Methods, systems, and apparatus, including instructions encoded on storage media, for performing reduction of gradient vectors for a network having one or more degraded nodes. A method comprises training a respective replica of a machine learning model on each node of multiple nodes organized in an n-dimensional network topology, combining the respective individual gradient vectors in the nodes to generate a final gradient vector by performing operations comprising: designating each group of nodes along the dimension as either a forwarding group or a critical group, updating, for each receiving node, a respective individual gradient vector with an intermediate gradient vector, performing a reduction on each critical group of nodes along the dimension to generate a respective partial final gradient vector for the critical group, and updating, for each critical group of nodes, an individual gradient vector for a representative node with the respective partial final gradient vector.