  Recently, new defense techniques have been developed to tolerate Byzantine
failures for distributed machine learning. The Byzantine model captures workers
that behave arbitrarily, including malicious and compromised workers. In this
paper, we break two prevailing Byzantine-tolerant techniques. Specifically we
show robust aggregation methods for synchronous SGD -- coordinate-wise median
and Krum -- can be broken using new attack strategies based on inner product
manipulation. We prove our results theoretically, as well as show empirical
validation.
