{"id":338,"date":"2008-02-07T23:38:07","date_gmt":"2008-02-08T04:38:07","guid":{"rendered":"http:\/\/www.randomideas.net\/?p=338"},"modified":"2008-02-07T23:38:07","modified_gmt":"2008-02-08T04:38:07","slug":"manifold-learning-to-derive-symbolic-rules","status":"publish","type":"post","link":"http:\/\/randomideas.net\/?p=338","title":{"rendered":"Manifold Learning to derive symbolic rules"},"content":{"rendered":"<p>As I mentioned before, the way I see manifold learning is as a statistical model of the concept of abstraction. Give a manifold learning algorithm a dataset with rotating teapots and it&#8217;ll give you back a manifold with one parameter: the angle of rotation. It no longer compares voxels; it compares <i>teapots<\/i>, which is <i>really<\/i> cool.<\/p>\n<p>So what would happen if we gave it symbolic rules? Encoding them meaningfully would be a non-trivial issue &#8211; I&#8217;m not certain it&#8217;s enough to use, say, Godel numbering &#8211; but if we could accomplish this, what would the output be? What do the rules describe, exactly? Mere symbols? Or is there some underlying concept behind the rules? Could the algorithm abstract away the symbols to get at the heart of these concepts?<\/p>\n","protected":false},"excerpt":{"rendered":"<p>As I mentioned before, the way I see manifold learning is as a statistical model of the concept of abstraction. Give a manifold learning algorithm a dataset with rotating teapots and it&#8217;ll give you back a manifold with one parameter: the angle of rotation. It no longer compares voxels; it compares teapots, which is really [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[6,16],"tags":[],"class_list":["post-338","post","type-post","status-publish","format-standard","hentry","category-ideas","category-research"],"_links":{"self":[{"href":"http:\/\/randomideas.net\/index.php?rest_route=\/wp\/v2\/posts\/338","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/randomideas.net\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/randomideas.net\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/randomideas.net\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/randomideas.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=338"}],"version-history":[{"count":0,"href":"http:\/\/randomideas.net\/index.php?rest_route=\/wp\/v2\/posts\/338\/revisions"}],"wp:attachment":[{"href":"http:\/\/randomideas.net\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=338"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/randomideas.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=338"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/randomideas.net\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=338"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}