{"id":9347,"date":"2024-01-18T17:24:24","date_gmt":"2024-01-18T17:24:24","guid":{"rendered":"https:\/\/dailyai.com\/?p=9347"},"modified":"2024-01-19T10:57:11","modified_gmt":"2024-01-19T10:57:11","slug":"alphageometry-ais-landmark-achievement-in-geometry","status":"publish","type":"post","link":"https:\/\/dailyai.com\/nb\/2024\/01\/alphageometry-ais-landmark-achievement-in-geometry\/","title":{"rendered":"AlphaGeometry: AIs banebrytende prestasjon innen geometri"},"content":{"rendered":"<p><b>DeepMind-forskere har utviklet AlphaGeometry, et AI-system med en enest\u00e5ende evne til \u00e5 l\u00f8se geometrioppgaver p\u00e5 olympiadeniv\u00e5.\u00a0<\/b><\/p>\n<p><span style=\"font-weight: 400;\">Olympiadeoppgaver er komplekse matematiske problemer som vanligvis stilles i internasjonale matematikkonkurranser, for eksempel den internasjonale matematikkolympiaden (IMO). <\/span><\/p>\n<p><span style=\"font-weight: 400;\">Disse problemene krever en dyp forst\u00e5else av matematiske konsepter, kreative probleml\u00f8sningsferdigheter og et strengt logisk resonnement, som dekker omr\u00e5der som algebra, kombinatorikk og geometri, som denne forskningen er rettet mot.\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Den <\/span><a href=\"https:\/\/www.nature.com\/articles\/s41586-023-06747-5\"><span style=\"font-weight: 400;\">DeepMind<\/span><\/a> studie<span style=\"font-weight: 400;\">publisert i Nature, markerer en milep\u00e6l i AIs evne til \u00e5 l\u00f8se matematiske problemer.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Modellsystemet, kalt AlphaGeometry, l\u00f8ste 25 av 30 oppgaver fra den internasjonale matematikkolympiaden, en enorm forbedring i forhold til det forrige toppmoderne AI-systemet, som bare l\u00f8ste 10 oppgaver.\u00a0<\/span><\/p>\n<figure id=\"attachment_9349\" aria-describedby=\"caption-attachment-9349\" style=\"width: 1024px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-9349 size-large\" src=\"https:\/\/dailyai.com\/wp-content\/uploads\/2024\/01\/AlphaGeometry-1024x586.png\" alt=\"\" width=\"1024\" height=\"586\" srcset=\"https:\/\/dailyai.com\/wp-content\/uploads\/2024\/01\/AlphaGeometry-1024x586.png 1024w, https:\/\/dailyai.com\/wp-content\/uploads\/2024\/01\/AlphaGeometry-300x172.png 300w, https:\/\/dailyai.com\/wp-content\/uploads\/2024\/01\/AlphaGeometry-768x439.png 768w, https:\/\/dailyai.com\/wp-content\/uploads\/2024\/01\/AlphaGeometry-1536x879.png 1536w, https:\/\/dailyai.com\/wp-content\/uploads\/2024\/01\/AlphaGeometry-370x212.png 370w, https:\/\/dailyai.com\/wp-content\/uploads\/2024\/01\/AlphaGeometry-800x458.png 800w, https:\/\/dailyai.com\/wp-content\/uploads\/2024\/01\/AlphaGeometry-20x11.png 20w, https:\/\/dailyai.com\/wp-content\/uploads\/2024\/01\/AlphaGeometry-740x423.png 740w, https:\/\/dailyai.com\/wp-content\/uploads\/2024\/01\/AlphaGeometry-1600x915.png 1600w, https:\/\/dailyai.com\/wp-content\/uploads\/2024\/01\/AlphaGeometry-84x48.png 84w, https:\/\/dailyai.com\/wp-content\/uploads\/2024\/01\/AlphaGeometry.png 1926w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption id=\"caption-attachment-9349\" class=\"wp-caption-text\">AlphaGeometry knuste tidligere AI-modeller, men ligger like bak de beste matematikerne. Kilde: <a href=\"https:\/\/www.nature.com\/articles\/s41586-023-06747-5\">DeepMind via Nature<\/a>.