  Implicitly defined, continuous, differentiable signal representations
parameterized by neural networks have emerged as a powerful paradigm, offering
many possible benefits over conventional representations. However, current
network architectures for such implicit neural representations are incapable of
modeling signals with fine detail, and fail to represent a signal's spatial and
temporal derivatives, despite the fact that these are essential to many
physical signals defined implicitly as the solution to partial differential
equations. We propose to leverage periodic activation functions for implicit
neural representations and demonstrate that these networks, dubbed sinusoidal
representation networks or Sirens, are ideally suited for representing complex
natural signals and their derivatives. We analyze Siren activation statistics
to propose a principled initialization scheme and demonstrate the
representation of images, wavefields, video, sound, and their derivatives.
Further, we show how Sirens can be leveraged to solve challenging boundary
value problems, such as particular Eikonal equations (yielding signed distance
functions), the Poisson equation, and the Helmholtz and wave equations. Lastly,
we combine Sirens with hypernetworks to learn priors over the space of Siren
functions.
