{"id":34942,"date":"2022-06-04T19:31:18","date_gmt":"2022-06-04T11:31:18","guid":{"rendered":"https:\/\/swarma.org\/?p=34942"},"modified":"2022-06-04T19:31:18","modified_gmt":"2022-06-04T11:31:18","slug":"prl%e9%80%9f%e9%80%92%ef%bc%9a%e6%9c%ba%e5%99%a8%e5%ad%a6%e4%b9%a0%e5%af%bb%e6%89%be%e9%9a%90%e8%97%8f%e7%9a%84%e5%af%b9%e7%a7%b0%e6%80%a7","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=34942","title":{"rendered":"PRL\u901f\u9012\uff1a\u673a\u5668\u5b66\u4e60\u5bfb\u627e\u9690\u85cf\u7684\u5bf9\u79f0\u6027"},"content":{"rendered":"
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\u9690\u85cf\u5bf9\u79f0\u6027\u88ab\u5b9a\u4e49\u4e3a\uff0c\u53ea\u6709\u5728\u5fc5\u987b\u88ab\u53d1\u73b0\u7684\u65b0\u5750\u6807\u7cfb\u4e2d\u624d\u4f1a\u663e\u73b0\u7684\u5bf9\u79f0\u6027\u3002\u672c\u6587\u63d0\u51fa\u4e00\u79cd\u81ea\u52a8\u5bfb\u627e\u9690\u85cf\u5bf9\u79f0\u7684\u65b9\u6cd5\uff0c\u5176\u6838\u5fc3\u601d\u60f3\u662f\u5c06\u4e0d\u5bf9\u79f0\u6027\u91cf\u5316\u4e3a\u5bf9\u67d0\u4e9b\u504f\u5fae\u5206\u65b9\u7a0b\u7684\u7834\u574f\uff0c\u5e76\u5728\u6240\u6709\u53ef\u9006\u53d8\u6362\uff08\u53c2\u6570\u5316\u4e3a\u53ef\u9006\u795e\u7ecf\u7f51\u7edc\uff09\u7684\u7a7a\u95f4\u4e2d\u4ee5\u6570\u503c\u65b9\u5f0f\u6700\u5c0f\u5316\u8fd9\u79cd\u7834\u574f\u3002\u4f8b\u5982\uff0c\u8be5\u65b9\u6cd5\u91cd\u65b0\u53d1\u73b0\u4e86\u8457\u540d\u7684 Gullstrand-Painlev\u00e9 \u5ea6\u89c4\uff0c\u8be5\u5ea6\u89c4\u663e\u793a\u4e86\u975e\u65cb\u8f6c\u9ed1\u6d1e\u53f2\u74e6\u897f\u5ea6\u89c4\u4e2d\u9690\u85cf\u7684\u5e73\u79fb\u5bf9\u79f0\u6027\uff0c\u4ee5\u53ca\u54c8\u5bc6\u987f\u6027\uff08Hamiltonicity\uff09\u3001\u6a21\u5757\u5316\uff08modularity\uff09\u548c\u5176\u4ed6\u4f20\u7edf\u4e0a\u4e0d\u88ab\u89c6\u4e3a\u5bf9\u79f0\u6027\u7684\u7b80\u5316\u7279\u5f81\u3002<\/span><\/strong><\/p>\n


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Machine Learning Hidden Symmetries<\/span><\/p>\n

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https:\/\/journals.aps.org\/prl\/abstract\/10.1103\/PhysRevLett.128.180201<\/span><\/section>\n<\/section>\n<\/section>\n<\/blockquote>\n


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\u83f2\u5229\u666e\u00b7\u5b89\u5fb7\u68ee<\/span>\uff08Philip Anderson\uff09<\/span>\u6709\u53e5\u540d\u8a00\uff1a\u201c\u8bf4\u7269\u7406\u5b66\u662f\u5173\u4e8e\u5bf9\u79f0\u6027\u7684\u7814\u7a76\u53ea\u662f\u7a0d\u5fae\u5938\u5f20\u4e86\u4e00\u70b9\u201d\u3002\u4e8b\u5b9e\u8bc1\u660e\uff0c\u5728\u7269\u7406\u5b66\u548c\u673a\u5668\u5b66\u4e60\u4e2d\uff0c\u53d1\u73b0\u5bf9\u79f0\u6027\u5bf9\u52a0\u6df1\u7406\u89e3\u548c\u6709\u6548\u89e3\u51b3\u95ee\u9898\u90fd\u975e\u5e38\u6709\u7528\u3002<\/span><\/section>\n
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\u8bba\u6587 Abstract<\/strong><\/span><\/p>\n<\/section>\n<\/section>\n<\/section>\n

