Deep learning emerges as an important new resource-intensive workload and has been successfully applied in computer vision, speech, natural language processing, and so on. Distributed deep learning is becoming a necessity to cope with growing data and model sizes. Its computation is typically characterized by a simple tensor data abstraction to model multi-dimensional matrices, a data-flow graph to model computation, and iterative executions with relatively frequent synchronizations, thereby making it substantially different from Map/Reduce style distributed big data computation. RPC, commonly used as the communication primitive, has been adopted by popular deep learning frameworks such as TensorFlow, which uses gRPC. We show that RPC is sub-optimal for distributed deep learning computation, especially on an RDMA-capable network. The tensor abstraction and data-flow graph, coupled with an RDMA network, offers the opportunity to reduce the unnecessary overhead (e.g., memory copy) without sacrificing programmability and generality. In particular, from a data access point of view, a remote machine is abstracted just as a device on an RDMA channel, with a simple memory interface for allocating, reading, and writing memory regions. Our graph analyzer looks at both the data flow graph and the tensors to optimize memory allocation and remote data access using this interface. The result is up to 25 times speedup in representative deep learning benchmarks against the standard gRPC in TensorFlow and up to 169% improvement even against an RPC implementation optimized for RDMA, leading to faster convergence in the training process.