High-dimensional Deep learning (DL) reconstructions (e.g. 3D, 2D+time, 3D+time) can exploit multi-dimensional information and achieve improved results over lower dimensional ones. However, the size of the network and its depth for these large-scale reconstructions are currently limited by GPU memory. Here, we use a memory-efficient learning (MEL) framework, which favorably trades off storage with minimal increased computation and enables deeper high-dimensional DL reconstruction on a single GPU. We demonstrate improved image quality with learned high-dimensional reconstruction enabled by MEL for in-vivo 3D MRI and 2D cardiac cine imaging applications. MEL uses much less GPU memory while minimally increasing training time.