# Spherical CNNs

- Published: 30 Jan 2018

L. C. Blum and J.-L. Reymond. 970 million druglike small molecules for virtual screening in the chemical universe database GDB-13. J. Am. Chem. Soc., 131:8732, 2009.

W. Boomsma and J. Frellsen. Spherical convolutions and their application in molecular modelling. In I Guyon, U V Luxburg, S Bengio, H Wallach, R Fergus, S Vishwanathan, and R Garnett, editors, Advances in Neural Information Processing Systems 30, pages 3436-3446. Curran Associates, Inc., 2017. [OpenAIRE]

A.X. Chang, T. Funkhouser, L. Guibas, P. Hanrahan, Q. Huang, Z. Li, S. Savarese, M. Savva, S. Song, H. Su, et al. Shapenet: An information-rich 3d model repository. arXiv preprint arXiv:1512.03012, 2015. [OpenAIRE]

G.S. Chirikjian and A.B. Kyatkin. Engineering Applications of Noncommutative Harmonic Analysis. CRC Press, 1 edition, may 2001. ISBN 9781420041767. [OpenAIRE]

T.S. Cohen and M. Welling. Group equivariant convolutional networks. In Proceedings of The 33rd International Conference on Machine Learning (ICML), volume 48, pages 2990-2999, 2016.

T.S. Cohen and M. Welling. Steerable CNNs. In ICLR, 2017.

T.S. Cohen, M. Geiger, J. Koehler, and M. Welling. Convolutional networks for spherical signals. In ICML Workshop on Principled Approaches to Deep Learning, 2017.

S. Dieleman, K. W. Willett, and J. Dambre. Rotation-invariant convolutional neural networks for galaxy morphology prediction. Monthly Notices of the Royal Astronomical Society, 450(2), 2015.

S. Dieleman, J. De Fauw, and K. Kavukcuoglu. Exploiting Cyclic Symmetry in Convolutional Neural Networks. In International Conference on Machine Learning (ICML), 2016. [OpenAIRE]

J.B. Drake, P.H. Worley, and E.F. D'Azevedo. Algorithm 888: Spherical harmonic transform algorithms. ACM Trans. Math. Softw., 35(3):23:1-23:23, 2008. doi: 10.1145/1391989.1404581.

J.R. Driscoll and D.M. Healy. Computing Fourier transforms and convolutions on the 2-sphere. Advances in applied mathematics, 1994.

G.B. Folland. A Course in Abstract Harmonic Analysis. CRC Press, 1995.

R. Gens and P. Domingos. Deep Symmetry Networks. In Advances in Neural Information Processing Systems (NIPS), 2014.

B. Gutman, Y. Wang, T. Chan, P.M. Thompson, and others. Shape registration with spherical cross correlation. 2nd MICCAI workshop, 2008.

N. Guttenberg, N. Virgo, O. Witkowski, H. Aoki, and R. Kanai. Permutation-equivariant neural networks applied to dynamics prediction. 2016. [OpenAIRE]

###### Related research

L. C. Blum and J.-L. Reymond. 970 million druglike small molecules for virtual screening in the chemical universe database GDB-13. J. Am. Chem. Soc., 131:8732, 2009.

W. Boomsma and J. Frellsen. Spherical convolutions and their application in molecular modelling. In I Guyon, U V Luxburg, S Bengio, H Wallach, R Fergus, S Vishwanathan, and R Garnett, editors, Advances in Neural Information Processing Systems 30, pages 3436-3446. Curran Associates, Inc., 2017. [OpenAIRE]

A.X. Chang, T. Funkhouser, L. Guibas, P. Hanrahan, Q. Huang, Z. Li, S. Savarese, M. Savva, S. Song, H. Su, et al. Shapenet: An information-rich 3d model repository. arXiv preprint arXiv:1512.03012, 2015. [OpenAIRE]

G.S. Chirikjian and A.B. Kyatkin. Engineering Applications of Noncommutative Harmonic Analysis. CRC Press, 1 edition, may 2001. ISBN 9781420041767. [OpenAIRE]

T.S. Cohen and M. Welling. Group equivariant convolutional networks. In Proceedings of The 33rd International Conference on Machine Learning (ICML), volume 48, pages 2990-2999, 2016.

T.S. Cohen and M. Welling. Steerable CNNs. In ICLR, 2017.

T.S. Cohen, M. Geiger, J. Koehler, and M. Welling. Convolutional networks for spherical signals. In ICML Workshop on Principled Approaches to Deep Learning, 2017.

S. Dieleman, K. W. Willett, and J. Dambre. Rotation-invariant convolutional neural networks for galaxy morphology prediction. Monthly Notices of the Royal Astronomical Society, 450(2), 2015.

S. Dieleman, J. De Fauw, and K. Kavukcuoglu. Exploiting Cyclic Symmetry in Convolutional Neural Networks. In International Conference on Machine Learning (ICML), 2016. [OpenAIRE]

J.B. Drake, P.H. Worley, and E.F. D'Azevedo. Algorithm 888: Spherical harmonic transform algorithms. ACM Trans. Math. Softw., 35(3):23:1-23:23, 2008. doi: 10.1145/1391989.1404581.

J.R. Driscoll and D.M. Healy. Computing Fourier transforms and convolutions on the 2-sphere. Advances in applied mathematics, 1994.

G.B. Folland. A Course in Abstract Harmonic Analysis. CRC Press, 1995.

R. Gens and P. Domingos. Deep Symmetry Networks. In Advances in Neural Information Processing Systems (NIPS), 2014.

B. Gutman, Y. Wang, T. Chan, P.M. Thompson, and others. Shape registration with spherical cross correlation. 2nd MICCAI workshop, 2008.

N. Guttenberg, N. Virgo, O. Witkowski, H. Aoki, and R. Kanai. Permutation-equivariant neural networks applied to dynamics prediction. 2016. [OpenAIRE]