The DOI matches its Crossref record; 6 of the 6 references it cites were found in a registry or an index.
Regularization Algorithms for Learning That Are Equivalent to Multilayer Networks
Abstract
Learning an input-output mapping from a set of examples, of the type that many neural networks have been constructed to perform, can be regarded as synthesizing an approximation of a multidimensional function (that is, solving the problem of hypersurface reconstruction). From this point of view, this form of learning is closely related to classical approximation techniques, such as generalized splines and regularization theory. A theory is reported that shows the equivalence between regularization and a class of three-layer networks called regularization networks or hyper basis functions. These networks are not only equivalent to generalized splines but are also closely related to the classical radial basis functions used for interpolation tasks and to several pattern recognition and neural network algorithms. They also have an interesting interpretation in terms of prototypes that are synthesized and optimally combined during the learning stage.
Overview
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.
Integrity signals
Registry
Cites
Statistics
Verification
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.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
Learning representations by back-propagating errors
Rumelhart, D. E., Hinton, G. E., & Williams, R. J. (1986) · Nature · doi:10.1038/323533a0 · Cited by 31,892
Approximation by superpositions of a sigmoidal function
Cybenko, G. (1989) · Mathematics of Control, Signals, and Systems · doi:10.1007/bf02551274 · Cited by 13,883
Self-organized formation of topologically correct feature maps
Kohonen, T. (1982) · Biological Cybernetics · doi:10.1007/bf00337288 · Cited by 9,529
Spline Models for Observational Data
Wahba, G. (1990) · doi:10.1137/1.9781611970128 · Cited by 4,184
Marr, D. (1969) · The Journal of Physiology · doi:10.1113/jphysiol.1969.sp008820 · Cited by 3,253
A theory of cerebellar function
Albus, J. S. (1971) · Mathematical Biosciences · doi:10.1016/0025-5564(71)90051-4 · Cited by 2,539
Cited by
A training algorithm for optimal margin classifiers
Boser, B. E., Guyon, I. M., & Vapnik, V. N. (1992) · Proceedings of the fifth annual workshop on Computational learning theory · doi:10.1145/130385.130401 · Cited by 11,992
Neural Networks and the Bias/Variance Dilemma
Geman, S., Bienenstock, E., & Doursat, R. (1992) · Neural Computation · doi:10.1162/neco.1992.4.1.1 · Cited by 3,578
Engineering Design via Surrogate Modelling: A Practical Guide
Forrester, A. I. J., Sóbester, A., & Keane, A. J. (2008) · doi:10.1002/9780470770801 · Cited by 2,309
ANI-1: an extensible neural network potential with DFT accuracy at force field computational cost
Smith, J. S., Isayev, O., & Roitberg, A. E. (2017) · Chemical Science · doi:10.1039/c6sc05720a · Cited by 1,921
Data-driven Soft Sensors in the process industry
Kadlec, P., Gabrys, B., & Strandt, S. (2009) · Computers & Chemical Engineering · doi:10.1016/j.compchemeng.2008.12.012 · Cited by 1,845
Object perception as Bayesian inference
Kersten, D., Mamassian, P., & Yuille, A. (2004) · Annual Review of Psychology · doi:10.1146/annurev.psych.55.090902.142005 · Cited by 1,269
First- and Second-Order Methods for Learning: Between Steepest Descent and Newton's Method
Battiti, R. (1992) · Neural Computation · doi:10.1162/neco.1992.4.2.141 · Cited by 1,193
On the computational architecture of the neocortex: II The role of cortico-cortical loops
Mumford, D. (1992) · Biological Cybernetics · doi:10.1007/bf00198477 · Cited by 1,074
Shape representation in the inferior temporal cortex of monkeys
Logothetis, N. K., Pauls, J., & Poggio, T. (1995) · Current Biology · doi:10.1016/s0960-9822(95)00108-4 · Cited by 963
Self-citationOn the computational architecture of the neocortex: I. The role of the thalamo-cortical loop
Mumford, D. (1991) · Biological Cybernetics · doi:10.1007/bf00202389 · Cited by 929
Zhang, K., Ginzburg, I., McNaughton, B. L., & Sejnowski, T. J. (1998) · Journal of Neurophysiology · doi:10.1152/jn.1998.79.2.1017 · Cited by 741
Modeling chemical processes using prior knowledge and neural networks'
Thompson, M. L., & Kramer, M. A. (1994) · AIChE Journal · doi:10.1002/aic.690400806 · Cited by 596
Viewpoint Dependence in Scene Recognition
Diwadkar, V. A., & McNamara, T. P. (1997) · Psychological Science · doi:10.1111/j.1467-9280.1997.tb00442.x · Cited by 312
Multiple views of spatial memory
Shelton, A. L., & Mcnamara, T. P. (1997) · Psychonomic Bulletin & Review · doi:10.3758/bf03210780 · Cited by 308
Spatial generalization from learning dynamics of reaching movements
Shadmehr, R., & Moussavi, Z. M. K. (2000) · The Journal of Neuroscience · doi:10.1523/jneurosci.20-20-07807.2000 · Cited by 249
Orientation and Perspective Dependence in Route and Survey Learning.
Shelton, A. L., & McNamara, T. P. (2004) · Journal of Experimental Psychology: Learning, Memory, and Cognition · doi:10.1037/0278-7393.30.1.158 · Cited by 195
Metadata
- Authors
- Poggio, T., & Girosi, F.
- Venue
- Science
- Published
- 1990-02-23
- Volume
- 247
- Issue
- 4945
- Pages
- 978-982
- ISSN
- 0036-8075 (ISSN-L)
- 1095-9203
- OpenAlex
- W2086472796
- Cited by
- 1,026
- References
- 6
- FWCI
- 37.98
- Type
- journal article
- Language
- en
- Open access
- closed
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
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
