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It is widely believed that engineering a model to be invariant/equivariant improves generalisation.
A generalized inverse for matrices
Penrose, R · 1955
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On isotropic cartesian tensors
Hodge, P. G · 1961
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Some aspects of discrimination function coefficients
Gupta, S. D · 1968
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Linear representations of finite groups
Serre, J.-P · 1977
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On the existence of complete invariant feature spaces in pattern recognition
Schulz-Mirbach, H · 1992
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Hints and the VC dimension
Abu-Mostafa, Y. S · 1993
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Constructing invariant features by averaging techniques
Schulz-Mirbach, H · 1994
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Incorporating invariances in support vector learning machines
Schölkopf, B., Burges, C., and Vapnik, V · 1996
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Representation theory and invariant neural networks
Wood, J. and Shawe-Taylor, J · 1996
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Invariance in kernel methods by haar integration kernels
Haasdonk, B., Vossen, A., and Burkhardt, H · 2005
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Foundations of modern probability
Kallenberg, O · 2006
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Aspects of multivariate statistical theory , volume 197
Muirhead, R. J · 2009
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On the mean and variance of the generalized inverse of a singular wishart matrix
Cook, R. D., Forzani, L., et al · 2011
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Lecture notes on representation theory, October 2012
Wadsley, S · 2012
Cited alongside, same era.
Robustness and generalization
Xu, H. and Mannor, S · 2012
Cited alongside, same era.
Unsupervised learning of invariant representations in hierarchical architectures, 2014
Anselmi, F., Leibo, J. Z., Rosasco, L., Mutch, J., Tacchetti, A., and Poggio, T · 2014
Cited alongside, same era.
Learning with group invariant features: A kernel perspective
Mroueh, Y., Voinea, S., and Poggio, T. A · 2015
Cited alongside, same era.
Very deep convolutional networks for large-scale image recognition
Simonyan, K. and Zisserman, A · 2015
Cited alongside, same era.
Going deeper with convolutions
Szegedy, C., Liu, W., Jia, Y., Sermanet, P., Reed, S., Anguelov, D., Erhan, D., Vanhoucke, V., and Rabinovich, A · 2015
Cited alongside, same era.
On the generalization of equivariance and convolution in neural networks to the action of compact groups
Kondor, R. and Trivedi, S · 2018
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3d g-cnns for pulmonary nodule detection
Winkels, M. and Cohen, T. S · 2018
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Universal approximations of invariant maps by neural networks, 2018
Yarotsky, D · 2018
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Nearly-tight VC-dimension and pseudodimension bounds for piecewise linear neural networks
Bartlett, P. L., Harvey, N., Liaw, C., and Mehrabian, A · 2019
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A general theory of equivariant cnns on homogeneous spaces
Cohen, T. S., Geiger, M., and Weiler, M · 2019
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Surprises in high-dimensional ridgeless least squares interpolation
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Group equivariant convolutional networks
Cohen, T. and Welling, M · 2016
Cited alongside, same era.
A course in abstract harmonic analysis , volume 29
Folland, G. B · 2016
Cited alongside, same era.
Deep residual learning for image recognition
He, K., Zhang, X., Ren, S., and Sun, J · 2016
Cited alongside, same era.
Equivariance through parameter-sharing
Ravanbakhsh, S., Schneider, J., and Poczos, B · 2017
Cited alongside, same era.
Generalization error of invariant classifiers
Sokolic, J., Giryes, R., Sapiro, G., and Rodrigues, M · 2017
Cited alongside, same era.
Deep sets
Zaheer, M., Kottur, S., Ravanbakhsh, S., Poczos, B., Salakhutdinov, R. R., and Smola, A. J · 2017
Cited alongside, same era.
Hastie, T., Montanari, A., Rosset, S., and Tibshirani, R. J · 2019
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An analysis of the effect of invariance on generalization in neural networks
Lyle, C., Kwiatkowksa, M., and Gal, Y · 2019
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On the universality of invariant networks
Maron, H., Fetaya, E., Segol, N., and Lipman, Y · 2019
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Improved generalization bound of group invariant / equivariant deep networks via quotient feature space, 2019
Sannai, A. and Imaizumi, M · 2019
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High-dimensional statistics: A non-asymptotic viewpoint , volume 48
Wainwright, M. J · 2019
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Probabilistic symmetries and invariant neural networks
Bloem-Reddy, B. and Teh, Y. W · 2020
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On the benefits of invariance in neural networks, 2020
Lyle, C., van der Wilk, M., Kwiatkowska, M., Gal, Y., and Bloem-Reddy, B · 2020
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Ab initio solution of the many-electron schrödinger equation with deep neural networks
Pfau, D., Spencer, J. S., Matthews, A. G., and Foulkes, W. M. C · 2020
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