SIREN: Implicit Neural Representations with Periodic Activation Functions (Paper Explained)

Implicit neural representations are created when a neural network is used to represent a signal as a function. SIRENs are a particular type of INR that can be applied to a variety of signals, such as images, sound, or 3D shapes. This is an interesting departure from regular machine learning and required me to think differently.

OUTLINE: 0:00 - Intro & Overview 2:15 - Implicit Neural Representations 9:40 - Representing Images 14:30 - SIRENs 18:05 - Initialization 20:15 - Derivatives of SIRENs 23:05 - Poisson Image Reconstruction 28:20 - Poisson Image Editing 31:35 - Shapes with Signed Distance Functions 45:55 - Paper Website 48:55 - Other Applications 50:45 - Hypernetworks over SIRENs 54:30 - Broader Impact

Paper: https://arxiv.org/abs/2006.09661 Website: https://vsitzmann.github.io/siren/

Abstract: 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.

Authors: Vincent Sitzmann, Julien N. P. Martel, Alexander W. Bergman, David B. Lindell, Gordon Wetzstein

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