Fetching the paper…
Reading the bibliography…
In this paper, we explain the universal approximation capabilities of deep residual neural networks through geometric nonlinear control.
Excitatory and inhibitory interactions in localized populations of model neurons
H.R. Wilson and J. D. Cowan · 1972
Earlier work this paper cites.
Neurons with graded response have collective computational properties like those of two-state neurons
J. Hopfield · 1984
Earlier work this paper cites.
Introduction to neural networks for intelligent control
B. Bavarian · 1988
Earlier work this paper cites.
A multilayered neural network controller
D. Psaltis, A. Sideris, and A. A. Yamamura · 1988
Earlier work this paper cites.
Approximation by superpositions of a sigmoidal function
G. Cybenko · 1989
Earlier work this paper cites.
Convergent activation dynamics in continuous time networks
Morris W. Hirsch · 1989
Earlier work this paper cites.
Qualitative analysis of neural networks
A. N. Michel, J. A. Farrell, and W. Porod · 1989
Earlier work this paper cites.
Neural networks for control systems
P. J. Antsaklis · 1990
Earlier work this paper cites.
Approximation capabilities of multilayer feedforward networks
K. Hornik · 1991
Earlier work this paper cites.
Uniqueness of weights for neural networks
D. Albertini, E. D. Sontag, and V. Maillot · 1993
Earlier work this paper cites.
For neural networks, function determines form
F. Albertini and E. D. Sontag · 1993
Earlier work this paper cites.
Approximation of dynamical systems by continuous time recurrent neural networks
K. Funahashi and Y. Nakamura · 1993
Earlier work this paper cites.
Monotone flows and order intervals
J.-L. Gouze and K.P. Hadeler · 1994
Earlier work this paper cites.
Geometric Control Theory
V. Jurdjevic · 1996
Earlier work this paper cites.
Complete controllability of continuous-time recurrent neural networks
E. D. Sontag and H. Sussmann · 1997
Earlier work this paper cites.
Approximation theory of the mlp model in neural networks [j]
A Pinkus · 1999
Cited alongside, same era.
Further results on controllability of recurrent neural networks
E. D. Sontag and Y. Qiao · 1999
Cited alongside, same era.
Advanced determinant calculus
C. Krattenthaler · 2001
Cited alongside, same era.
Monotone dynamical systems
Morris W Hirsch and Hal Smith · 2006
Cited alongside, same era.
Control of inhomogeneous quantum ensembles
J-S. Li and N. Khaneja · 2006
Cited alongside, same era.
Optimal control of the Liouville equation
R. W. Brockett · 2007
Cited alongside, same era.
Monotone Dynamical Systems: An Introduction to the Theory of Competitive and Cooperative Systems
ResNet with one-neuron hidden layers is a universal approximator
H. Lin and S. Jegelka · 2018
Later among the works it cites.
Beyond finite layer neural networks: Bridging deep architectures and numerical differential equations
Y. Lu, A. Zhong, Q. Li, and B. Dong · 2018
Later among the works it cites.
Deep neural networks, generic universal interpolation, and controlled ODEs
C. Cuchiero, M. Larsson, and J. Teichmann · 2019
Later among the works it cites.
Deep, skinny neural networks are not universal approximators
J. Johnson · 2019
Later among the works it cites.
Deep learning via dynamical systems: An approximation perspective
Q. Li, T. Lin, and Z. Shen · 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…
H. L. Smith · 2008
Cited alongside, same era.
Introduction to Smooth Manifolds
John M. Lee · 2013
Cited alongside, same era.
Necessary conditions for controllability of nonlinear networked control systems
C. Aguilar and B. Gharesifard · 2014
Cited alongside, same era.
Do deep nets really need to be deep?
L. J. Ba and R. Caruana · 2014
Cited alongside, same era.
Uniform ensemble controllability for one-parameter families of time-invariant linear systems
U. Helmke and M. Schönlein · 2014
Cited alongside, same era.
Deep residual learning for image recognition
K. He, X. Zhang, S. Ren, and J. Sun · 2016
Cited alongside, same era.
Small ReLU networks are powerful memorizers: a tight analysis of memorization capacity
Chulhee Yun, Suvrit Sra, and Ali Jadbabaie · 2019
Later among the works it cites.
Control in the spaces of ensembles of points
A. Agrachev and A. Sarychev · 2020
Closest in time.
Control on the manifolds of mappings as a setting for deep learning
A. Agrachev and A. Sarychev · 2020
Closest in time.
Large-time asymptotics in deep learning
C. Esteve, B. Geshkovski, D. Pighin, and E. Zuazua · 2020
Closest in time.
Universal approximation with deep narrow networks
P. Kidger and T. Lyons · 2020
Closest in time.
Memory capacity of neural networks with threshold and ReLU activations
Roman Vershynin · 2020
Closest in time.
Training deep residual networks for uniform approximation guarantees
M. Marchi, B. Gharesifard, and P. Tabuada · 2021
Closest in time.
Minimum width for universal approximation
Sejun Park, Chulhee Yun, Jaeho Lee, and Jinwoo Shin · 2021
Closest in time.
Universal approximation power of deep residual neural networks via nonlinear control theory
P. Tabuada and B. Gharesifard · 2021
Closest in time.