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Oral
Implicit Neural Representations with Periodic Activation Functions
Vincent Sitzmann · Julien N.P Martel · Alexander Bergman · David Lindell · Gordon Wetzstein

Tue Dec 08 06:00 PM -- 06:15 PM (PST) @ Orals & Spotlights: Deep Learning/Theory
in Orals & Spotlights Track 13: Deep Learning/Theory »

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.

Author Information

Vincent Sitzmann (MIT)

Vincent is an incoming Assistant Professor at MIT EECS, where he will lead the Scene Representation Group (scenerepresentations.org). Currently, he is a Postdoc at MIT's CSAIL with Josh Tenenbaum, Bill Freeman, and Fredo Durand. He finished his Ph.D. at Stanford University. His research interest lies in neural scene representations - the way neural networks learn to represent information on our world. His goal is to allow independent agents to reason about our world given visual observations, such as inferring a complete model of a scene with information on geometry, material, lighting etc. from only few observations, a task that is simple for humans, but currently impossible for AI.

Julien N.P Martel (Stanford University)
Alexander Bergman (Stanford University)
David Lindell (Stanford University)
Gordon Wetzstein (Stanford University)

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