Fetching the paper…
Reading the bibliography…
The universal approximation property of various machine learning models is currently only understood on a case-by-case basis, limiting the rapid development of new theoretically justified neural network architectures and blurring our understanding of our current models' potential.
Hamiltonian systems and transformation in hilbert space
B. O. Koopman · 1931
Earlier work this paper cites.
Normierte Ringe
I. Gelfand · 1941
Earlier work this paper cites.
A logical calculus of the ideas immanent in nervous activity
W. S. McCulloch and W. Pitts · 1943
Earlier work this paper cites.
La dualité dans les espaces F et LF
J. Dieudonné and L. Schwartz · 1949
Earlier work this paper cites.
On embedding uniform and topological spaces
R. F. Arens and J. Eells, Jr · 1956
Earlier work this paper cites.
On the representation of continuous functions of many variables by superposition of continuous functions of one variable and addition
A. N. Kolmogorov · 1957
Earlier work this paper cites.
Subreflexive normed linear spaces
R. R. Phelps · 1957
Earlier work this paper cites.
The perceptron: a probabilistic model for information storage and organization in the brain
F. Rosenblatt · 1958
Earlier work this paper cites.
Structure of categories
J. R. Isbell · 1966
Earlier work this paper cites.
A proof of the topological equivalence of all separable infinite-dimensional Banach spaces
M. I. Kadec · 1967
Earlier work this paper cites.
Éléments de mathématique. Topologie générale. Chapitres 1 à 4
N. Bourbaki · 1971
Earlier work this paper cites.
Weighted spaces of vector-valued continuous functions
J. a. B. Prolla · 1971
Earlier work this paper cites.
Modern general topology
J.-i. Nagata · 1974
Earlier work this paper cites.
M M -structure and the Banach-Stone theorem
E. Behrends and U. Schmidt-Bichler · 1980
Earlier work this paper cites.
Espaces vectoriels topologiques. Chapitres 1 à 5
N. Bourbaki · 1981
Earlier work this paper cites.
Locally convex spaces
H. Jarchow · 1981
Earlier work this paper cites.
Barrelled locally convex spaces , volume 131 of North-Holland Mathematics Studies
P. Pérez Carreras and J. Bonet · 1987
Earlier work this paper cites.
Approximation by superpositions of a sigmoidal function
G. Cybenko · 1989
Earlier work this paper cites.
Multilayer feedforward networks are universal approximators
K. Hornik, M. Stinchcombe, and H. White · 1989
Earlier work this paper cites.
Introductory functional analysis with applications
E. Kreyszig · 1989
Earlier work this paper cites.
Universal approximation of an unknown mapping and its derivatives using multilayer feedforward networks
K. Hornik, M. Stinchcombe, and H. White · 1990
Earlier work this paper cites.
Approximation capabilities of multilayer feedforward networks
K. Hornik · 1991
Earlier work this paper cites.
Dynamic binding in a neural network for shape recognition
J. Hummel and I. Biederman · 1992
Earlier work this paper cites.
Universal approximation bounds for superpositions of a sigmoidal function
A. R. Barron · 1993
Earlier work this paper cites.
Rate of approximation results motivated by robust neural network learning
C. Darken, M. Donahue, L. Gurvits, and E. Sontag · 1993
Earlier work this paper cites.
Multilayer feedforward networks with a nonpolynomial activation function can approximate any function
M. Leshno, V. Y. Lin, A. Pinkus, and S. Schocken · 1993
Earlier work this paper cites.
Composition operators on function spaces , volume 179 of North-Holland Mathematics Studies
R. K. Singh and J. S. Manhas · 1993
Earlier work this paper cites.
Mixture density networks
C. M. Bishop · 1994
Cited alongside, same era.
Approximation theory of the MLP model in neural networks
A. Pinkus · 1999
Cited alongside, same era.
Topology
J. R. Munkres · 2000
Cited alongside, same era.
Distance-based classification with Lipschitz functions
U. von Luxburg and O. Bousquet · 2003
Cited alongside, same era.
Universal kernels
C. A. Micchelli, Y. Xu, and H. Zhang · 2006
Cited alongside, same era.
Universal multi-task kernels
A. Caponnetto, C. A. Micchelli, M. Pontil, and Y. Ying · 2008
Cited alongside, same era.
