In recent years, deep neural networks (DNNs), have yielded strong results on a wide range of applications. Graphics Processing Units (GPUs) have been one key enabling factor leading to the current popularity of DNNs. However, despite increasing hardware flexibility and software programming toolchain maturity, high efficiency GPU programming remains difficult: it suffers from high complexity, low productivity, and low portability. GPU vendors such as NVIDIA have spent enormous effort to write special-purpose DNN libraries. However, on other hardware targets, especially mobile GPUs, such vendor libraries are not generally available. Thus, the development of portable, open, high-performance, energy-efficient GPU code for DNN operations would enable broader deployment of DNN-based algorithms. Toward this end, this work presents a framework to enable productive, high-efficiency GPU programming for DNN computations across hardware platforms and programming models. In particular, the framework provides specific support for metaprogramming, autotuning, and DNN-tailored data types. Using our framework, we explore implementing DNN operations on three different hardware targets: NVIDIA, AMD, and Qualcomm GPUs. On NVIDIA GPUs, we show both portability between OpenCL and CUDA as well competitive performance compared to the vendor library. On Qualcomm GPUs, we show that our framework enables productive development of target-specific optimizations, and achieves reasonable absolute performance. Finally, On AMD GPUs, we show initial results that indicate our framework can yield reasonable performance on a new platform with minimal effort.