Fetching the paper…
Reading the bibliography…
Training neural networks under a strict Lipschitz constraint is useful for provable adversarial robustness, generalization bounds, interpretable gradients, and Wasserstein distance estimation.
An iterative algorithm for computing the best estimate of an orthogonal matrix
Björck, Å. and Bowie, C · 1971
Earlier work this paper cites.
Approximation by superpositions of a sigmoidal function
Cybenko, G · 1989
Earlier work this paper cites.
Approximation capabilities of multilayer feedforward networks
Hornik, K · 1991
Earlier work this paper cites.
Improving generalization performance using double backpropagation
Drucker, H. and Le Cun, Y · 1992
Earlier work this paper cites.
The sample complexity of pattern classification with neural networks: the size of the weights is more important than the size of the network
Bartlett, P · 1998
Earlier work this paper cites.
Optimal transport: old and new , volume 338
Villani, C · 2008
Earlier work this paper cites.
Optimization algorithms on matrix manifolds
Absil, P.-A., Mahony, R., and Sepulchre, R · 2009
Earlier work this paper cites.
Learning multiple layers of features from tiny images
Krizhevsky, A · 2009
Earlier work this paper cites.
Programming guide, 2010
Nvidia, C · 2010
Earlier work this paper cites.
Lipschitz functions on topometric spaces
Yaacov, I. B · 2010
Earlier work this paper cites.
Invariant scattering convolution networks
Bruna, J. and Mallat, S · 2012
Earlier work this paper cites.
ImageNet classification with deep convolutional neural networks
Krizhevsky, A., Sutskever, I., and Hinton, G. E · 2012
Earlier work this paper cites.
Maxout networks
Goodfellow, I., Warde-Farley, D., Mirza, M., Courville, A., and Bengio, Y · 2013
Earlier work this paper cites.
Intriguing properties of neural networks
Szegedy, C., Zaremba, W., Sutskever, I., Bruna, J., Erhan, D., Goodfellow, I. J., and Fergus, R · 2013
Earlier work this paper cites.
Explaining and harnessing adversarial examples
Goodfellow, I. J., Shlens, J., and Szegedy, C · 2014
Earlier work this paper cites.
On the number of linear regions of deep neural networks
Montufar, G. F., Pascanu, R., Cho, K., and Bengio, Y · 2014
Earlier work this paper cites.
Adam: A method for stochastic optimization
Kingma, D. and Ba, J · 2015
Earlier work this paper cites.
Deep learning face attributes in the wild
Liu, Z., Luo, P., Wang, X., and Tang, X · 2015
Earlier work this paper cites.
Variational inference with normalizing flows
Rezende, D. J. and Mohamed, S · 2015
Earlier work this paper cites.
Unitary evolution recurrent neural networks
Arjovsky, M., Shah, A., and Bengio, Y · 2016
Cited alongside, same era.
Towards evaluating the robustness of neural networks
Carlini, N. and Wagner, D · 2016
Cited alongside, same era.
InfoGAN: Interpretable representation learning by information maximizing generative adversarial nets
Chen, X., Duan, Y., Houthooft, R., Schulman, J., Sutskever, I., and Abbeel, P · 2016
Cited alongside, same era.
Norm-preserving orthogonal permutation linear unit activation functions (oplu)
Chernodub, A. and Nowicki, D · 2016
Cited alongside, same era.
Fast projection onto the simplex and the 𝒍 𝟏 \boldsymbol{l}_{\mathbf{1}} ball
Condat, L · 2016
Cited alongside, same era.
Resurrecting the sigmoid in deep learning through dynamical isometry: theory and practice
Pennington, J., Schoenholz, S., and Ganguli, S · 2017
Later among the works it cites.
Robust large margin deep neural networks
Sokolić, J., Giryes, R., Sapiro, G., and Rodrigues, M. R · 2017
Later among the works it cites.
Learning structured weight uncertainty in bayesian neural networks
Sun, S., Chen, C., and Carin, L · 2017
Later among the works it cites.
A new trick for calculating Jacobian vector products
Townsend, J · 2017
Later among the works it cites.
Spectral norm regularization for improving the generalizability of deep learning
Yoshida, Y. and Miyato, T · 2017
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Deep residual learning for image recognition
He, K., Zhang, X., Ren, S., and Sun, J · 2016
Cited alongside, same era.
Understanding and improving convolutional neural networks via concatenated rectified linear units
Shang, W., Sohn, K., Almeida, D., and Lee, H · 2016
Cited alongside, same era.
Full-capacity unitary recurrent neural networks
Wisdom, S., Powers, T., Hershey, J., Le Roux, J., and Atlas, L · 2016
Cited alongside, same era.
Zagoruyko, S. and Komodakis, N · 2016
Cited alongside, same era.
Arjovsky, M., Chintala, S., and Bottou, L · 2017
Cited alongside, same era.
Spectrally-normalized margin bounds for neural networks
Bartlett, P. L., Foster, D. J., and Telgarsky, M. J · 2017
Cited alongside, same era.
Parseval networks: Improving robustness to adversarial examples
Cisse, M., Bojanowski, P., Grave, E., Dauphin, Y., and Usunier, N · 2017
Cited alongside, same era.
Chen, M., Pennington, J., and Schoenholz, S. S · 2018
Closest in time.
Gemici, M., Akata, Z., and Welling, M · 2018
Closest in time.
Regularisation of neural networks by enforcing lipschitz continuity
Gouk, H., Frank, E., Pfahringer, B., and Cree, M · 2018
Closest in time.
Limitations of the Lipschitz constant as a defense against adversarial examples
Huster, T., Chiang, C.-Y. J., and Chadha, R · 2018
Closest in time.
Aggregated momentum: Stability through passive damping
Lucas, J., Zemel, R., and Grosse, R · 2018
Closest in time.
Spectral normalization for generative adversarial networks
Miyato, T., Kataoka, T., Koyama, M., and Yoshida, Y · 2018
Closest in time.
A PAC-bayesian approach to spectrally-normalized margin bounds for neural networks
Neyshabur, B., Bhojanapalli, S., and Srebro, N · 2018
Closest in time.
Computational optimal transport
Peyré, G. and Cuturi, M · 2018
Closest in time.
The singular values of convolutional layers
Sedghi, H., Gupta, V., and Long, P. M · 2018
Closest in time.
Adversarial vulnerability of neural networks increases with input dimension
Simon-Gabriel, C.-J., Ollivier, Y., Schölkopf, B., Bottou, L., and Lopez-Paz, D · 2018
Closest in time.
There is no free lunch in adversarial robustness (but there are unexpected benefits)
Tsipras, D., Santurkar, S., Engstrom, L., Turner, A., and Madry, A · 2018
Closest in time.
Tsuzuku, Y., Sato, I., and Sugiyama, M · 2018
Closest in time.
Sylvester normalizing flows for variational inference
van den Berg, R., Hasenclever, L., Tomczak, J. M., and Welling, M · 2018
Closest in time.
Xiao, L., Bahri, Y., Sohl-Dickstein, J., Schoenholz, S. S., and Pennington, J · 2018
Closest in time.