{"id":9851,"date":"2024-02-08T17:29:19","date_gmt":"2024-02-08T17:29:19","guid":{"rendered":"https:\/\/dailyai.com\/?p=9851"},"modified":"2024-02-09T11:55:57","modified_gmt":"2024-02-09T11:55:57","slug":"symmetry-could-solve-small-dataset-woes-says-mit-researchers","status":"publish","type":"post","link":"https:\/\/dailyai.com\/da\/2024\/02\/symmetry-could-solve-small-dataset-woes-says-mit-researchers\/","title":{"rendered":"Symmetri kan l\u00f8se problemer med sm\u00e5 datas\u00e6t, siger MIT-forskere"},"content":{"rendered":"

MIT-forskere har fundet ud af, hvordan man ved at udnytte begrebet symmetri i datas\u00e6t kan reducere m\u00e6ngden af data, der skal bruges til at tr\u00e6ne modeller.<\/strong><\/p>\n

Denne opdagelse er dokumenteret i en unders\u00f8gelse kan hentes via ArXiv<\/a> af Behrooz Tahmasebi, ph.d.-studerende ved MIT, og hans vejleder, Stefanie Jegelka, lektor ved MIT,<\/span>\u00a0er forankret i en matematisk indsigt fra en \u00e5rhundrede gammel lov, der er kendt som Weyls lov.\u00a0<\/span><\/p>\n

Weyls lov, som oprindeligt blev formuleret af den tyske matematiker Hermann Weyl for over 110 \u00e5r siden, blev designet til at m\u00e5le kompleksiteten af spektral information, som f.eks. vibrationerne i musikinstrumenter.\u00a0<\/span><\/p>\n

Tahmasebi blev inspireret af denne lov, da han studerede differentialligninger, og s\u00e5 dens potentiale til at reducere kompleksiteten af datainput i neurale netv\u00e6rk. Ved at forst\u00e5 symmetrier i et datas\u00e6t kunne en maskinl\u00e6ringsmodel g\u00f8res mere effektiv og hurtigere uden at tilf\u00f8je flere data numerisk.\u00a0<\/span><\/p>\n

Tahmasebi og Jegelkas artikel forklarer, hvordan udnyttelse af symmetrier eller \"invarianser\" i datas\u00e6t kan forenkle maskinl\u00e6ringsopgaver, hvilket igen kr\u00e6ver mindre tr\u00e6ningsdata.\u00a0<\/span><\/p>\n

Det lyder meget komplekst, men princippet er relativt ligetil. T\u00e6nk f.eks. p\u00e5 bogstavet \"X\" - uanset om du roterer det eller vender det, ligner det stadig et \"X\". N\u00e5r modeller inden for maskinl\u00e6ring forst\u00e5r denne id\u00e9, kan de l\u00e6re mere effektivt. De indser, at selv om et billede af en kat bliver vendt p\u00e5 hovedet eller spejlet, viser det stadig en kat.<\/p>\n

Det hj\u00e6lper modellen med at g\u00f8re bedre brug af sine data, l\u00e6re af hvert eksempel p\u00e5 flere m\u00e5der og reducere behovet for en enorm m\u00e6ngde data for at opn\u00e5 pr\u00e6cise resultater.<\/p>\n

Denne unders\u00f8gelse g\u00e5r dog dybere end symmetri i konventionel forstand. Kernel Ridge Regression (KRR) invarians omfatter symmetriske transformationer som rotationer, refleksioner og andre dataegenskaber, der forbliver u\u00e6ndrede under specifikke operationer.<\/p>\n

\"S\u00e5 vidt jeg ved, er det f\u00f8rste gang, at Weyls lov er blevet brugt til at bestemme, hvordan maskinl\u00e6ring kan forbedres af symmetri,\" siger Tahmasebi.\u00a0<\/span><\/p>\n

Forskningen blev oprindeligt pr\u00e6senteret p\u00e5 konferencen Neural Information Processing Systems i december 2023.<\/span><\/p>\n

Det er is\u00e6r vigtigt inden for omr\u00e5der som computerbaseret kemi og kosmologi, hvor kvalitetsdata er begr\u00e6nsede. <\/span>Sparsomme data er almindelige<\/span><\/a> p\u00e5 omr\u00e5der, hvor datas\u00e6ttene er us\u00e6dvanligt store, men faktisk er de brugbare data i s\u00e6ttene meget begr\u00e6nsede.\u00a0<\/span><\/p>\n

I rummets uendelighed kan du for eksempel finde et lillebitte stykke brugbart data i et ufatteligt stort hav af ingenting.\u00a0-<\/strong> s\u00e5 du er n\u00f8dt til at f\u00e5 det lille stykke data til at fungere - og symmetri er et nyttigt v\u00e6rkt\u00f8j til at opn\u00e5 det.<\/p>\n

Soledad Villar, en anvendt matematiker ved Johns Hopkins University, bem\u00e6rkede om unders\u00f8gelsen: \"Modeller, der opfylder problemets symmetrier, er ikke kun korrekte, men kan ogs\u00e5 producere forudsigelser med mindre fejl ved hj\u00e6lp af en lille m\u00e6ngde tr\u00e6ningspunkter.\"\u00a0<\/span><\/p>\n

