Deep neural network accelerators (DNNs) with independent datapaths for simultaneous processing of different classes of operations and related methods are described. An example DNN accelerator includes an instruction dispatcher for receiving chains of instructions having both instructions for performing a first class of operations and a second class of operations corresponding to a neural network model. The DNN accelerator further includes a first datapath and a second datapath, where each is configured to execute at least one instruction chain locally before outputting any results. The instruction dispatcher is configured to forward instructions for performing the first class of operations to the first datapath and forward instructions for performing the second class of operations to the second datapath to overlap in time a performance of at least a subset of the first class of operations with a performance of at least a subset of the second class of operations.