Fetching the paper…
Reading the bibliography…
We investigate what can be learned from translating numerical algorithms into neural networks.
Hopfield, J.J.: Neural networks and physical systems with emergent collective computational abilities. Proceedings of the National Academy of Sciences 79
1982
Earlier work this paper cites.
Perona, P., Malik, J.: Scale space and edge detection using anisotropic diffusion. IEEE Transactions on Pattern Analysis and Machine Intelligence 12
1990
Earlier work this paper cites.
De Felice, P., Marangi, C., Nardulli, G., Pasquariello, G., Tedesco, L.: Dynamics of neural networks with non-monotone activation function. Network: Computation in Neural Systems 4
1993
Earlier work this paper cites.
Meilijson, I., Ruppin, E.: Optimal signalling in attractor neural networks. In: Tesauro, G., Touretzky, D., Leen, T. (eds.) Proc. 7th Annual Conference on Neural Information Processing Systems. Advances in Neural Information Processing Systems, vol. 7, pp. 485–492. Denver, CO (Dec 1994)
1994
Earlier work this paper cites.
Weickert, J., Benhamouda, B.: A semidiscrete nonlinear scale-space theory and its relation to the Perona–Malik paradox. In: Solina, F., Kropatsch, W.G., Klette, R., Bajcsy, R. (eds.) Advances in Computer Vision, pp. 1–10. Springer, Wien (1997)
1997
Earlier work this paper cites.
Weickert, J.: Anisotropic Diffusion in Image Processing. Teubner, Stuttgart (1998)
1998
Earlier work this paper cites.
Briggs, W.L., Henson, V.E., McCormick, S.F.: A Multigrid Tutorial. SIAM, Philadelphia, second edn. (2000)
2000
Earlier work this paper cites.
You, Y.L., Kaveh, M.: Fourth-order partial differential equations for noise removal. IEEE Transactions on Image Processing 9
2000
Earlier work this paper cites.
Didas, S., Weickert, J., Burgeth, B.: Properties of higher order nonlinear diffusion filtering. Journal of Mathematical Imaging and Vision 35
2009
Earlier work this paper cites.
Goodfellow, I., Warde-Farley, D., Mirza, M., Courville, A., Bengio, Y.: Maxout networks. In: Dasgupta, S., McAllester, D. (eds.) Proc. 30th International Conference on Machine Learning. Proceedings of Machine Learning Research, vol. 28, pp. 1319–1327. Atlanta, GA (Jun 2013)
2013
Cited alongside, same era.
Ronneberger, O., Fischer, P., Brox, T.: U-net: Convolutional networks for biomedical image segmentation. In: Navab, N., Hornegger, J., Wells, W., Frangi, A. (eds.) Medical Image Computing and Computer-Assisted Intervention – MICCAI 2015, Lecture Notes in Computer Science, vol. 9351, pp. 234–241. Springer, Cham (2015)
2015
Cited alongside, same era.
Chen, Y., Pock, T.: Trainable nonlinear reaction diffusion: A flexible framework for fast and effective image restoration. IEEE Transactions on Pattern Analysis and Machine Intelligence 39
2016
Cited alongside, same era.
Hafner, D., Ochs, P., Weickert, J., Reißel, M., Grewenig, S.: FSI schemes: Fast semi-iterative solvers for PDEs and optimisation methods. In: Rosenhahn, B., Andres, B. (eds.) Pattern Recognition, Lecture Notes in Computer Science, vol. 9796, pp. 91–102. Springer, Cham (2016)
Greenfeld, D., Galun, M., Kimmel, R., Yavneh, I., Basri, R.: Learning to optimize multigrid PDE solvers. In: Chaudhuri, K., Salakhutdinov, R. (eds.) Proc. 36th International Conference on Machine Learning. Proceedings of Machine Learning Research, vol. 97, pp. 2415–2423. Long Beach, CA (Jun 2019)
2019
Later among the works it cites.
He, J., Xu, J.: MgNet: A unified framework of multigrid and convolutional neural network. Science China Mathematics 62
2019
Later among the works it cites.
Ouala, S., Pascual, A., Fablet, R.: Residual integration neural network. In: Proc. 2019 IEEE International Conference on Acoustics, Speech and Signal Processing. pp. 3622–3626. IEEE Computer Society Press, Brighton, UK (May 2019)
2019
Later among the works it cites.
2020
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
2016
Cited alongside, same era.
He, K., Zhang, X., Ren, S., Sun, J.: Deep residual learning for image recognition. In: Proc. 2016 IEEE Conference on Computer Vision and Pattern Recognition. pp. 770–778. IEEE Computer Society Press, Las Vegas, NV (Jun 2016)
2016
Cited alongside, same era.
Newell, A., Yang, K., Deng, J.: Stacked hourglass networks for human pose estimation. In: Leibe, B., Matas, J., Sebe, N., Welling, M. (eds.) Computer Vision – ECCV 2016, Lecture Notes in Computer Science, vol. 9912, pp. 483–499. Springer, Cham (2016)
2016
Cited alongside, same era.
Huang, G., Liu, Z., van der Maaten, L., Weinberger, K.Q.: Densely connected convolutional networks. In: Proc. 2017 IEEE Conference on Computer Vision and Pattern Recognition. pp. 4700–4708. IEEE Computer Society Press, Honolulu, HI (Jul 2017)
2017
Cited alongside, same era.
Lu, Y., Zhong, A., Li, Q., Dong, B.: Beyond finite layer neural networks: Bridging deep architectures and numerical differential equations. In: Dy, J., Krause, A. (eds.) Proc. 35th International Conference on Machine Learning. Proceedings of Machine Learning Research, vol. 80, pp. 3276–3285. Stockholm, Sweden (Jul 2018)
2018
Cited alongside, same era.
Ochs, P., Meinhardt, T., Leal-Taixe, L., Möller, M.: Lifting layers: Analysis and applications. In: Ferrari, V., Herbert, M., Sminchisescu, C., Weiss, Y. (eds.) Computer Vision – ECCV 2018, Lecture Notes in Computer Science, vol. 11205, pp. 53–68. Springer, Cham (2018)
2018
Cited alongside, same era.
2020
Later among the works it cites.
Rousseau, F., Drumetz, L., Fablet, R.: Residual networks as flows of diffeomorphisms. Journal of Mathematical Imaging and Vision 62
2020
Later among the works it cites.
Ruthotto, L., Haber, E.: Deep neural networks motivated by partial differential equations. Journal of Mathematical Imaging and Vision 62
2020
Later among the works it cites.
2020
Later among the works it cites.
Zhang, L., Schaeffer, H.: Forward stability of ResNet and its variants. Journal of Mathematical Imaging and Vision 62
2020
Later among the works it cites.