Fordele og resultater<\/h2>\n

Forskerne identificerede to typer forbedringer ved at bruge symmetrier: et line\u00e6rt boost, hvor effektiviteten stiger i forhold til symmetrien, og en eksponentiel gevinst, som giver en uforholdsm\u00e6ssig stor fordel, n\u00e5r man har at g\u00f8re med symmetrier, der sp\u00e6nder over flere dimensioner.\u00a0<\/span><\/p>\n

\"Det er et nyt bidrag, som dybest set fort\u00e6ller os, at symmetrier i h\u00f8jere dimensioner er vigtigere, fordi de kan give os en eksponentiel gevinst,\" uddyber Tahmasebi.<\/span><\/p>\n

Lad os se n\u00e6rmere p\u00e5 det:<\/span><\/p>\n

    \n
  1. Brug af symmetrier til at forbedre data<\/b>: Ved at genkende m\u00f8nstre eller symmetrier i data (f.eks. hvordan et objekt ser ens ud, selv n\u00e5r det roteres eller vendes), kan en maskinl\u00e6ringsmodel l\u00e6re, som om den har flere data, end den faktisk har. Denne tilgang \u00f8ger modellens effektivitet, s\u00e5 den kan l\u00e6re mere af mindre.<\/span><\/li>\n
  2. Forenkling af l\u00e6ringsopgaven<\/b>: Deres anden opdagelse handler om at g\u00f8re modellens funktioner lettere ved at fokusere p\u00e5 disse symmetrier. Da modellen l\u00e6rer at ignorere \u00e6ndringer, der ikke betyder noget (som f.eks. et objekts position eller retning), skal den h\u00e5ndtere mindre komplicerede oplysninger. Det betyder, at modellen kan opn\u00e5 gode resultater med f\u00e6rre eksempler, hvilket fremskynder l\u00e6ringsprocessen og forbedrer ydeevnen.<\/span><\/li>\n<\/ol>\n

    Haggai Maron, datalog ved Technion og NVIDIA, roste arbejdet for dets nye perspektiv, <\/span>fort\u00e6ller MIT<\/span><\/a>\"Dette teoretiske bidrag giver matematisk st\u00f8tte til det nye underomr\u00e5de 'Geometrisk dyb l\u00e6ring'.\"<\/span><\/p>\n

    Forskerne fremh\u00e6ver direkte den potentielle indvirkning p\u00e5 beregningskemi, hvor principperne fra deres unders\u00f8gelse f.eks. kan fremskynde l\u00e6gemiddelopdagelsesprocesser.\u00a0<\/span><\/p>\n

    Ved at udnytte symmetrier i molekyl\u00e6re strukturer kan maskinl\u00e6ringsmodeller forudsige interaktioner og egenskaber med f\u00e6rre datapunkter, hvilket g\u00f8r screening af potentielle l\u00e6gemiddelforbindelser hurtigere og mere effektiv.\u00a0<\/span><\/p>\n

    Symmetrier kan ogs\u00e5 hj\u00e6lpe med at analysere kosmiske f\u00e6nomener, hvor datas\u00e6ttene er ekstremt store, men hvor det er sparsomt med brugbare data.\u00a0<\/span><\/p>\n

    Eksempler kunne v\u00e6re at udnytte symmetrier til at studere kosmisk mikrob\u00f8lgebaggrundsstr\u00e5ling eller galaksernes struktur for at f\u00e5 mere indsigt ud af begr\u00e6nsede data.\u00a0<\/span><\/p>","protected":false},"excerpt":{"rendered":"

    MIT-forskere har fundet ud af, hvordan man ved at udnytte begrebet symmetri i datas\u00e6t kan reducere m\u00e6ngden af data, der skal bruges til at tr\u00e6ne modeller. Denne opdagelse, som er dokumenteret i en unders\u00f8gelse, der kan hentes via ArXiv, af Behrooz Tahmasebi, en ph.d.-studerende ved MIT, og hans r\u00e5dgiver, Stefanie Jegelka, lektor ved MIT, har rod i en matematisk indsigt fra en \u00e5rhundrede gammel lov, der er kendt som Weyls lov. Weyls lov, der oprindeligt blev formuleret af den tyske matematiker Hermann Weyl for over 110 \u00e5r siden, blev designet til at m\u00e5le kompleksiteten af spektral information, som f.eks. vibrationerne i musikinstrumenter. Inspireret af denne lov, mens han studerede differentialligninger, s\u00e5 Tahmasebi<\/p>","protected":false},"author":2,"featured_media":9852,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[84],"tags":[298,105],"class_list":["post-9851","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-industry","tag-astronomy","tag-machine-learning"],"yoast_head":"\nSymmetry could solve small dataset woes, says MIT researchers | DailyAI<\/title>\n<meta name=\"description\" content=\"MIT researchers have uncovered how leveraging the concept of symmetry within datasets can reduce the volume of data needed for training models.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" 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