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We study the sample complexity of learning neural networks, by providing new bounds on their Rademacher complexity assuming norm constraints on the parameter matrix of each layer.
Probability in Banach Spaces
Michel Ledoux and Michel Talagrand · 1991
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The sample complexity of pattern classification with neural networks: the size of the weights is more important than the size of the network
Peter L Bartlett · 1998
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Rademacher and gaussian complexities: Risk bounds and structural results
Peter L Bartlett and Shahar Mendelson · 2002
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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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Neural network learning: Theoretical foundations
Martin Anthony and Peter L Bartlett · 2009
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Concentration inequalities: A nonasymptotic theory of independence
Stéphane Boucheron, Gábor Lugosi, and Pascal Massart · 2013
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In search of the real inductive bias: On the role of implicit regularization in deep learning
Behnam Neyshabur, Ryota Tomioka, and Nathan Srebro · 2014
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Understanding machine learning: From theory to algorithms
Shai Shalev-Shwartz and Shai Ben-David · 2014
Cited alongside, same era.
Norm-based capacity control in neural networks
Behnam Neyshabur, Ryota Tomioka, and Nathan Srebro · 2015
Later among the works it cites.
Understanding deep learning requires rethinking generalization
Chiyuan Zhang, Samy Bengio, Moritz Hardt, Benjamin Recht, and Oriol Vinyals · 2016
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Spectrally-normalized margin bounds for neural networks
Peter Bartlett, Dylan J Foster, and Matus Telgarsky · 2017
Closest in time.
A pac-bayesian approach to spectrally-normalized margin bounds for neural networks
Behnam Neyshabur, Srinadh Bhojanapalli, David McAllester, and Nathan Srebro · 2017
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