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We develop a variational framework to understand the properties of the functions learned by neural networks fit to data.
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Multilayer feedforward networks with a nonpolynomial activation function can approximate any function
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The Calderón reproducing formula, windowed X-ray transforms, and Radon transforms in L p L^{p} -spaces
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Harmonic analysis of neural networks
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A generalized representer theorem
B. Schölkopf, R. Herbrich, and A. J. Smola · 2001
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Rademacher and gaussian complexities: Risk bounds and structural results
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Learning with kernels: support vector machines, regularization, optimization, and beyond
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ℓ 1 \ell_{1} regularization in infinite dimensional feature spaces
S. Rosset, G. Swirszcz, N. Srebro, and J. Zhu · 2007
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Breaking the coherence barrier: A new theory for compressed sensing
B. Adcock, A. C. Hansen, C. Poon, and B. Roman · 2017
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Breaking the curse of dimensionality with convex neural networks
F. Bach · 2017
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Neural network with unbounded activation functions is universal approximator
S. Sonoda and N. Murata · 2017
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Splines are universal solutions of linear inverse problems with generalized TV regularization
M. Unser, J. Fageot, and J. P. Ward · 2017
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A spline theory of deep learning
R. Balestriero and R. Baraniuk · 2018
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Some problems in the theory of ridge functions
S. V. Konyagin, A. A. Kuleshov, and V. E. Maiorov · 2018
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Reproducing kernel Banach spaces for machine learning
H. Zhang, Y. Xu, and J. Zhang · 2009
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Best approximation by ridge functions in L p L_{p} -spaces
V. E. Maiorov · 2010
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Scattered Data Approximation
H. Wendland · 2010
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Morrey and Campanato Meet Besov, Lizorkin and Triebel
W. Yuan, W. Sickel, and D. Yang · 2010
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Fourier analysis: an introduction , volume 1
E. M. Stein and R. Shakarchi · 2011
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Topological Vector Spaces
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Provable approximation properties for deep neural networks
U. Shaham, A. Cloninger, and R. R. Coifman · 2018
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Complexity, statistical risk, and metric entropy of deep nets using total path variation
A. R. Barron and J. M. Klusowski · 2019
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On representer theorems and convex regularization
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Gradient descent provably optimizes over-parameterized neural networks
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Deep neural network approximation theory
P. Grohs, D. Perekrestenko, D. Elbrächter, and H. Bölcskei · 2019
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How do infinite width bounded norm networks look in function space?
P. H. P. Savarese, I. Evron, D. Soudry, and N. Srebro · 2019
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A representer theorem for deep neural networks
M. Unser · 2019
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Native banach spaces for splines and variational inverse problems
M. Unser and J. Fageot · 2019
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Regularization matters: Generalization and optimization of neural nets vs their induced kernel
C. Wei, J. D. Lee, Q. Liu, and T. Ma · 2019
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Gradient dynamics of shallow univariate ReLU networks
F. Williams, M. Trager, D. Panozzo, C. Silva, D. Zorin, and J. Bruna · 2019
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Generalized Mercer kernels and reproducing kernel Banach spaces , volume 258
Y. Xu and Q. Ye · 2019
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Sparsity of solutions for variational inverse problems with finite-dimensional data
K. Bredies and M. Carioni · 2020
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Convex duality of deep neural networks
T. Ergen and M. Pilanci · 2020
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Dimension independent bounds for general shallow networks
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A function space view of bounded norm infinite width ReLU nets: The multivariate case
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A unifying representer theorem for inverse problems and machine learning
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