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We study the relationship between geometry and capacity measures for deep neural networks from an invariance viewpoint.
A simple weight decay can improve generalization
Anders Krogh and John A Hertz · 1992
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Flat minima
Sepp Hochreiter and Jürgen Schmidhuber · 1997
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Natural gradient works efficiently in learning
Shun-Ichi Amari · 1998
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Neural network learning: Theoretical foundations
Martin Anthony and Peter L Bartlett · 1999
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Empirical margin distributions and bounding the generalization error of combined classifiers
Vladimir Koltchinskii and Dmitry Panchenko · 2002
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Imagenet classification with deep convolutional neural networks
Alex Krizhevsky, Ilya Sutskever, and Geoffrey E Hinton · 2012
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Optimizing neural networks with kronecker-factored approximate curvature
James Martens and Roger Grosse · 2015
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Path-sgd: Path-normalized optimization in deep neural networks
Behnam Neyshabur, Ruslan R Salakhutdinov, and Nati Srebro · 2015
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Norm-based capacity control in neural networks
Behnam Neyshabur, Ryota Tomioka, and Nathan Srebro · 2015
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Uniqueness of the fisher–rao metric on the space of smooth densities
Martin Bauer, Martins Bruveris, and Peter W Michor · 2016
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Understanding deep learning requires rethinking generalization
Chiyuan Zhang, Samy Bengio, Moritz Hardt, Benjamin Recht, and Oriol Vinyals · 2016
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Sharp minima can generalize for deep nets
Laurent Dinh, Razvan Pascanu, Samy Bengio, and Yoshua Bengio · 2017
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Exploring generalization in deep learning
Behnam Neyshabur, Srinadh Bhojanapalli, David McAllester, and Nathan Srebro · 2017
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Shai Shalev-Shwartz, Ohad Shamir, and Shaked Shammah · 2017
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Blog post on “(liang et al., 2017), generalization and the fisher-rao norm”, 2018
Ferenc Huszár · 2018
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Universal statistics of fisher information in deep neural networks: Mean field approach
Ryo Karakida, Shotaro Akaho, and Shun-ichi Amari · 2018
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Peter Bartlett, Dylan J Foster, and Matus Telgarsky · 2017
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