{"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\/da\/2024\/01\/alphageometry-ais-landmark-achievement-in-geometry\/","title":{"rendered":"AlphaGeometry: AI's skels\u00e6ttende pr\u00e6station inden for geometri"},"content":{"rendered":"<p><b>DeepMind-forskere har udviklet AlphaGeometry, et AI-system med en hidtil uset evne til at l\u00f8se geometriske problemer p\u00e5 olympiadeniveau.\u00a0<\/b><\/p>\n<p><span style=\"font-weight: 400;\">Olympiadens matematiske problemer er komplekse matematiske problemer, der typisk stilles i internationale matematikkonkurrencer, som f.eks. den internationale matematikolympiade (IMO). <\/span><\/p>\n<p><span style=\"font-weight: 400;\">Disse problemer kr\u00e6ver en dyb forst\u00e5else af matematiske begreber, kreative probleml\u00f8sningsevner og stringent logisk r\u00e6sonnement, der d\u00e6kker omr\u00e5der som algebra, kombinatorik og geometri, som denne forskning er rettet mod.\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> unders\u00f8gelse<span style=\"font-weight: 400;\">offentliggjort i Nature, markerer en milep\u00e6l i AI's evne til at l\u00f8se matematiske problemer.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Modelsystemet, kaldet AlphaGeometry, l\u00f8ste 25 ud af 30 problemer fra den internationale matematikolympiade, hvilket er en enorm forbedring i forhold til det tidligere state-of-the-art AI-system, som kun l\u00f8ste 10.\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 smadrede tidligere AI-modeller, men ligger lige bag de bedste matematikere. Kilde: <a href=\"https:\/\/www.nature.com\/articles\/s41586-023-06747-5\">DeepMind via naturen<\/a>.<\/figcaption><\/figure>\n<p><span style=\"font-weight: 400;\">Det afspejler n\u00e6sten pr\u00e6stationen hos de menneskelige guldmedaljevindere, som i gennemsnit l\u00f8ste 25,9 problemer - hvilket er et ret bem\u00e6rkelsesv\u00e6rdigt nik til f\u00e6rdighederne i de menneskelige olympiader. Unders\u00f8gelsens forfatter Trieu H. Trinh beskriver artiklen 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 at opn\u00e5 dette kombinerer AI-systemet en neural sprogmodel med en symbolsk deduktionsmotor. Den neurale model foresl\u00e5r hurtigt potentielle konstruktioner, og den symbolske motor udleder n\u00f8je l\u00f8sninger. Denne dobbelte tilgang g\u00f8r det lettere at finde en balance mellem hastighed og n\u00f8jagtighed i probleml\u00f8sningen.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">En n\u00f8gle til AlphaGeometrys succes er genereringen af 100 millioner unikke syntetiske tr\u00e6ningseksempler. Denne tilgang gjorde det muligt for AI'en at tr\u00e6ne uden menneskelige input og overvinde 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 brugt til at tr\u00e6ne AlphaGeometry. Kilde: <a href=\"https:\/\/www.nature.com\/articles\/s41586-023-06747-5\">DeepMind via naturen<\/a>.<\/figcaption><\/figure>\n<p><span style=\"font-weight: 400;\">Fields-medaljevinderen og IMO-guldmedaljevinderen Ng\u00f4 B\u1ea3o Ch\u00e2u udtrykte sin forbl\u00f8ffelse over denne pr\u00e6station, <\/span><a href=\"https:\/\/deepmind.google\/discover\/blog\/alphageometry-an-olympiad-level-ai-system-for-geometry\/\"><span style=\"font-weight: 400;\">i et blogindl\u00e6g fra Google<\/span><\/a><span style=\"font-weight: 400;\">\"Det giver perfekt mening for mig, at forskere i kunstig intelligens pr\u00f8ver kr\u00e6fter med IMO-geometriproblemerne f\u00f8rst, fordi det at finde l\u00f8sninger p\u00e5 dem fungerer lidt som skak i den forstand, at vi har et ret lille antal fornuftige tr\u00e6k p\u00e5 hvert trin. Men jeg synes stadig, det er forbl\u00f8ffende, at de kunne f\u00e5 det til at fungere. Det er en imponerende pr\u00e6station.\"<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Evan Chen, en matematisk tr\u00e6ner og tidligere olympisk guldmedaljevinder, roste ogs\u00e5 AI'en: \"AlphaGeometrys output er imponerende, fordi det b\u00e5de er verificerbart og rent ... Den bruger klassiske geometriske regler med vinkler og lignende trekanter, pr\u00e6cis som studerende g\u00f8r.\"<\/span><\/p>\n<p>Se Chens video om olympiaden nedenfor for at f\u00e5 en fornemmelse af, hvor uhyrligt sv\u00e6re disse problemer er.<\/p>\n<p><iframe loading=\"lazy\" title=\"Episode 1 med Evan Chen | MIN vej 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 at l\u00f8se komplekse geometriproblemer p\u00e5 olympiadeniveau demonstrerer ikke kun AI's voksende evne til at r\u00e6sonnere logisk, men \u00e5bner ogs\u00e5 nye muligheder inden for matematik og AI-udvikling.