{"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\/nb\/2024\/02\/symmetry-could-solve-small-dataset-woes-says-mit-researchers\/","title":{"rendered":"Symmetri kan l\u00f8se problemene med sm\u00e5 datasett, mener MIT-forskere"},"content":{"rendered":"

MIT-forskere har avdekket hvordan man ved \u00e5 utnytte symmetri i datasett kan redusere datamengden som trengs for \u00e5 trene opp modeller.<\/strong><\/p>\n

Denne oppdagelsen, dokumentert i en studie kan hentes via ArXiv<\/a> av Behrooz Tahmasebi, doktorgradsstudent ved MIT, og hans veileder, Stefanie Jegelka, f\u00f8rsteamanuensis ved MIT,<\/span>\u00a0er forankret i en matematisk innsikt fra en hundre \u00e5r gammel lov som er kjent som Weyls lov.\u00a0<\/span><\/p>\n

Weyls lov, som opprinnelig ble formulert av den tyske matematikeren Hermann Weyl for over 110 \u00e5r siden, ble utviklet for \u00e5 m\u00e5le kompleksiteten i spektral informasjon, som for eksempel vibrasjonene i musikkinstrumenter.\u00a0<\/span><\/p>\n

Tahmasebi ble inspirert av denne loven da han studerte differensialligninger, og s\u00e5 at den kunne brukes til \u00e5 redusere kompleksiteten i datainput til nevrale nettverk. Ved \u00e5 forst\u00e5 symmetrier i et datasett kunne en maskinl\u00e6ringsmodell gj\u00f8res mer effektiv og raskere uten \u00e5 legge til mer data numerisk.\u00a0<\/span><\/p>\n

Tahmasebi og Jegelkas artikkel forklarer hvordan utnyttelse av symmetrier, eller \"invarianser\", i datasett kan forenkle maskinl\u00e6ringsoppgaver, noe som i sin tur krever mindre treningsdata.\u00a0<\/span><\/p>\n

Det h\u00f8res veldig komplisert ut, men prinsippet er relativt enkelt. Tenk for eksempel p\u00e5 bokstaven \"X\" - uansett om du roterer den eller snur den, ser den fortsatt ut som en \"X\". N\u00e5r modeller innen maskinl\u00e6ring forst\u00e5r denne ideen, kan de l\u00e6re mer effektivt. De skj\u00f8nner at selv om et bilde av en katt snus opp ned eller speilvendes, viser det fortsatt en katt.<\/p>\n

Dette bidrar til at modellen utnytter dataene bedre, l\u00e6rer av hvert eksempel p\u00e5 flere m\u00e5ter og reduserer behovet for store datamengder for \u00e5 oppn\u00e5 n\u00f8yaktige resultater.<\/p>\n

Denne studien g\u00e5r imidlertid dypere enn symmetri i konvensjonell forstand. Kernel Ridge Regression (KRR) omfatter symmetriske transformasjoner som rotasjoner, refleksjoner og andre dataegenskaper som forblir uendret under spesifikke operasjoner.<\/p>\n

\"S\u00e5 vidt jeg vet, er dette f\u00f8rste gang Weyls lov har blitt brukt til \u00e5 finne ut hvordan maskinl\u00e6ring kan forbedres ved hjelp av symmetri\", sier Tahmasebi.\u00a0<\/span><\/p>\n

Forskningen ble f\u00f8rst presentert p\u00e5 konferansen Neural Information Processing Systems i desember 2023.<\/span><\/p>\n

Dette er spesielt viktig p\u00e5 felt som beregningskjemi og kosmologi, der det er begrenset med data av h\u00f8y kvalitet. <\/span>Sparsomme data er vanlig<\/span><\/a> p\u00e5 omr\u00e5der der datasettene er sv\u00e6rt store, men hvor det i realiteten er sv\u00e6rt begrenset med nyttige data.\u00a0<\/span><\/p>\n

I verdensrommet kan du for eksempel finne en liten flekk med nyttige data i et ufattelig stort hav av ingenting\u00a0-<\/strong> s\u00e5 du m\u00e5 f\u00e5 dataflekken til \u00e5 fungere - og symmetri er et nyttig verkt\u00f8y for \u00e5 oppn\u00e5 det.<\/p>\n

Soledad Villar, matematiker ved Johns Hopkins University, sier om studien: \"Modeller som tilfredsstiller symmetriene i problemet, er ikke bare korrekte, men kan ogs\u00e5 gi prediksjoner med mindre feil ved hjelp av et lite antall treningspunkter.\"\u00a0<\/span><\/p>\n

