Cited by 309Neural Networks and ApplicationsMathematical Analysis and Transform MethodsMachine Learning and ELM

Neural network with unbounded activation functions is universal approximator

Open access
Sonoda, Sho, Murata, Noboru·2017·Applied and Computational Harmonic Analysis

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Integrity signals

Registry

Crossref · 10.1016/j.acha.2015.12.005

Cites

38 of 38 references verified0 citation errors · 0 not checkable

Statistics

Claims the paper makes

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

The self-check needs the paper’s full text.

Cites

Flagged first, then by citations

Research works printed but not linked: 10

  1. [6][6] A. L. Maas, A. Y. Hannun, A. Y. Ng, Rectifier nonlinearities improve neural network acoustic models, in: ICML 2013 Work. Deep Learn. Audio, Speech, Lang. Process., Atlanta, 2013. URL https://sites.google.com/site/deeplearningicml2013/relu\_hybrid\_icml2013\_final. pdf -
  2. [14][14] P. C. Kainen, V. K˚ urkov´ combinations of Heaviside plane waves, J. Approx. Theory 147 (1) (2007) 1-10. 2006.12.009 . URL http://linkinghub.elsevier.com/retrieve/pii/S0021904507000081 -
  3. [17][17] S. Helgason, Integral Geometry and Radon Transforms, Springer-Verlag New York, 2011. doi:10. 1007/978-1-4419-6055-9 . -
  4. [24][24] E. J. Cand` es, Ridgelets: theory and applications, Ph.D. thesis, Standford University (1998). -
  5. [32][32] L. Schwartz, Th´ eorie des Distributions, nouvelle Edition, Hermann, Paris, 1966. -
  6. [33][33] F. Tr` eves, Tological Vector Spaces, Distributions and Kernels, Academic Press, 1967. -
  7. [34][34] W. Rudin, Functional Analysis, 2nd Edition, Higher Mathematics Series, McGraw-Hill Education, 1991. -
  8. [36][36] K. Yosida, Functional Analysis, 6th Edition, Springer-Verlag Berlin Heidelberg, 1995. doi:10.1007/ 978-3-642-61859-8 . -
  9. [38][38] M. Holschneider, Wavelets: An Analysis Tool, Oxford mathematical monographs, The Clarendon Press, 1995. -
  10. [41][41] I. M. Gel'fand, G. E. Shilov, Generalized Functions, Vol. 1: Properties and Operations, Academic Press, New York, 1964. -

Cited by

Sorted by citations

Authors
Sonoda, S., & Murata, N.
Affiliations
Waseda University (JP)
Corresponding author
Sonoda, Sho
Venue
Applied and Computational Harmonic Analysis
Publisher
Elsevier BV
Published
2017-09
Volume
43
Issue
2
Pages
233-268
ISSN
1063-5203 (ISSN-L)
OpenAlex
W2267236547
Cited by
303
References
36
Citations by year
2026: 13 · 2025: 34 · 2024: 37 · 2023: 32 · 2022: 33 · 2021: 47 · 2020: 40 · 2019: 31 · 2018: 22 · 2017: 9 · 2016: 5
FWCI
11.77
Type
journal article
Language
en
Open access
Locations
  • Applied and Computational Harmonic Analysis (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • arXiv (Cornell University)
Funders
JSPS (15J07517)
Topics
  • Physical Sciences › Computer Science › Artificial Intelligence › Neural Networks and Applications
  • Physical Sciences › Mathematics › Applied Mathematics › Mathematical Analysis and Transform Methods
  • Physical Sciences › Computer Science › Artificial Intelligence › Machine Learning and ELM
Keywords
universal approximation, artificial neural networks, unbounded activation functions, rectified linear units, ridgelet transform, Fourier slice theorem, Radon transform, admissibility conditions, low-pass filtering, backpropagation

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review