<\/figcaption><\/figure>\n<p><span style=\"font-weight: 400;\">Det gjenspeiler nesten prestasjonene til menneskelige gullmedaljevinnere, som i gjennomsnitt l\u00f8ste 25,9 problemer - noe som er et ganske bemerkelsesverdig nikk til ferdighetene i menneskelige olympiader. Studieforfatter Trieu H. Trinh beskriver papiret nedenfor.<br \/>\n<\/span><\/p>\n<p><iframe loading=\"lazy\" title=\"AlphaGeometry\" width=\"1080\" height=\"608\" src=\"https:\/\/www.youtube.com\/embed\/TuZhU1CiC0k?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe><\/p>\n<p><span style=\"font-weight: 400;\">For \u00e5 oppn\u00e5 dette kombinerer AI-systemet en nevral spr\u00e5kmodell med en symbolsk deduksjonsmotor. Den nevrale modellen foresl\u00e5r raskt potensielle konstruksjoner, og den symbolske motoren utleder l\u00f8sninger p\u00e5 en stringent m\u00e5te. Denne tosidige tiln\u00e6rmingen gir en balanse mellom hastighet og n\u00f8yaktighet i probleml\u00f8sningen.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">En n\u00f8kkel til AlphaGeometrys suksess er genereringen av 100 millioner unike syntetiske treningseksempler. Denne tiln\u00e6rmingen gjorde det mulig for den kunstige intelligensen \u00e5 trene uten menneskelig input, og dermed overvinne en stor dataflaskehals.<\/span><\/p>\n<figure id=\"attachment_9348\" aria-describedby=\"caption-attachment-9348\" style=\"width: 1024px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-9348 size-large\" src=\"https:\/\/dailyai.com\/wp-content\/uploads\/2024\/01\/trainingdata-1024x508.png\" alt=\"AI DeepMind\" width=\"1024\" height=\"508\" srcset=\"https:\/\/dailyai.com\/wp-content\/uploads\/2024\/01\/trainingdata-1024x508.png 1024w, https:\/\/dailyai.com\/wp-content\/uploads\/2024\/01\/trainingdata-300x149.png 300w, https:\/\/dailyai.com\/wp-content\/uploads\/2024\/01\/trainingdata-768x381.png 768w, https:\/\/dailyai.com\/wp-content\/uploads\/2024\/01\/trainingdata-1536x763.png 1536w, https:\/\/dailyai.com\/wp-content\/uploads\/2024\/01\/trainingdata-370x184.png 370w, https:\/\/dailyai.com\/wp-content\/uploads\/2024\/01\/trainingdata-800x397.png 800w, https:\/\/dailyai.com\/wp-content\/uploads\/2024\/01\/trainingdata-740x367.png 740w, https:\/\/dailyai.com\/wp-content\/uploads\/2024\/01\/trainingdata-20x10.png 20w, https:\/\/dailyai.com\/wp-content\/uploads\/2024\/01\/trainingdata-1600x794.png 1600w, https:\/\/dailyai.com\/wp-content\/uploads\/2024\/01\/trainingdata-97x48.png 97w, https:\/\/dailyai.com\/wp-content\/uploads\/2024\/01\/trainingdata.png 1821w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption id=\"caption-attachment-9348\" class=\"wp-caption-text\">Eksempler p\u00e5 syntetiske data som brukes til \u00e5 trene AlphaGeometry. Kilde: <a href=\"https:\/\/www.nature.com\/articles\/s41586-023-06747-5\">DeepMind via Nature<\/a>.<\/figcaption><\/figure>\n<p><span style=\"font-weight: 400;\">Fields-medaljevinner og IMO-gullmedaljevinner Ng\u00f4 B\u1ea3o Ch\u00e2u uttrykte sin forbl\u00f8ffelse over denne prestasjonen, <\/span><a href=\"https:\/\/deepmind.google\/discover\/blog\/alphageometry-an-olympiad-level-ai-system-for-geometry\/\"><span style=\"font-weight: 400;\">i et blogginnlegg fra Google<\/span><\/a><span style=\"font-weight: 400;\">\"Jeg synes det er helt logisk at forskere innen kunstig intelligens pr\u00f8ver seg p\u00e5 IMO-geometriproblemene f\u00f8rst, fordi det \u00e5 finne l\u00f8sninger p\u00e5 dem fungerer litt som sjakk, i den forstand at vi har et ganske lite antall fornuftige trekk p\u00e5 hvert trinn. Men jeg synes likevel det er forbl\u00f8ffende at de fikk det til \u00e5 fungere. Det er en imponerende prestasjon.