Fordeler og resultater<\/h2>\n

Forskerne identifiserte to typer forbedringer ved bruk av symmetrier: et line\u00e6rt l\u00f8ft, der effektiviteten \u00f8ker proporsjonalt med symmetrien, og en eksponentiell gevinst, som gir en uforholdsmessig stor fordel n\u00e5r man har \u00e5 gj\u00f8re med symmetrier som spenner over flere dimensjoner.\u00a0<\/span><\/p>\n

\"Dette er et nytt bidrag som i bunn og grunn forteller oss at symmetrier av h\u00f8yere dimensjon er viktigere fordi de kan gi oss en eksponentiell gevinst\", utdyper Tahmasebi.<\/span><\/p>\n

La oss bryte dette ned ytterligere:<\/span><\/p>\n

    \n
  1. Bruk av symmetrier for \u00e5 forbedre data<\/b>: Ved \u00e5 gjenkjenne m\u00f8nstre eller symmetrier i dataene (for eksempel hvordan et objekt ser likt ut selv n\u00e5r det roteres eller vendes), kan en maskinl\u00e6ringsmodell l\u00e6re som om den har mer data enn den faktisk har. Denne tiln\u00e6rmingen \u00f8ker modellens effektivitet, slik at den kan l\u00e6re mer av mindre.<\/span><\/li>\n
  2. Forenkling av l\u00e6ringsoppgaven<\/b>: Deres andre funn handler om \u00e5 gj\u00f8re modellens funksjoner enklere ved \u00e5 fokusere p\u00e5 disse symmetriene. Siden modellen l\u00e6rer seg \u00e5 ignorere endringer som ikke spiller noen rolle (som posisjonen eller retningen til et objekt), m\u00e5 den forholde seg til mindre komplisert informasjon. Det betyr at modellen kan oppn\u00e5 gode resultater med f\u00e6rre eksempler, noe som gj\u00f8r l\u00e6ringsprosessen raskere og ytelsen bedre.<\/span><\/li>\n<\/ol>\n

    Haggai Maron, datavitenskapsmann ved Technion og NVIDIA, ber\u00f8mmet arbeidet for det nye perspektivet, <\/span>forteller MIT<\/span><\/a>\"Dette teoretiske bidraget gir matematisk st\u00f8tte til det nye underfeltet \"geometrisk dyp l\u00e6ring\".\"<\/span><\/p>\n

    Forskerne fremhever direkte den potensielle effekten innen beregningskjemi, der prinsippene fra studien deres for eksempel kan fremskynde prosesser for legemiddeloppdagelse.\u00a0<\/span><\/p>\n

    Ved \u00e5 utnytte symmetrier i molekylstrukturer kan maskinl\u00e6ringsmodeller forutsi interaksjoner og egenskaper med f\u00e6rre datapunkter, noe som gj\u00f8r screening av potensielle legemiddelforbindelser raskere og mer effektiv.\u00a0<\/span><\/p>\n

    Symmetrier kan ogs\u00e5 bidra til \u00e5 analysere kosmiske fenomener, der datasettene er ekstremt store, men likevel tynt befolket av nyttige data.\u00a0<\/span><\/p>\n

    Eksempler p\u00e5 dette kan v\u00e6re \u00e5 utnytte symmetrier til \u00e5 studere kosmisk mikrob\u00f8lgebakgrunnsstr\u00e5ling eller galaksers struktur for \u00e5 f\u00e5 mer innsikt fra begrensede data.\u00a0<\/span><\/p>","protected":false},"excerpt":{"rendered":"

    MIT-forskere har avdekket hvordan utnyttelse av begrepet symmetri i datasett kan redusere datamengden som trengs for \u00e5 trene modeller. Denne oppdagelsen, som er dokumentert i en studie som kan hentes via ArXiv av Behrooz Tahmasebi, en doktorgradsstudent ved MIT, og hans r\u00e5dgiver, Stefanie Jegelka, f\u00f8rsteamanuensis ved MIT, er forankret i en matematisk innsikt fra en hundre \u00e5r gammel lov kjent som Weyls lov. Weyls lov, som opprinnelig ble formulert av den tyske matematikeren Hermann Weyl for over 110 \u00e5r siden, ble utviklet for \u00e5 m\u00e5le kompleksiteten i spektral informasjon, som for eksempel vibrasjonene i musikkinstrumenter. Tahmasebi ble inspirert av denne loven da han studerte differensialligninger, og s\u00e5<\/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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