We present an automated method for finding hidden symmetries, defined as symmetries that become manifest only in a new coordinate system that must be discovered. Its core idea is to quantify asymmetry as violation of certain partial differential equations, and to numerically minimize such violation over the space of all invertible transformations, parametrized as invertible neural networks. For example, our method rediscovers the famous Gullstrand-Painlev\u00e9 metric that manifests hidden translational symmetry in the Schwarzschild metric of nonrotating black holes, as well as Hamiltonicity, modularity, and other simplifying traits not traditionally viewed as symmetries.<\/span><\/section>\n

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[1] P. W. Anderson More is different, Science 177, 393 (1972), https:\/\/science.sciencemag.org\/content\/177\/4047\/393.full.pdf.     <\/span><\/p>\n

[2] D. J. Gross, Symmetry in physics: Wigner\u2019s legacy, Physics Today 48, 46 (1995).  <\/span><\/p>\n

[3] D. J. Gross and F. Wilczek, Asymptotically free gauge theories. i, Physical Review D 8, 3633 (1973).      <\/span><\/p>\n

[4] T. Cohen and M. Welling, Group equivariant convolutional networks, in International conference on machine learning (PMLR, 2016) pp. 2990\u20132999.      <\/span><\/p>\n

[5] N. Thomas, T. Smidt, S. Kearnes, L. Yang, L. Li, K. Kohlhoff, and P. Riley, Tensor field networks: Rotation-and translation-equivariant neural networks for 3d point clouds, arXiv preprint arXiv:1802.08219 (2018).      <\/span><\/p>\n

[6] F. B. Fuchs, D. E. Worrall, V. Fischer, and M. Welling, Se (3)-transformers: 3d roto-translation equivariant attention networks, arXiv preprint arXiv:2006.10503 (2020).      <\/span><\/p>\n

[7] R. Kondor, Z. Lin, and S. Trivedi, Clebsch-gordan nets: a fully fourier space spherical convolutional neural network, arXiv preprint arXiv:1806.09231 (2018).     <\/span><\/p>\n

[8] V. G. Satorras, E. Hoogeboom, and M. Welling, E(n) equivariant graph neural networks, arXiv preprint arXiv:2102.09844 (2021).      <\/span><\/p>\n

[9] G. Kanwar, M. S. Albergo, D. Boyda, K. Cranmer, D. C. Hackett, S. Racani`ere, D. J. Rezende, and P. E. Shanahan, Equivariant flow-based sampling for lattice gauge theory, Phys. Rev. Lett. 125, 121601 (2020).<\/span><\/p>\n

[10] D. Boyda, G. Kanwar, S. Racani`ere, D. J. Rezende, M. S. Albergo, K. Cranmer, D. C. Hackett, and P. E. Shanahan, Sampling using SU(n) gauge equivariant flows,  Phys. Rev. D 103, 074504 (2021).     <\/span><\/p>\n

[11]  C. Misner, K. Thorne, and J. Wheeler, Gravitation (Princeton University Press, 2017). <\/span><\/p>\n

[12] E. Noether, Invariante variationsprobleme, Nachrichten von der Gesellschaft der Wissenschaften zu Gottingen, Mathematisch-Physikalische Klasse 1918, 235 (1918). <\/span><\/p>\n


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\u96c6\u667a\u6591\u56fe\u9876\u520a\u8bba\u6587\u901f\u9012\u680f\u76ee\u4e0a\u7ebf\u4ee5\u6765\uff0c\u6301\u7eed\u6536\u5f55\u6765\u81eaNature\u3001Science<\/span>\u7b49\u9876\u520a\u7684\u6700\u65b0\u8bba\u6587\uff0c\u8ffd\u8e2a\u590d\u6742\u7cfb\u7edf\u3001\u7f51\u7edc\u79d1\u5b66\u3001\u8ba1\u7b97\u793e\u4f1a\u79d1\u5b66\u7b49\u9886\u57df\u7684\u524d\u6cbf\u8fdb\u5c55\u3002\u73b0\u5728\u6b63\u5f0f\u63a8\u51fa\u8ba2\u9605\u529f\u80fd\uff0c\u6bcf\u5468\u901a\u8fc7\u5fae\u4fe1\u670d\u52a1\u53f7\u300c\u96c6\u667a\u6591\u56fe\u300d\u63a8\u9001\u8bba\u6587\u4fe1\u606f\u3002\u626b\u63cf\u4e0b\u65b9\u4e8c\u7ef4\u7801\u5373\u53ef\u4e00\u952e\u8ba2\u9605\uff1a<\/span>
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