{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/deepsphere-efficient-spherical-convolutional","title":"DeepSphere: Efficient spherical Convolutional Neural Network with HEALPix sampling for cosmological applications","arxiv_id":"1810.12186","date":"2018-10-29","proceeding":null,"authors":["Nathanaël Perraudin","Michaël Defferrard","Tomasz Kacprzak","Raphael Sgier"],"abstract":"Convolutional Neural Networks (CNNs) are a cornerstone of the Deep Learning\ntoolbox and have led to many breakthroughs in Artificial Intelligence. These\nnetworks have mostly been developed for regular Euclidean domains such as those\nsupporting images, audio, or video. Because of their success, CNN-based methods\nare becoming increasingly popular in Cosmology. Cosmological data often comes\nas spherical maps, which make the use of the traditional CNNs more complicated.\nThe commonly used pixelization scheme for spherical maps is the Hierarchical\nEqual Area isoLatitude Pixelisation (HEALPix). We present a spherical CNN for\nanalysis of full and partial HEALPix maps, which we call DeepSphere. The\nspherical CNN is constructed by representing the sphere as a graph. Graphs are\nversatile data structures that can act as a discrete representation of a\ncontinuous manifold. Using the graph-based representation, we define many of\nthe standard CNN operations, such as convolution and pooling. With filters\nrestricted to being radial, our convolutions are equivariant to rotation on the\nsphere, and DeepSphere can be made invariant or equivariant to rotation. This\nway, DeepSphere is a special case of a graph CNN, tailored to the HEALPix\nsampling of the sphere. This approach is computationally more efficient than\nusing spherical harmonics to perform convolutions. We demonstrate the method on\na classification problem of weak lensing mass maps from two cosmological models\nand compare the performance of the CNN with that of two baseline classifiers.\nThe results show that the performance of DeepSphere is always superior or equal\nto both of these baselines. For high noise levels and for data covering only a\nsmaller fraction of the sphere, DeepSphere achieves typically 10% better\nclassification accuracy than those baselines. Finally, we show how learned\nfilters can be visualized to introspect the neural network.","url_abs":"http://arxiv.org/abs/1810.12186v2","url_pdf":"http://arxiv.org/pdf/1810.12186v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"deepsphere-efficient-spherical-convolutional","repo_url":"https://github.com/deepsphere/deepsphere-cosmo-tf1","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":null},{"paper_slug":"deepsphere-efficient-spherical-convolutional","repo_url":"https://github.com/deepsphere/code-iclr20","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":{"status":"ok","spdx":"MIT"}},{"paper_slug":"deepsphere-efficient-spherical-convolutional","repo_url":"https://github.com/deepsphere/deepsphere-cosmo-tf2","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":{"status":"unanswered"}},{"paper_slug":"deepsphere-efficient-spherical-convolutional","repo_url":"https://github.com/deepsphere/deepsphere-pytorch","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":null},{"paper_slug":"deepsphere-efficient-spherical-convolutional","repo_url":"https://github.com/deepsphere/deepsphere-tf1","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":{"status":"unanswered"}},{"paper_slug":"deepsphere-efficient-spherical-convolutional","repo_url":"https://github.com/deepsphere/paper-deepsphere-ascom2019","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"CC-BY-4.0"}}],"tasks":[{"task_slug":"classification","task_name":"General Classification"}],"methods":[{"method_slug":"convolution","method_name":"Convolution"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1810.12186","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}