Abstract: Methods, systems, and apparatus, including computer programs encoded on computer storage media, for solving mixed integer programs (MIPs) using neural networks. One of the methods includes obtaining data specifying parameters of a MIP; generating, from the parameters of the MIP, an input representation; processing the input representation using an encoder neural network to generate a respective embedding for each of the integer variables; generating a plurality of partial assignments by selecting a respective second, proper subset of the integer variables; and for each of the variables in the respective second subset, generating, using at least the respective embedding for the variable, a respective additional constraint on the value of the variable; generating, for each of the partial assignments, a corresponding candidate final assignment that assigns a respective value to each of the plurality of variables; and selecting, as a final assignment for the MIP, one of the candidate final assignments.

Abstract: Methods, systems, and apparatus, including computer programs encoded on computer storage media, for learning visual concepts using neural networks. One of the methods includes receiving a new symbol input comprising one or more symbols from a vocabulary; and generating a new output image that depicts concepts referred to by the new symbol input, comprising: processing the new symbol input using a symbol encoder neural network to generate a new symbol encoder output for the new symbol input; sampling, from the distribution parameterized by the new symbol encoder output, a respective value for each of a plurality of visual factors; and processing a new image decoder input comprising the respective values for the visual factors using an image decoder neural network to generate the new output image.

Abstract: Methods, systems, and apparatus, including computer programs encoded on computer storage media, for learning visual concepts using neural networks. One of the methods includes receiving a new symbol input comprising one or more symbols from a vocabulary; and generating a new output image that depicts concepts referred to by the new symbol input, comprising: processing the new symbol input using a symbol encoder neural network to generate a new symbol encoder output for the new symbol input; sampling, from the distribution parameterized by the new symbol encoder output, a respective value for each of a plurality of visual factors; and processing a new image decoder input comprising the respective values for the visual factors using an image decoder neural network to generate the new output image.

Abstract: Methods, systems, and apparatus, including computer programs encoded on computer storage media, for learning visual concepts using neural networks. One of the methods includes receiving a new symbol input comprising one or more symbols from a vocabulary; and generating a new output image that depicts concepts referred to by the new symbol input, comprising: processing the new symbol input using a symbol encoder neural network to generate a new symbol encoder output for the new symbol input; sampling, from the distribution parameterized by the new symbol encoder output, a respective value for each of a plurality of visual factors; and processing a new image decoder input comprising the respective values for the visual factors using an image decoder neural network to generate the new output image.

Abstract: Methods, systems, and apparatus, including computer programs encoded on computer storage media, for learning visual concepts using neural networks. One of the methods includes receiving a new symbol input comprising one or more symbols from a vocabulary; and generating a new output image that depicts concepts referred to by the new symbol input, comprising: processing the new symbol input using a symbol encoder neural network to generate a new symbol encoder output for the new symbol input; sampling, from the distribution parameterized by the new symbol encoder output, a respective value for each of a plurality of visual factors; and processing a new image decoder input comprising the respective values for the visual factors using an image decoder neural network to generate the new output image.