We use spatially-sparse two, three and four dimensional convolutional autoencoder networks to model sparse structures in 2D space, 3D space, and 3+1=4 dimensional space-time. We evaluate the resulting latent spaces by testing their usefulness for downstream tasks. Applications are to handwriting recognition in 2D, segmentation for parts in 3D objects, segmentation for objects in 3D scenes, and body-part segmentation for 4D wire-frame models generated from motion capture data.