\"<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Evan Chen, en matematikktrener og tidligere gullmedaljevinner i Olympiaden, ber\u00f8mmet ogs\u00e5 AI-en: \"AlphaGeometrys resultater er imponerende fordi de er b\u00e5de verifiserbare og rene ... Den bruker klassiske geometriske regler med vinkler og lignende trekanter akkurat slik elevene gj\u00f8r.\"<\/span><\/p>\n<p>Se Chens video om olympiaden nedenfor for \u00e5 f\u00e5 en f\u00f8lelse av hvor vanvittig vanskelige disse problemene er.<\/p>\n<p><iframe loading=\"lazy\" title=\"Episode 1 med Evan Chen | MIN vei til Olympiaden 2021\" width=\"1080\" height=\"608\" src=\"https:\/\/www.youtube.com\/embed\/JfTOfFOtiwk?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe><\/p>\n<p><span style=\"font-weight: 400;\">AlphaGeometrys evne til \u00e5 l\u00f8se komplekse geometrioppgaver p\u00e5 olympiadeniv\u00e5 demonstrerer ikke bare AIs \u00f8kende evne til \u00e5 resonnere logisk, men \u00e5pner ogs\u00e5 for nye muligheter innen matematikk og AI-utvikling.\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Den bidrar til flere banebrytende forskningsresultater fra DeepMind, blant annet <\/span><a href=\"https:\/\/dailyai.com\/nb\/2023\/11\/deepminds-gnome-system-discovered-millions-of-new-materials\/\"><span style=\"font-weight: 400;\">GNoME<\/span><\/a><span style=\"font-weight: 400;\">, <\/span><a href=\"https:\/\/dailyai.com\/nb\/2023\/07\/googles-ai-turns-vision-language-into-robotic-actions\/\"><span style=\"font-weight: 400;\">RT-2<\/span><\/a><span style=\"font-weight: 400;\">, <\/span><a href=\"https:\/\/dailyai.com\/nb\/2024\/01\/google-releases-a-suite-of-advanced-robotic-tools\/\"><span style=\"font-weight: 400;\">AutoRT<\/span><\/a><span style=\"font-weight: 400;\">, <\/span><a href=\"https:\/\/dailyai.com\/nb\/2023\/12\/deepmind-makes-major-breakthrough-in-mathematical-machine-learning\/\"><span style=\"font-weight: 400;\">FunSearch<\/span><\/a><span style=\"font-weight: 400;\">, <\/span><a href=\"https:\/\/dailyai.com\/nb\/2023\/09\/deepminds-alphamissense-accelerates-the-hunt-for-disease-causing-genes\/\"><span style=\"font-weight: 400;\">AlphaMissense<\/span><\/a><span style=\"font-weight: 400;\">, og <\/span><a href=\"https:\/\/dailyai.com\/nb\/2023\/09\/google-turns-25-will-ai-herald-another-25-years-of-success\/\"><span style=\"font-weight: 400;\">AlphaFold<\/span><\/a><span style=\"font-weight: 400;\">for \u00e5 nevne noen fra nyere tid.\u00a0<\/span><\/p>\n<h2><span style=\"font-weight: 400;\">Mer om studien<\/span><\/h2>\n<p><span style=\"font-weight: 400;\">Slik fungerer AlphaGeometry i fem destillerte trinn:<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><b>Syntetisk generering av teoremerker<\/b><span style=\"font-weight: 400;\">: AlphaGeometry starter med \u00e5 generere et stort sett med tilfeldige geometriske problemer. Dette gj\u00f8res ved \u00e5 lage en rekke geometriske utsagn, for eksempel \"punkt A ligger p\u00e5 linjestykket BC\" eller \"vinkel XYZ er 45 grader\". Disse utsagnene danner premissene eller utgangspunktene for potensielle teoremer.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><b>Symbolsk deduksjon<\/b><span style=\"font-weight: 400;\">: Ved hjelp av disse premissene begynner AI-ens symbolske deduksjonsmotor \u00e5 resonnere seg frem til konklusjoner. Den bruker geometriske regler og logikk for \u00e5 utlede nye p\u00e5stander fra de gitte premissene, og utforsker systematisk ulike kombinasjoner og relasjoner.