\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Det bidrager til flere banebrydende forskningsresultater fra DeepMind, herunder <\/span><a href=\"https:\/\/dailyai.com\/da\/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\/da\/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\/da\/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\/da\/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\/da\/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\/da\/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 blot at n\u00e6vne nogle f\u00e5 fra den seneste tid.\u00a0<\/span><\/p>\n<h2><span style=\"font-weight: 400;\">Mere om unders\u00f8gelsen<\/span><\/h2>\n<p><span style=\"font-weight: 400;\">Her er, hvordan AlphaGeometry fungerer i fem destillerede trin:<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><b>Syntetisk teorigenerering<\/b><span style=\"font-weight: 400;\">: AlphaGeometry starter med at generere et stort s\u00e6t tilf\u00e6ldige geometriske problemer. Dette g\u00f8res ved at skabe en r\u00e6kke geometriske udsagn som \"punkt A ligger p\u00e5 linjestykket BC\" eller \"vinkel XYZ er 45 grader\". Disse udsagn udg\u00f8r pr\u00e6misserne eller udgangspunktet for potentielle s\u00e6tninger.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><b>Symbolsk deduktion<\/b><span style=\"font-weight: 400;\">: Ved hj\u00e6lp af disse pr\u00e6misser begynder AI'ens symbolske deduktionsmotor at r\u00e6sonnere sig frem til konklusioner. Den anvender geometriske regler og logik til at udlede nye udsagn fra de givne pr\u00e6misser og udforsker systematisk forskellige kombinationer og relationer.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><b>Oprettelse af hj\u00e6lpekonstruktioner<\/b><span style=\"font-weight: 400;\">: Ofte kr\u00e6ver l\u00f8sningen af komplekse geometriske problemer, at man indf\u00f8rer nye elementer (som ekstra punkter eller linjer), der ikke er en del af den oprindelige opstilling. Disse kaldes hj\u00e6lpekonstruktioner. AlphaGeometrys motor er designet til at identificere, hvorn\u00e5r og hvilke hj\u00e6lpekonstruktioner der er n\u00f8dvendige for at komme videre med en l\u00f8sning.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><b>Tr\u00e6ning af sprogmodellen<\/b><span style=\"font-weight: 400;\">: En transformerbaseret sprogmodel tr\u00e6nes p\u00e5 de data, der genereres i ovenst\u00e5ende trin. Denne model l\u00e6rer at forst\u00e5 m\u00f8nstrene og logikken i geometriske r\u00e6sonnementer. Den bliver bedre til at forudsige, hvilke hj\u00e6lpekonstruktioner eller trin der kan v\u00e6re n\u00f8dvendige for at 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 sidste trin tackler AlphaGeometry nye geometriske problemer ved at kombinere sprogmodellens forudsigelseskraft med den symbolske deduktionsmotors logiske stringens. AI'en foresl\u00e5r hj\u00e6lpekonstruktioner og kontrollerer, om de f\u00f8rer til en l\u00f8sning, og gentager denne proces, indtil den finder et gyldigt bevis eller har udt\u00f8mt sine muligheder.<\/span><\/li>\n<\/ul>\n<p><span style=\"font-weight: 400;\">DeepMinds appetit p\u00e5 at l\u00f8se forskningsproblemer inden for maskinl\u00e6ring er bestemt kun vokset, og det illustrerer endnu en gang AI's udviklingshastighed. Lad os dog ikke glemme, at menneskelige matematikolympiader stadig har en fordel - bare.<\/span><\/p>","protected":false},"excerpt":{"rendered":"<p>DeepMind-forskere har udviklet AlphaGeometry, et AI-system med en hidtil uset evne til at l\u00f8se geometriproblemer p\u00e5 olympiadeniveau.  Olympiadens matematiske problemer er komplekse matematiske problemer, der typisk stilles i internationale matematikkonkurrencer som f.eks. den internationale matematikolympiade (IMO). Disse problemer kr\u00e6ver en dyb forst\u00e5else af matematiske begreber, kreative probleml\u00f8sningsevner og stringent logisk r\u00e6sonnement, der d\u00e6kker omr\u00e5der som algebra, kombinatorik og geometri, som denne forskning er rettet mod.  DeepMind-unders\u00f8gelsen, der er offentliggjort i Nature, markerer en milep\u00e6l i AI's evne til at l\u00f8se matematiske problemer. Modelsystemet, kaldet AlphaGeometry, l\u00f8ste med succes 25 ud af 30 problemer fra den internationale matematiske olympiade, hvilket 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\" 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