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However, deep neural networks such as CNNs do not explicitly encode objects and relations among them. This limits their success on tasks that require a deep logical understanding of visual scenes, such as Kandinsky patterns and Bongard problems. To overcome these limitations, we introduce<jats:inline-formula><jats:alternatives><jats:tex-math>$$\\alpha {\\textit{ILP}}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow><mml:mi>\u03b1<\/mml:mi><mml:mi>ILP<\/mml:mi><\/mml:mrow><\/mml:math><\/jats:alternatives><\/jats:inline-formula>, a novel differentiable inductive logic programming framework that learns to represent scenes as logic programs\u2014intuitively, logical atoms correspond to objects, attributes, and relations, and clauses encode high-level scene information.<jats:inline-formula><jats:alternatives><jats:tex-math>$$\\alpha$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>\u03b1<\/mml:mi><\/mml:math><\/jats:alternatives><\/jats:inline-formula>ILP has an end-to-end reasoning architecture from visual inputs. Using it,<jats:inline-formula><jats:alternatives><jats:tex-math>$$\\alpha$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>\u03b1<\/mml:mi><\/mml:math><\/jats:alternatives><\/jats:inline-formula>ILP performs differentiable inductive logic programming on complex visual scenes, i.e., the logical rules are learned by gradient descent. Our extensive experiments on<jats:italic>Kandinsky patterns<\/jats:italic>and<jats:italic>CLEVR-Hans<\/jats:italic>benchmarks demonstrate the accuracy and efficiency of<jats:inline-formula><jats:alternatives><jats:tex-math>$$\\alpha {\\textit{ILP}}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow><mml:mi>\u03b1<\/mml:mi><mml:mi>ILP<\/mml:mi><\/mml:mrow><\/mml:math><\/jats:alternatives><\/jats:inline-formula>in learning complex visual-logical concepts.<\/jats:p>","DOI":"10.1007\/s10994-023-06320-1","type":"journal-article","created":{"date-parts":[[2023,3,14]],"date-time":"2023-03-14T22:02:30Z","timestamp":1678831350000},"page":"1465-1497","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":19,"title":["$$\\alpha$$ILP: thinking visual scenes as differentiable logic programs"],"prefix":"10.1007","volume":"112","author":[{"given":"Hikaru","family":"Shindo","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Viktor","family":"Pfanschilling","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Devendra Singh","family":"Dhami","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kristian","family":"Kersting","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2023,3,14]]},"reference":[{"key":"6320_CR1","unstructured":"Amizadeh, S., Palangi, H., Polozov, A., Huang, Y., & Koishida, K. 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