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><b>Opprette hjelpekonstruksjoner<\/b><span style=\"font-weight: 400;\">: For \u00e5 l\u00f8se komplekse geometriske problemer m\u00e5 man ofte introdusere nye elementer (for eksempel flere punkter eller linjer) som ikke er en del av det opprinnelige oppsettet. Disse kalles hjelpekonstruksjoner. AlphaGeometrys motor er utviklet for \u00e5 identifisere n\u00e5r og hvilke hjelpekonstruksjoner som er n\u00f8dvendige for \u00e5 komme videre mot en l\u00f8sning.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><b>Trening av spr\u00e5kmodellen<\/b><span style=\"font-weight: 400;\">: En transformatorbasert spr\u00e5kmodell trenes opp p\u00e5 dataene som er generert i trinnene ovenfor. Denne modellen l\u00e6rer seg \u00e5 forst\u00e5 m\u00f8nstrene og logikken i geometriske resonnementer. Den blir bedre til \u00e5 forutsi hvilke hjelpekonstruksjoner eller trinn som kan v\u00e6re n\u00f8dvendige for \u00e5 l\u00f8se lignende problemer i fremtiden.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><b>Iterativ probleml\u00f8sning<\/b><span style=\"font-weight: 400;\">: I det siste trinnet takler AlphaGeometry nye geometriproblemer ved \u00e5 kombinere spr\u00e5kmodellens prediksjonskraft med den symbolske deduksjonsmotorens logiske stringens. Den kunstige intelligensen foresl\u00e5r hjelpekonstruksjoner og sjekker om de f\u00f8rer til en l\u00f8sning, og itererer denne prosessen til den finner et gyldig bevis eller har brukt opp alle alternativene.<\/span><\/li>\n<\/ul>\n<p><span style=\"font-weight: 400;\">DeepMinds appetitt p\u00e5 \u00e5 l\u00f8se forskningsproblemer innen maskinl\u00e6ring har bare vokst, og dette illustrerer nok en gang AIs utviklingstempo. Men la oss ikke glemme at menneskelige matteolympiader fortsatt har et forsprang - akkurat.<\/span><\/p>","protected":false},"excerpt":{"rendered":"<p>DeepMind-forskere har utviklet AlphaGeometry, et AI-system med enest\u00e5ende evne til \u00e5 l\u00f8se geometrioppgaver p\u00e5 olympiadeniv\u00e5.  Olympiadeoppgaver er komplekse matematiske problemer som vanligvis stilles i internasjonale matematikkonkurranser, som for eksempel den internasjonale matematikkolympiaden (IMO). Disse oppgavene krever en dyp forst\u00e5else av matematiske konsepter, kreative probleml\u00f8sningsferdigheter og strenge logiske resonnementer, og dekker omr\u00e5der som algebra, kombinatorikk og geometri, som denne forskningen er rettet mot.  DeepMind-studien, som er publisert i Nature, markerer en milep\u00e6l i AIs evne til \u00e5 l\u00f8se matematiske problemer. Modellsystemet, kalt AlphaGeometry, l\u00f8ste 25 av 30 oppgaver fra den internasjonale matematikkolympiaden, noe som er en enorm forbedring i forhold til<\/p>","protected":false},"author":2,"featured_media":8908,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[84],"tags":[147,102,105],"class_list":["post-9347","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-industry","tag-deepmind","tag-google","tag-machine-learning"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>AlphaGeometry: AI&#039;s landmark achievement in geometry | DailyAI<\/title>\n<meta name=\"description\" content=\"DeepMind researchers have developed AlphaGeometry, an AI system with unprecedented ability to solve Olympiad-level geometry problems.\u00a0\" \/>\n<meta name=\"robots\" content=\"index, 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