{"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\/sv\/2024\/02\/symmetry-could-solve-small-dataset-woes-says-mit-researchers\/","title":{"rendered":"Symmetri kan l\u00f6sa problemen med sm\u00e5 dataset, s\u00e4ger MIT-forskare"},"content":{"rendered":"

MIT-forskare har uppt\u00e4ckt hur man genom att utnyttja begreppet symmetri inom dataset kan minska den datavolym som beh\u00f6vs f\u00f6r att tr\u00e4na modeller.<\/strong><\/p>\n

Denna uppt\u00e4ckt, som dokumenterats i en studie kan h\u00e4mtas via ArXiv<\/a> av Behrooz Tahmasebi, doktorand vid MIT, och hans handledare Stefanie Jegelka, docent vid MIT,<\/span>\u00a0har sina r\u00f6tter i en matematisk insikt fr\u00e5n en hundra \u00e5r gammal lag som kallas Weyls lag.\u00a0<\/span><\/p>\n

Weyls lag, som ursprungligen formulerades av den tyske matematikern Hermann Weyl f\u00f6r \u00f6ver 110 \u00e5r sedan, utformades f\u00f6r att m\u00e4ta komplexiteten i spektral information, t.ex. vibrationerna i musikinstrument.\u00a0<\/span><\/p>\n

Tahmasebi blev inspirerad av denna lag n\u00e4r han studerade differentialekvationer och s\u00e5g dess potential att minska komplexiteten i datainmatningen till neurala n\u00e4tverk. Genom att f\u00f6rst\u00e5 de symmetrier som finns i ett dataset kan en maskininl\u00e4rningsmodell g\u00f6ras effektivare och snabbare utan att man beh\u00f6ver l\u00e4gga till mer data numeriskt.\u00a0<\/span><\/p>\n

Tahmasebi och Jegelkas artikel f\u00f6rklarar hur man genom att utnyttja symmetrier, eller \"invarianter\", inom dataset kan f\u00f6renkla maskininl\u00e4rningsuppgifter, vilket i sin tur kr\u00e4ver mindre tr\u00e4ningsdata.\u00a0<\/span><\/p>\n

Det l\u00e5ter v\u00e4ldigt komplext, men principen \u00e4r relativt enkel. T\u00e4nk till exempel p\u00e5 bokstaven \"X\" - oavsett om du roterar den eller v\u00e4nder den, ser den fortfarande ut som en \"X\". N\u00e4r modeller inom maskininl\u00e4rning f\u00f6rst\u00e5r den h\u00e4r id\u00e9n kan de l\u00e4ra sig mer effektivt. De inser att \u00e4ven om en bild av en katt v\u00e4nds upp och ner eller speglas, s\u00e5 visar den fortfarande en katt.<\/p>\n

Detta hj\u00e4lper modellen att anv\u00e4nda sina data p\u00e5 ett b\u00e4ttre s\u00e4tt, l\u00e4ra sig av varje exempel p\u00e5 flera s\u00e4tt och minska behovet av en enorm m\u00e4ngd data f\u00f6r att uppn\u00e5 korrekta resultat.<\/p>\n

Den h\u00e4r studien g\u00e5r dock djupare \u00e4n symmetri i konventionell mening. Invarianterna i Kernel Ridge Regression (KRR) omfattar symmetriska transformationer som rotationer, reflektioner och andra dataegenskaper som f\u00f6rblir of\u00f6r\u00e4ndrade under specifika operationer.<\/p>\n

\"S\u00e5 vitt jag vet \u00e4r det f\u00f6rsta g\u00e5ngen Weyls lag anv\u00e4nds f\u00f6r att fastst\u00e4lla hur maskininl\u00e4rning kan f\u00f6rb\u00e4ttras genom symmetri\", s\u00e4ger Tahmasebi.\u00a0<\/span><\/p>\n

Forskningen presenterades ursprungligen vid konferensen Neural Information Processing Systems i december 2023.<\/span><\/p>\n

Detta \u00e4r s\u00e4rskilt viktigt inom omr\u00e5den som ber\u00e4kningskemi och kosmologi, d\u00e4r kvalitetsdata \u00e4r begr\u00e4nsade. <\/span>Glesa data \u00e4r vanligt<\/span><\/a> inom omr\u00e5den d\u00e4r datam\u00e4ngderna \u00e4r exceptionellt stora, men i sj\u00e4lva verket \u00e4r anv\u00e4ndbara data i datam\u00e4ngderna mycket begr\u00e4nsade.\u00a0<\/span><\/p>\n

I rymdens o\u00e4ndlighet kan du till exempel hitta en liten fl\u00e4ck med anv\u00e4ndbar data bland ett ofattbart stort hav av ingenting\u00a0-<\/strong> s\u00e5 du m\u00e5ste f\u00e5 den d\u00e4r dataflecken att fungera - och symmetri \u00e4r ett bra verktyg f\u00f6r att uppn\u00e5 det.<\/p>\n

Soledad Villar, till\u00e4mpad matematiker vid Johns Hopkins University, s\u00e4ger om studien: \"Modeller som uppfyller symmetrierna i problemet \u00e4r inte bara korrekta utan kan ocks\u00e5 ge f\u00f6ruts\u00e4gelser med mindre fel, med hj\u00e4lp av en liten m\u00e4ngd tr\u00e4ningspunkter.\"\u00a0<\/span><\/p>\n

