Abstract: Methods, systems and apparatus, including computer programs encoded on computer storage media. One of the methods includes obtaining a plurality of images of a macromolecule having a plurality of atoms, training a decoder neural network on the plurality of images, and after the training, generating a plurality of conformations for at least a portion of the macromolecule that each include respective three-dimensional coordinates of each of the plurality of atoms, wherein generating each conformation includes sampling a conformation latent representation from a prior distribution over conformation latent representations, processing a respective input including the sampled conformation latent representation using the decoder neural network to generate a conformation output that specifies three-dimensional coordinates of each of the plurality of atoms for the conformation, and generating the conformation from the conformation output.

Abstract: Methods, systems, and apparatus, including computer programs encoded on computer storage media, for selecting an optimal feature point in a continuous domain for a group of agents. A computer-implemented system obtains, for each of a plurality of agents, respective training data that comprises a respective utility score for each of a plurality of discrete points in the continuous domain. The system trains, for each of the plurality of agents and on the respective training data for the agents, a respective neural network that is configured to receive an input comprising a point in the continuous domain and to generate as output a predicted utility score for the agent at the point.

Abstract: Methods, systems, and apparatus, including computer programs encoded on a computer storage medium, for efficiently allocating resources among participants. Methods can include receiving valuation data specifying, for each of a plurality of entities, a respective valuation for each of a plurality of resource subsets, each resource subset comprising a different combination of one or more resources of a plurality of resources. After receiving valuation data, assigning each resource in the plurality of resources to a respective entity of the plurality of entities based on the valuations and generating, for each particular entity, a respective input representation that is derived from valuations of every other entity in the plurality of entities other than the particular entity. The input representation for each particular entity is processed using a neural network to generate a rule for the particular entity and a payment based on the rule output for the entities.

Abstract: Methods, systems, and apparatus, including computer programs encoded on a computer storage medium, for efficiently allocating resources among participants. Methods can include receiving valuation data specifying, for each of a plurality of entities, a respective valuation for each of a plurality of resource subsets, each resource subset comprising a different combination of one or more resources of a plurality of resources. After receiving valuation data, assigning each resource in the plurality of resources to a respective entity of the plurality of entities based on the valuations and generating, for each particular entity, a respective input representation that is derived from valuations of every other entity in the plurality of entities other than the particular entity. The input representation for each particular entity is processed using a neural network to generate a rule for the particular entity and a payment based on the rule output for the entities.