{"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\/fr\/2024\/02\/symmetry-could-solve-small-dataset-woes-says-mit-researchers\/","title":{"rendered":"La sym\u00e9trie pourrait r\u00e9soudre les probl\u00e8mes li\u00e9s aux petits ensembles de donn\u00e9es, selon des chercheurs du MIT"},"content":{"rendered":"

Des chercheurs du MIT ont d\u00e9couvert comment l'exploitation du concept de sym\u00e9trie dans les ensembles de donn\u00e9es peut r\u00e9duire le volume de donn\u00e9es n\u00e9cessaires \u00e0 la formation des mod\u00e8les.<\/strong><\/p>\n

Cette d\u00e9couverte, document\u00e9e dans une \u00e9tude r\u00e9cup\u00e9rable via ArXiv<\/a> par Behrooz Tahmasebi, doctorant au MIT, et sa conseill\u00e8re, Stefanie Jegelka, professeur associ\u00e9 au MIT,<\/span>\u00a0trouve son origine dans une intuition math\u00e9matique issue d'une loi centenaire connue sous le nom de loi de Weyl.\u00a0<\/span><\/p>\n

La loi de Weyl, formul\u00e9e \u00e0 l'origine par le math\u00e9maticien allemand Hermann Weyl il y a plus de 110 ans, a \u00e9t\u00e9 con\u00e7ue pour mesurer la complexit\u00e9 des informations spectrales, telles que les vibrations des instruments de musique.\u00a0<\/span><\/p>\n

Inspir\u00e9 par cette loi alors qu'il \u00e9tudiait les \u00e9quations diff\u00e9rentielles, Tahmasebi a vu son potentiel pour r\u00e9duire la complexit\u00e9 des donn\u00e9es introduites dans les r\u00e9seaux neuronaux. En comprenant les sym\u00e9tries inh\u00e9rentes \u00e0 un ensemble de donn\u00e9es, un mod\u00e8le d'apprentissage automatique pourrait \u00eatre rendu plus efficace et plus rapide sans ajouter de donn\u00e9es num\u00e9riques suppl\u00e9mentaires.\u00a0<\/span><\/p>\n

L'article de Tahmasebi et Jegelka explique comment l'exploitation des sym\u00e9tries, ou \"invariances\", dans les ensembles de donn\u00e9es peut simplifier les t\u00e2ches d'apprentissage automatique, ce qui n\u00e9cessite moins de donn\u00e9es de formation.\u00a0<\/span><\/p>\n

Cela semble tr\u00e8s complexe, mais le principe est relativement simple. Par exemple, pensez \u00e0 la lettre \"X\" : que vous la fassiez pivoter ou que vous la retourniez, elle ressemble toujours \u00e0 un \"X\". Dans le domaine de l'apprentissage automatique, lorsque les mod\u00e8les comprennent cette id\u00e9e, ils peuvent apprendre plus efficacement. Ils se rendent compte que m\u00eame si l'image d'un chat est retourn\u00e9e ou refl\u00e9t\u00e9e, elle repr\u00e9sente toujours un chat.<\/p>\n

Cela permet au mod\u00e8le de mieux utiliser ses donn\u00e9es, d'apprendre de chaque exemple de multiples fa\u00e7ons et de r\u00e9duire la n\u00e9cessit\u00e9 de disposer d'une grande quantit\u00e9 de donn\u00e9es pour obtenir des r\u00e9sultats pr\u00e9cis.<\/p>\n

Toutefois, cette \u00e9tude va plus loin que la sym\u00e9trie au sens conventionnel du terme. Les invariances de la r\u00e9gression Kernel Ridge (KRR) englobent les transformations sym\u00e9triques telles que les rotations, les r\u00e9flexions et d'autres caract\u00e9ristiques des donn\u00e9es qui restent inchang\u00e9es dans le cadre d'op\u00e9rations sp\u00e9cifiques.<\/p>\n

\"\u00c0 ma connaissance, c'est la premi\u00e8re fois que la loi de Weyl est utilis\u00e9e pour d\u00e9terminer comment l'apprentissage automatique peut \u00eatre am\u00e9lior\u00e9 par la sym\u00e9trie\", a d\u00e9clar\u00e9 M. Tahmasebi.\u00a0<\/span><\/p>\n

La recherche a \u00e9t\u00e9 initialement pr\u00e9sent\u00e9e lors de la conf\u00e9rence Neural Information Processing Systems de d\u00e9cembre 2023.<\/span><\/p>\n

Cela est particuli\u00e8rement important dans des domaines tels que la chimie computationnelle et la cosmologie, o\u00f9 les donn\u00e9es de qualit\u00e9 sont limit\u00e9es. <\/span>Les donn\u00e9es \u00e9parses sont courantes<\/span><\/a> dans des domaines o\u00f9 les ensembles de donn\u00e9es sont exceptionnellement vastes, alors qu'en r\u00e9alit\u00e9, les donn\u00e9es utiles contenues dans ces ensembles sont tr\u00e8s limit\u00e9es.\u00a0<\/span><\/p>\n

Par exemple, dans l'immensit\u00e9 de l'espace, vous pourriez trouver une minuscule parcelle de donn\u00e9es utiles dans une mer de n\u00e9ant d'une taille insondable\u00a0-<\/strong> Il faut donc faire en sorte que ce point de donn\u00e9es fonctionne - et la sym\u00e9trie est un outil utile pour y parvenir.<\/p>\n

