Binary STT-MRAM is a highly anticipated embedded nonvolatile memory technology in advanced logic nodes < 28 nm. How to enable its in-memory computing (IMC) capability is critical for enhancing AI Edge. Based on the soon-available STTMRAM, we report the first binary deep convolutional neural network (NV-BNN) capable of both local and remote learning. Exploiting intrinsic cumulative switching probability, accurate online training of CIFAR-10 color images (∼ 90%) is realized using a relaxed endurance spec (switching ≤ 20 times) and hybrid digital/IMC design. For offline training, the accuracy loss due to imprecise weight placement can be mitigated using a rapid noniterative training-with-noise and fine-tuning scheme.