Abstract: A robust machine learning system is provided for robust machine learning. The robust machine learning system includes a processor, and a memory storing a robust machine learning program and a Group Representation Network (GRepsNet), wherein the robust machine learning program runining on the processor. In this case the processor is configured to receive an input dataset represented by a first group representation via input layers connected to the GrepsNet, pass/transmit the input dataset through the GRepsNet configured to generate an output dataset represented by an output group representation from the input dataset, wherein the output group is equivalent to the first group, and generate the output dataset from output layers connected to the GRepsNet.