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Implicit Neural Representations with Periodic Activation Functions

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Document pages: 35 pages

Abstract: Implicitly defined, continuous, differentiable signal representationsparameterized by neural networks have emerged as a powerful paradigm, offeringmany possible benefits over conventional representations. However, currentnetwork architectures for such implicit neural representations are incapable ofmodeling signals with fine detail, and fail to represent a signal s spatial andtemporal derivatives, despite the fact that these are essential to manyphysical signals defined implicitly as the solution to partial differentialequations. We propose to leverage periodic activation functions for implicitneural representations and demonstrate that these networks, dubbed sinusoidalrepresentation networks or Sirens, are ideally suited for representing complexnatural signals and their derivatives. We analyze Siren activation statisticsto propose a principled initialization scheme and demonstrate therepresentation of images, wavefields, video, sound, and their derivatives.Further, we show how Sirens can be leveraged to solve challenging boundaryvalue problems, such as particular Eikonal equations (yielding signed distancefunctions), the Poisson equation, and the Helmholtz and wave equations. Lastly,we combine Sirens with hypernetworks to learn priors over the space of Sirenfunctions.

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