F\u00f6rdelar och resultat<\/h2>\n

Forskarna identifierade tv\u00e5 typer av f\u00f6rb\u00e4ttringar genom att anv\u00e4nda symmetrier: en linj\u00e4r boost, d\u00e4r effektiviteten \u00f6kar i proportion till symmetrin, och en exponentiell vinst, som ger en oproportionerligt stor f\u00f6rdel n\u00e4r man har att g\u00f6ra med symmetrier som sp\u00e4nner \u00f6ver flera dimensioner.\u00a0<\/span><\/p>\n

\"Det h\u00e4r \u00e4r ett nytt bidrag som i princip s\u00e4ger oss att symmetrier av h\u00f6gre dimension \u00e4r viktigare eftersom de kan ge oss en exponentiell vinst\", s\u00e4ger Tahmasebi.<\/span><\/p>\n

L\u00e5t oss bryta ner detta ytterligare:<\/span><\/p>\n

    \n
  1. Anv\u00e4nda symmetrier f\u00f6r att f\u00f6rb\u00e4ttra data<\/b>: Genom att k\u00e4nna igen m\u00f6nster eller symmetrier i data (som hur ett objekt ser likadant ut \u00e4ven n\u00e4r det roteras eller v\u00e4nds) kan en maskininl\u00e4rningsmodell l\u00e4ra sig som om den har mer data \u00e4n den faktiskt g\u00f6r. Detta tillv\u00e4gag\u00e5ngss\u00e4tt \u00f6kar modellens effektivitet, s\u00e5 att den kan l\u00e4ra sig mer fr\u00e5n mindre.<\/span><\/li>\n
  2. F\u00f6renkla inl\u00e4rningsuppgiften<\/b>: Deras andra uppt\u00e4ckt handlar om att g\u00f6ra modellens funktioner enklare genom att fokusera p\u00e5 dessa symmetrier. Eftersom modellen l\u00e4r sig att ignorera f\u00f6r\u00e4ndringar som inte spelar n\u00e5gon roll (som ett objekts position eller orientering), m\u00e5ste den hantera mindre komplicerad information. Detta inneb\u00e4r att modellen kan uppn\u00e5 goda resultat med f\u00e4rre exempel, vilket p\u00e5skyndar inl\u00e4rningsprocessen och f\u00f6rb\u00e4ttrar prestandan.<\/span><\/li>\n<\/ol>\n

    Haggai Maron, datavetare vid Technion och NVIDIA, ber\u00f6mde arbetet f\u00f6r dess nya perspektiv, <\/span>ber\u00e4ttar f\u00f6r MIT<\/span><\/a>, \"Detta teoretiska bidrag ger matematiskt st\u00f6d till det framv\u00e4xande delomr\u00e5det 'Geometric Deep Learning'.\"<\/span><\/p>\n

    Forskarna lyfter direkt fram den potentiella effekten inom ber\u00e4kningskemi, d\u00e4r principerna fr\u00e5n deras studie till exempel skulle kunna p\u00e5skynda l\u00e4kemedelsuppt\u00e4cktsprocesser.\u00a0<\/span><\/p>\n

    Genom att utnyttja symmetrier i molekylstrukturer kan maskininl\u00e4rningsmodeller f\u00f6ruts\u00e4ga interaktioner och egenskaper med f\u00e4rre datapunkter, vilket g\u00f6r screening av potentiella l\u00e4kemedelssubstanser snabbare och mer effektiv.\u00a0<\/span><\/p>\n

    Symmetrier kan ocks\u00e5 vara till hj\u00e4lp vid analys av kosmiska fenomen, d\u00e4r datam\u00e4ngderna \u00e4r extremt stora men d\u00e4r det finns f\u00e5 anv\u00e4ndbara data.\u00a0<\/span><\/p>\n

    Exempel p\u00e5 detta kan vara att utnyttja symmetrier f\u00f6r att studera den kosmiska bakgrundsstr\u00e5lningen eller galaxernas struktur f\u00f6r att f\u00e5 ut mer av begr\u00e4nsade data.\u00a0<\/span><\/p>","protected":false},"excerpt":{"rendered":"

    MIT-forskare har uppt\u00e4ckt hur utnyttjandet av begreppet symmetri inom dataset kan minska volymen data som beh\u00f6vs f\u00f6r tr\u00e4ningsmodeller. Denna uppt\u00e4ckt, dokumenterad i en studie som kan h\u00e4mtas via ArXiv av Behrooz Tahmasebi, doktorand vid MIT, och hans r\u00e5dgivare Stefanie Jegelka, docent vid MIT, grundar sig p\u00e5 en matematisk insikt fr\u00e5n en hundra \u00e5r gammal lag som kallas Weyls lag. Weyls lag, som ursprungligen formulerades av den tyske matematikern Hermann Weyl f\u00f6r \u00f6ver 110 \u00e5r sedan, utformades f\u00f6r att m\u00e4ta komplexiteten i spektral information, som t.ex. vibrationerna i musikinstrument. Tahmasebi inspirerades av denna lag n\u00e4r han studerade differentialekvationer och s\u00e5g<\/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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