Methods, systems, and apparatus, including computer programs encoded on computer storage media, for distributing tensor computations across computing devices. One of the methods includes: receiving specification data that specifies a distribution of tensor computations among a plurality of computing devices, wherein each tensor computation (i) is defined to receive, as input, one or more respective input tensors each having one or more respective input dimensions, (ii) is defined to generate, as output, one or more respective output tensors each having one or more respective output dimensions, or both, wherein the specification data specifies a respective layout for each input and output tensor that assigns each dimension of the input or output tensor to one or more of the plurality of computing devices; assigning, based on the layouts for the input and output tensors, respective device-local operations to each of the computing devices; and causing the tensor computations to be executed.