{"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\/pt\/2024\/02\/symmetry-could-solve-small-dataset-woes-says-mit-researchers\/","title":{"rendered":"A simetria pode resolver os problemas dos pequenos conjuntos de dados, dizem os investigadores do MIT"},"content":{"rendered":"

Os investigadores do MIT descobriram como a utiliza\u00e7\u00e3o do conceito de simetria nos conjuntos de dados pode reduzir o volume de dados necess\u00e1rios para treinar modelos.<\/strong><\/p>\n

Esta descoberta, documentada num estudo recuper\u00e1vel via ArXiv<\/a> por Behrooz Tahmasebi, um estudante de doutoramento do MIT, e a sua orientadora, Stefanie Jegelka, professora associada do MIT,<\/span>\u00a0tem origem num insight matem\u00e1tico de uma lei centen\u00e1ria conhecida como lei de Weyl.\u00a0<\/span><\/p>\n

A lei de Weyl, originalmente formulada pelo matem\u00e1tico alem\u00e3o Hermann Weyl h\u00e1 mais de 110 anos, foi concebida para medir a complexidade da informa\u00e7\u00e3o espetral, como as vibra\u00e7\u00f5es dos instrumentos musicais.\u00a0<\/span><\/p>\n

Inspirado por esta lei enquanto estudava equa\u00e7\u00f5es diferenciais, Tahmasebi viu o seu potencial para reduzir a complexidade da introdu\u00e7\u00e3o de dados nas redes neuronais. Ao compreender as simetrias inerentes a um conjunto de dados, um modelo de aprendizagem autom\u00e1tica poderia tornar-se mais eficiente e mais r\u00e1pido sem adicionar mais dados numericamente.\u00a0<\/span><\/p>\n

O artigo de Tahmasebi e Jegelka explica como a explora\u00e7\u00e3o de simetrias, ou \"invari\u00e2ncias\", em conjuntos de dados pode simplificar as tarefas de aprendizagem autom\u00e1tica, exigindo, por sua vez, menos dados de treino.\u00a0<\/span><\/p>\n

Isto parece muito complexo, mas o princ\u00edpio \u00e9 relativamente simples. Por exemplo, pense na letra \"X\" - quer a rode ou inverta, continua a parecer um \"X\". Na aprendizagem autom\u00e1tica, quando os modelos compreendem esta ideia, podem aprender de forma mais eficiente. Percebem que, mesmo que uma imagem de um gato seja virada ao contr\u00e1rio ou espelhada, continua a mostrar um gato.<\/p>\n

Isto ajuda o modelo a utilizar melhor os seus dados, aprendendo com cada exemplo de v\u00e1rias formas e reduzindo a necessidade de uma grande quantidade de dados para obter resultados exactos.<\/p>\n

No entanto, este estudo vai mais longe do que a simetria num sentido convencional. As invari\u00e2ncias do Kernel Ridge Regression (KRR) abrangem transforma\u00e7\u00f5es sim\u00e9tricas como rota\u00e7\u00f5es, reflex\u00f5es e outras caracter\u00edsticas dos dados que permanecem inalteradas sob opera\u00e7\u00f5es espec\u00edficas.<\/p>\n

\"Tanto quanto sei, esta \u00e9 a primeira vez que a lei de Weyl \u00e9 utilizada para determinar como a aprendizagem autom\u00e1tica pode ser melhorada pela simetria\", afirmou Tahmasebi.\u00a0<\/span><\/p>\n

A investiga\u00e7\u00e3o foi inicialmente apresentada na confer\u00eancia Neural Information Processing Systems de dezembro de 2023.<\/span><\/p>\n

Isto \u00e9 particularmente importante em dom\u00ednios como a qu\u00edmica computacional e a cosmologia, em que os dados de qualidade s\u00e3o limitados. <\/span>Dados esparsos s\u00e3o comuns<\/span><\/a> em dom\u00ednios em que os conjuntos de dados s\u00e3o excecionalmente grandes, mas, na realidade, os dados \u00fateis dentro desses conjuntos s\u00e3o muito limitados.\u00a0<\/span><\/p>\n

Por exemplo, na vastid\u00e3o do espa\u00e7o, pode encontrar-se uma pequena part\u00edcula de dados \u00fateis num mar insondavelmente grande de nada\u00a0-<\/strong> por isso, \u00e9 preciso fazer com que essa part\u00edcula de dados funcione - e a simetria \u00e9 uma ferramenta \u00fatil para o conseguir.<\/p>\n

Soledad Villar, matem\u00e1tica aplicada da Universidade Johns Hopkins, referiu-se ao estudo: \"Os modelos que satisfazem as simetrias do problema n\u00e3o s\u00f3 est\u00e3o correctos como tamb\u00e9m podem produzir previs\u00f5es com erros menores, utilizando uma pequena quantidade de pontos de treino\".\u00a0<\/span><\/p>\n

