Fetching the paper…
Reading the bibliography…
High-dimensional depth separation results for neural networks show that certain functions can be efficiently approximated by two-hidden-layer networks but not by one-hidden-layer ones in high-dimensions $d$.
Complexity of linear regions in deep networks
Boris Hanin and David Rolnick · 1901
Earlier work this paper cites.
Lectures on approximation by polynomials , volume 16
John Charles Burkill · 1959
Earlier work this paper cites.
Centrally symmetric convex bodies and distributions
Wolfgang Weil · 1976
Earlier work this paper cites.
An introduction to the approximation of functions
Theodore J Rivlin · 1981
Earlier work this paper cites.
Approximation of zonoids by zonotopes
Jean Bourgain, Joram Lindenstrauss, and Vitali Milman · 1989
Earlier work this paper cites.
Universal approximation bounds for superpositions of a sigmoidal function
Andrew R Barron · 1993
Earlier work this paper cites.
Inversion of fractional integrals related to the spherical radon transform
Boris Rubin · 1998
Earlier work this paper cites.
Approximation theory of the mlp model
Allan Pinkus · 1999
Earlier work this paper cites.
On the near optimality of the stochastic approximation of smooth functions by neural networks
VE Maiorov and Ron Meir · 2000
Earlier work this paper cites.
Spherical harmonics and approximations on the unit sphere: an introduction , volume 2044
Kendall Atkinson and Weimin Han · 2012
Earlier work this paper cites.
Approximation theory and harmonic analysis on spheres and balls , volume 23
Feng Dai and Yuan Xu · 2013
Earlier work this paper cites.
On the number of response regions of deep feed forward networks with piece-wise linear activations
Razvan Pascanu, Guido Montufar, and Yoshua Bengio · 2013
Earlier work this paper cites.
On the complexity of neural network classifiers: A comparison between shallow and deep architectures
Monica Bianchini and Franco Scarselli · 2014
Earlier work this paper cites.
Spherical harmonics in p dimensions
Costas Efthimiou and Christopher Frye · 2014
Earlier work this paper cites.
On the number of linear regions of deep neural networks
Guido F Montufar, Razvan Pascanu, Kyunghyun Cho, and Yoshua Bengio · 2014
Earlier work this paper cites.
Understanding deep neural networks with rectified linear units
Raman Arora, Amitabh Basu, Poorya Mianjy, and Anirbit Mukherjee · 2016
Cited alongside, same era.
Reverse hölder’s inequality for spherical harmonics
Feng Dai, Han Feng, and Sergey Tikhonov · 2016
Cited alongside, same era.
The power of depth for feedforward neural networks
Ronen Eldan and Ohad Shamir · 2016
Cited alongside, same era.
Why deep neural networks for function approximation?
Shiyu Liang and Rayadurgam Srikant · 2016
Cited alongside, same era.
Exponential expressivity in deep neural networks through transient chaos
Ben Poole, Subhaneil Lahiri, Maithra Raghu, Jascha Sohl-Dickstein, and Surya Ganguli · 2016
Cited alongside, same era.
Depth-width trade-offs for relu networks via sharkovsky’s theorem
Vaggos Chatziafratis, Sai Ganesh Nagarajan, Ioannis Panageas, and Xiao Wang · 2019
Later among the works it cites.
Efficient deep learning of gmms
Shirin Jalali, Carl Nuzman, and Iraj Saniee · 2019
Later among the works it cites.
Is deeper better only when shallow is good?
Eran Malach and Shai Shalev-Shwartz · 2019
Later among the works it cites.
A function space view of bounded norm infinite width relu nets: The multivariate case
Greg Ongie, Rebecca Willett, Daniel Soudry, and Nathan Srebro · 2019
Later among the works it cites.
On the spectral bias of neural networks
Nasim Rahaman, Aristide Baratin, Devansh Arpit, Felix Draxler, Min Lin, Fred Hamprecht, Yoshua Bengio, and Aaron Courville · 2019
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Matus Telgarsky · 2016
Cited alongside, same era.
Error bounds for approximations with deep relu networks
Dmitry Yarotsky · 2016
Cited alongside, same era.
Breaking the curse of dimensionality with convex neural networks
Francis Bach · 2017
Cited alongside, same era.
Depth separation for neural networks
Amit Daniely · 2017
Cited alongside, same era.
Why and when can deep-but not shallow-networks avoid the curse of dimensionality: a review
Tomaso Poggio, Hrushikesh Mhaskar, Lorenzo Rosasco, Brando Miranda, and Qianli Liao · 2017
Cited alongside, same era.
On the expressive power of deep neural networks
Maithra Raghu, Ben Poole, Jon Kleinberg, Surya Ganguli, and Jascha Sohl Dickstein · 2017
Cited alongside, same era.
The power of deeper networks for expressing natural functions
David Rolnick and Max Tegmark · 2017
Cited alongside, same era.
Depth separations in neural networks: What is actually being separated?
Itay Safran, Ronen Eldan, and Ohad Shamir · 2019
Later among the works it cites.
Sharp representation theorems for relu networks with precise dependence on depth
Guy Bresler and Dheeraj Nagaraj · 2020
Later among the works it cites.
Depth-width trade-offs for neural networks via topological entropy
Kaifeng Bu, Yaobo Zhang, and Qingxian Luo · 2020
Later among the works it cites.
Expressivity of deep neural networks
Ingo Gühring, Mones Raslan, and Gitta Kutyniok · 2020
Later among the works it cites.
Neural network theory, 2020
Philipp Christian Petersen · 2020
Later among the works it cites.
Donsub Rim, Luca Venturi, Joan Bruna, and Benjamin Peherstorfer · 2020
Later among the works it cites.
Neural networks with small weights and depth-separation barriers
Gal Vardi and Ohad Shamir · 2020
Later among the works it cites.
On the approximation power of two-layer networks of random relus
Daniel Hsu, Clayton Sanford, Rocco A Servedio, and Emmanouil-Vasileios Vlatakis-Gkaragkounis · 2021
Closest in time.
The connection between approximation, depth separation and learnability in neural networks
Eran Malach, Gilad Jehudai, Shai Shalev-Shwartz, and Ohad Shamir · 2021
Closest in time.
Size and depth separation in approximating natural functions with neural networks
Gal Vardi, Daniel Reichman, Toniann Pitassi, and Ohad Shamir · 2021
Closest in time.