The geometric median on riemannian manifolds with application to robust atlas estimation
P. T. Fletcher, S. Venkatasubramanian, and S. Joshi · 2009
Hyperbolic neural networks
O. Ganea, G. Becigneul, and T. Hofmann · 2018
Later among the works it cites.
Searching for activation functions
Q. V. L. Prajit Ramachandran, Barret Zoph · 2018
Later among the works it cites.
A survey on deep transfer learning
C. Tan, F. Sun, T. Kong, W. Zhang, C. Yang, and C. Liu · 2018
Later among the works it cites.
Lipschitz algebras
N. Weaver · 2018
Later among the works it cites.
Deep learning for biology
S. Webb · 2018
Later among the works it cites.
Low-rank plus sparse decomposition of covariance matrices using neural network parametrization
M. Baes, C. Herrera, A. Neufeld, and P. Ruyssen · 2019
Closest in time.
Deep optimal stopping
S. Becker, P. Cheridito, and A. Jentzen · 2019
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Cited alongside, same era.
Universal kernel-based learning with applications to regular languages
L. Kontorovich and B. Nadler · 2009
Cited alongside, same era.
The graph neural network model
F. Scarselli, M. Gori, A. C. Tsoi, M. Hagenbuchner, and G. Monfardini · 2009
Cited alongside, same era.
Linear chaos
K.-G. Grosse-Erdmann and A. Peris Manguillot · 2011
Cited alongside, same era.
Riemannian Geometry and Geometric Analysis
J. Jost · 2011
Cited alongside, same era.
Regression on fixed-rank positive semidefinite matrices: a Riemannian approach
G. Meyer, S. Bonnabel, and R. Sepulchre · 2011
Cited alongside, same era.
Closest in time.
Deep hedging
H. Buehler, L. Gonon, J. Teichmann, and B. Wood · 2019
Closest in time.
Deep learning: new computational modelling techniques for genomics
G. Eraslan, Ž. Avsec, J. Gagneur, and F. J. Theis · 2019
Closest in time.
Differentiable reservoir computing
L. Grigoryeva and J.-P. Ortega · 2019
Closest in time.
Universal function approximation by deep neural nets with bounded width and relu activations
B. Hanin · 2019
Closest in time.
Dynamics of weighted composition operators on function spaces defined by local properties
T. Kalmes · 2019
Closest in time.
Self-attention generative adversarial networks
H. Zhang, I. Goodfellow, D. Metaxas, and A. Odena · 2019
Closest in time.
Linear extension operators between spaces of Lipschitz maps and optimal transport
L. Ambrosio and D. Puglisi · 2020
Closest in time.
Extending and improving conical bicombings
G. Basso · 2020
Closest in time.
Approximation spaces of deep neural networks
R. Gribonval, G. Kutyniok, M. Nielsen, and F. Voigtlaender · 2020
Closest in time.
Deep learning volatility: a deep neural network perspective on pricing and calibration in (rough) volatility models
B. Horvath, A. Muguruza, and M. Tomas · 2020
Closest in time.
Hydra: a method for strain-minimizing hyperbolic embedding of network- and distance-based data
M. Keller-Ressel and S. Nargang · 2020
Closest in time.
Universal Approximation with Deep Narrow Networks
P. Kidger and T. Lyons · 2020
Closest in time.
Non-euclidean universal approximation
A. Kratsios and E. Bilokopytov · 2020
Closest in time.
Deep arbitrage-free learning in a generalized HJM framework via arbitrage-regularization
A. Kratsios and C. Hyndman · 2020
Closest in time.
Topological properties of the set of functions generated by neural networks of fixed size
P. Petersen, M. Raslan, and F. Voigtlaender · 2020
Closest in time.
Cot-gan: Generating sequential data via causal optimal transport
T. Xu, W. Le, M. Munn, and B. Acciaio · 2020
Closest in time.
Adversarial attacks on deep-learning models in natural language processing: A survey
W. E. Zhang, Q. Z. Sheng, A. Alhazmi, and C. Li · 2020
Closest in time.
Minimum width for universal approximation
S. Park, C. Yun, J. Lee, and J. Shin · 2021
Closest in time.
A survey on Lipschitz-free Banach spaces
G. Godefroy · 2080
Closest in time.