Deep neural networks (DNNs) continue to grow rapidly in size, making them infeasible to train on a single device (e.g. GPU). Pipeline parallelism is commonly used in existing DNN systems to support large-scale DNN training by partitioning a DNN into multiple stages, which concurrently perform DNN computation for different micro-batches of training samples in a pipeline fashion. However, existing pipeline-parallel approaches only consider sequential pipeline stages and thus ignore the topology of a DNN, resulting in missed model-parallel opportunities.

A method is investigated for finding a collision-free path for a mobile robot with a few degrees of freedom in a time-varying domain. The environment contains a set of obstacles with arbitrary known motion patterns. In a time-varying environment, paths are time-dependent, i.e., a path needs to be specified as a function of time, since connectivity in the environment changes over time. Given a time-varying environment, a start time, and a start location, a method is presented for finding a collision-free path from start to goal points for a finite-size robot subject to a speed bound. Our method makes use of a heuristic approach based on a transient pixel representation.>