Soledad Villar, math\u00e9maticienne appliqu\u00e9e \u00e0 l'universit\u00e9 Johns Hopkins, a d\u00e9clar\u00e9 \u00e0 propos de l'\u00e9tude : \"Les mod\u00e8les qui satisfont aux sym\u00e9tries du probl\u00e8me sont non seulement corrects, mais ils peuvent \u00e9galement produire des pr\u00e9dictions avec des erreurs plus faibles, en utilisant un petit nombre de points d'entra\u00eenement.\"\u00a0<\/span><\/p>\n

Avantages et r\u00e9sultats<\/h2>\n

Les chercheurs ont identifi\u00e9 deux types d'am\u00e9liorations r\u00e9sultant de l'utilisation des sym\u00e9tries : un gain lin\u00e9aire, o\u00f9 l'efficacit\u00e9 augmente proportionnellement \u00e0 la sym\u00e9trie, et un gain exponentiel, qui offre un avantage disproportionn\u00e9 lorsqu'il s'agit de sym\u00e9tries couvrant plusieurs dimensions.\u00a0<\/span><\/p>\n

\"Il s'agit d'une nouvelle contribution qui nous dit essentiellement que les sym\u00e9tries de dimension sup\u00e9rieure sont plus importantes parce qu'elles peuvent nous apporter un gain exponentiel\", a expliqu\u00e9 M. Tahmasebi.<\/span><\/p>\n

Voyons cela plus en d\u00e9tail :<\/span><\/p>\n

    \n
  1. Utiliser les sym\u00e9tries pour am\u00e9liorer les donn\u00e9es<\/b>: En reconnaissant des mod\u00e8les ou des sym\u00e9tries dans les donn\u00e9es (comme l'aspect identique d'un objet m\u00eame lorsqu'il est tourn\u00e9 ou retourn\u00e9), un mod\u00e8le d'apprentissage automatique peut apprendre comme s'il disposait de plus de donn\u00e9es qu'il n'en a en r\u00e9alit\u00e9. Cette approche accro\u00eet l'efficacit\u00e9 du mod\u00e8le, lui permettant d'apprendre davantage \u00e0 partir de moins de donn\u00e9es.<\/span><\/li>\n
  2. Simplifier la t\u00e2che d'apprentissage<\/b>: Leur deuxi\u00e8me d\u00e9couverte consiste \u00e0 faciliter les fonctions du mod\u00e8le en se concentrant sur ces sym\u00e9tries. Comme le mod\u00e8le apprend \u00e0 ignorer les changements qui n'ont pas d'importance (comme la position ou l'orientation d'un objet), il doit traiter des informations moins compliqu\u00e9es. Cela signifie que le mod\u00e8le peut obtenir de bons r\u00e9sultats avec moins d'exemples, ce qui acc\u00e9l\u00e8re le processus d'apprentissage et am\u00e9liore les performances.<\/span><\/li>\n<\/ol>\n

    Haggai Maron, informaticien au Technion et chez NVIDIA, a salu\u00e9 le travail pour sa nouvelle perspective, <\/span>dire au MIT<\/span><\/a>Cette contribution th\u00e9orique apporte un soutien math\u00e9matique au sous-domaine \u00e9mergent de l'\"apprentissage profond g\u00e9om\u00e9trique\".<\/span><\/p>\n

    Les chercheurs soulignent directement l'impact potentiel sur la chimie computationnelle, o\u00f9 les principes de leur \u00e9tude pourraient acc\u00e9l\u00e9rer les processus de d\u00e9couverte de m\u00e9dicaments, par exemple.\u00a0<\/span><\/p>\n

    En exploitant les sym\u00e9tries des structures mol\u00e9culaires, les mod\u00e8les d'apprentissage automatique peuvent pr\u00e9dire les interactions et les propri\u00e9t\u00e9s avec moins de points de donn\u00e9es, ce qui rend le criblage de compos\u00e9s m\u00e9dicamenteux potentiels plus rapide et plus efficace.\u00a0<\/span><\/p>\n

    Les sym\u00e9tries pourraient \u00e9galement faciliter l'analyse des ph\u00e9nom\u00e8nes cosmiques, o\u00f9 les ensembles de donn\u00e9es sont extr\u00eamement vastes mais peu peupl\u00e9s de donn\u00e9es utiles.\u00a0<\/span><\/p>\n

    On peut citer comme exemple l'exploitation des sym\u00e9tries pour \u00e9tudier le rayonnement cosmique de fond ou la structure des galaxies afin d'obtenir davantage d'informations \u00e0 partir de donn\u00e9es limit\u00e9es.\u00a0<\/span><\/p>","protected":false},"excerpt":{"rendered":"

    Des chercheurs du MIT ont d\u00e9couvert comment l'exploitation du concept de sym\u00e9trie dans les ensembles de donn\u00e9es peut r\u00e9duire le volume de donn\u00e9es n\u00e9cessaires \u00e0 la formation des mod\u00e8les. Cette d\u00e9couverte, document\u00e9e dans une \u00e9tude consultable sur ArXiv par Behrooz Tahmasebi, doctorant au MIT, et sa conseill\u00e8re, Stefanie Jegelka, professeur associ\u00e9 au MIT, trouve son origine dans une intuition math\u00e9matique issue d'une loi centenaire connue sous le nom de loi de Weyl. La loi de Weyl, formul\u00e9e \u00e0 l'origine par le math\u00e9maticien allemand Hermann Weyl il y a plus de 110 ans, a \u00e9t\u00e9 con\u00e7ue pour mesurer la complexit\u00e9 des informations spectrales, telles que les vibrations des instruments de musique. Inspir\u00e9 par cette loi alors qu'il \u00e9tudiait les \u00e9quations diff\u00e9rentielles, Tahmasebi a vu<\/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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