  Neural representations have emerged as a new paradigm for applications in
rendering, imaging, geometric modeling, and simulation. Compared to traditional
representations such as meshes, point clouds, or volumes they can be flexibly
incorporated into differentiable learning-based pipelines. While recent
improvements to neural representations now make it possible to represent
signals with fine details at moderate resolutions (e.g., for images and 3D
shapes), adequately representing large-scale or complex scenes has proven a
challenge. Current neural representations fail to accurately represent images
at resolutions greater than a megapixel or 3D scenes with more than a few
hundred thousand polygons. Here, we introduce a new hybrid implicit-explicit
network architecture and training strategy that adaptively allocates resources
during training and inference based on the local complexity of a signal of
interest. Our approach uses a multiscale block-coordinate decomposition,
similar to a quadtree or octree, that is optimized during training. The network
architecture operates in two stages: using the bulk of the network parameters,
a coordinate encoder generates a feature grid in a single forward pass. Then,
hundreds or thousands of samples within each block can be efficiently evaluated
using a lightweight feature decoder. With this hybrid implicit-explicit network
architecture, we demonstrate the first experiments that fit gigapixel images to
nearly 40 dB peak signal-to-noise ratio. Notably this represents an increase in
scale of over 1000x compared to the resolution of previously demonstrated
image-fitting experiments. Moreover, our approach is able to represent 3D
shapes significantly faster and better than previous techniques; it reduces
training times from days to hours or minutes and memory requirements by over an
order of magnitude.
