Implicit Neural Representations with Periodic Activation Functions (2020)

Vincent Sitzmann and co-authors submitted an arXiv paper on 17 June 2020 proposing sinusoidal representation networks, or Sirens, which use periodic activation functions for implicit neural representations. The authors report that Sirens represent images, wavefields, video, sound and their derivatives, and solve boundary value problems including Eikonal equations yielding signed distance functions, the Poisson equation, and the Helmholtz and wave equations. The paper also combines Sirens with hypernetworks to learn priors over the space of Siren functions.

Computer Science Computer Vision and Pattern Recognition Submitted on 17 Jun 2020 Title:Implicit Neural Representations with Periodic Activation Functions View PDF https://arxiv.org/pdf/2006.09661 HTML experimental https://arxiv.org/html/2006.09661v1 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. Submission history From: Vincent Sitzmann view email https://arxiv.org/show-email/a7d0c71f/2006.09661 v1 Wed, 17 Jun 2020 05:13:33 UTC 9,551 KB Bibliographic and Citation Tools Bibliographic Explorer What is the Explorer? https://info.arxiv.org/labs/showcase.html arxiv-bibliographic-explorer Connected Papers What is Connected Papers? https://www.connectedpapers.com/about Litmaps What is Litmaps? https://www.litmaps.co/ scite Smart Citations What are Smart Citations? https://www.scite.ai/ Code, Data and Media Associated with this Article alphaXiv What is alphaXiv? https://alphaxiv.org/ CatalyzeX Code Finder for Papers What is CatalyzeX? https://www.catalyzex.com DagsHub What is DagsHub? https://dagshub.com/ Gotit.pub What is GotitPub? http://gotit.pub/faq Hugging Face What is Huggingface? https://huggingface.co/huggingface ScienceCast What is ScienceCast? https://sciencecast.org/welcome Demos Recommenders and Search Tools Influence Flower What are Influence Flowers? https://influencemap.cmlab.dev/ CORE Recommender What is CORE? https://core.ac.uk/services/recommender arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs https://info.arxiv.org/labs/index.html .