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We present a theoretical and empirical study of the gradient dynamics of overparameterized shallow ReLU networks with one-dimensional input, solving least-squares interpolation.
Theory of reproducing kernels
Nachman Aronszajn · 1950
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Generalized gradients and applications
Frank H Clarke · 1975
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Random features for large-scale kernel machines
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Representation by integrating reproducing kernels
Thomas Hotz and Fabian JE Telschow · 2012
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Efficient representation of low-dimensional manifolds using deep networks
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Sgd learns the conjugate kernel class of the network
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Spurious local minima are common in two-layer relu neural networks
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A note on lazy training in supervised differentiable programming
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On the global convergence of gradient descent for over-parameterized models using optimal transport
Lenaic Chizat and Francis Bach · 2018
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Gradient descent finds global minima of deep neural networks
Simon S Du, Jason D Lee, Haochuan Li, Liwei Wang, and Xiyu Zhai · 2018
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Gradient descent provably optimizes over-parameterized neural networks
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A generalization theory of gradient descent for learning over-parameterized deep relu networks
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I Daubechies, R DeVore, S Foucart, B Hanin, and G Petrova · 2019
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