-locale":[268875],"msr-impact-theme":[],"msr-pillar":[],"class_list":["post-811033","msr-project","type-msr-project","status-publish","hentry","msr-research-area-artificial-intelligence","msr-locale-en_us","msr-archive-status-active"],"msr_project_start":"2020-11-03","related-publications":[],"related-downloads":[],"related-videos":[],"related-groups":[],"related-events":[],"related-opportunities":[],"related-posts":[],"related-articles":[],"tab-content":[],"slides":[],"related-researchers":[{"type":"guest","display_name":"Coleman Haley","user_id":811018,"people_section":"Section name 0","alias":""},{"type":"user_nicename","display_name":"Paul Smolensky","user_id":36353,"people_section":"Section name 0","alias":"psmo"},{"type":"user_nicename","display_name":"Jianfeng Gao","user_id":32246,"people_section":"Section name 0","alias":"jfgao"}],"msr_research_lab":[],"msr_impact_theme":[],"_links":{"self":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-project\/811033","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-project"}],"about":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/types\/msr-project"}],"version-history":[{"count":1,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-project\/811033\/revisions"}],"predecessor-version":[{"id":811036,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-project\/811033\/revisions\/811036"}],"wp:attachment":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media?parent=811033"}],"wp:term":[{"taxonomy":"msr-research-area","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/research-area?post=811033"},{"taxonomy":"msr-locale","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-locale?post=811033"},{"taxonomy":"msr-impact-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-impact-theme?post=811033"},{"taxonomy":"msr-pillar","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-pillar?post=811033"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}