  Multi-Layer Perceptrons (MLPs) make powerful functional representations for
sampling and reconstruction problems involving low-dimensional signals like
images,shapes and light fields. Recent works have significantly improved their
ability to represent high-frequency content by using periodic activations or
positional encodings. This often came at the expense of generalization: modern
methods are typically optimized for a single signal. We present a new
representation that generalizes to multiple instances and achieves
state-of-the-art fidelity. We use a dual-MLP architecture to encode the
signals. A synthesis network creates a functional mapping from a
low-dimensional input (e.g. pixel-position) to the output domain (e.g. RGB
color). A modulation network maps a latent code corresponding to the target
signal to parameters that modulate the periodic activations of the synthesis
network. We also propose a local-functional representation which enables
generalization. The signal's domain is partitioned into a regular grid,with
each tile represented by a latent code. At test time, the signal is encoded
with high-fidelity by inferring (or directly optimizing) the latent code-book.
Our approach produces generalizable functional representations of images,
videos and shapes, and achieves higher reconstruction quality than prior works
that are optimized for a single signal.