Benef\u00edcios e resultados<\/h2>\n

Os investigadores identificaram dois tipos de melhorias decorrentes da utiliza\u00e7\u00e3o de simetrias: um aumento linear, em que a efici\u00eancia aumenta proporcionalmente \u00e0 simetria, e um ganho exponencial, que oferece um benef\u00edcio desproporcionalmente grande quando se trata de simetrias que abrangem v\u00e1rias dimens\u00f5es.\u00a0<\/span><\/p>\n

\"Esta \u00e9 uma nova contribui\u00e7\u00e3o que basicamente nos diz que as simetrias de dimens\u00e3o superior s\u00e3o mais importantes porque podem dar-nos um ganho exponencial\", explicou Tahmasebi.<\/span><\/p>\n

Vamos analisar melhor esta quest\u00e3o:<\/span><\/p>\n

    \n
  1. Utilizar simetrias para melhorar os dados<\/b>: Ao reconhecer padr\u00f5es ou simetrias nos dados (por exemplo, o facto de um objeto ter o mesmo aspeto mesmo quando rodado ou invertido), um modelo de aprendizagem autom\u00e1tica pode aprender como se tivesse mais dados do que tem na realidade. Esta abordagem aumenta a efici\u00eancia do modelo, permitindo-lhe aprender mais com menos.<\/span><\/li>\n
  2. Simplificar a tarefa de aprendizagem<\/b>: A sua segunda descoberta tem a ver com o facto de facilitar as fun\u00e7\u00f5es do modelo, concentrando-se nestas simetrias. Uma vez que o modelo aprende a ignorar as altera\u00e7\u00f5es que n\u00e3o interessam (como a posi\u00e7\u00e3o ou a orienta\u00e7\u00e3o de um objeto), tem de lidar com informa\u00e7\u00f5es menos complicadas. Isto significa que o modelo pode obter bons resultados com menos exemplos, acelerando o processo de aprendizagem e melhorando o desempenho.<\/span><\/li>\n<\/ol>\n

    Haggai Maron, um cientista inform\u00e1tico do Technion e da NVIDIA, elogiou o trabalho pela sua perspetiva inovadora, <\/span>informando o MIT<\/span><\/a>Esta contribui\u00e7\u00e3o te\u00f3rica d\u00e1 apoio matem\u00e1tico ao subcampo emergente da \"Aprendizagem Profunda Geom\u00e9trica\".<\/span><\/p>\n

    Os investigadores destacam diretamente o potencial impacto na qu\u00edmica computacional, onde os princ\u00edpios do seu estudo poderiam acelerar os processos de descoberta de medicamentos, por exemplo.\u00a0<\/span><\/p>\n

    Ao explorar as simetrias das estruturas moleculares, os modelos de aprendizagem autom\u00e1tica podem prever interac\u00e7\u00f5es e propriedades com menos pontos de dados, tornando o rastreio de potenciais compostos medicamentosos mais r\u00e1pido e eficiente.\u00a0<\/span><\/p>\n

    As simetrias tamb\u00e9m podem ajudar na an\u00e1lise de fen\u00f3menos c\u00f3smicos, onde os conjuntos de dados s\u00e3o extremamente grandes, mas escassamente povoados por dados \u00fateis.\u00a0<\/span><\/p>\n

    Os exemplos podem incluir a utiliza\u00e7\u00e3o de simetrias para estudar a radia\u00e7\u00e3o c\u00f3smica de fundo em micro-ondas ou a estrutura das gal\u00e1xias para extrair mais conhecimentos a partir de dados limitados.\u00a0<\/span><\/p>","protected":false},"excerpt":{"rendered":"

    Os investigadores do MIT descobriram como a utiliza\u00e7\u00e3o do conceito de simetria em conjuntos de dados pode reduzir o volume de dados necess\u00e1rios para treinar modelos. Esta descoberta, documentada num estudo que pode ser consultado no ArXiv por Behrooz Tahmasebi, um estudante de doutoramento do MIT, e pela sua orientadora, Stefanie Jegelka, uma professora associada do MIT, baseia-se numa vis\u00e3o matem\u00e1tica de uma lei centen\u00e1ria conhecida como lei de Weyl. A lei de Weyl, originalmente formulada pelo matem\u00e1tico alem\u00e3o Hermann Weyl h\u00e1 mais de 110 anos, foi concebida para medir a complexidade da informa\u00e7\u00e3o espetral, como as vibra\u00e7\u00f5es dos instrumentos musicais. Inspirado por esta lei enquanto estudava equa\u00e7\u00f5es diferenciais, Tahmasebi viu<\/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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