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Journal ArticleDOI

On the approximate realization of continuous mappings by neural networks

01 May 1989-Neural Networks (Elsevier Science Ltd.)-Vol. 2, Iss: 3, pp 183-192
TL;DR: It is proved that any continuous mapping can be approximately realized by Rumelhart-Hinton-Williams' multilayer neural networks with at least one hidden layer whose output functions are sigmoid functions.
About: This article is published in Neural Networks.The article was published on 1989-05-01. It has received 3989 citations till now. The article focuses on the topics: Universal approximation theorem & Sigmoid function.
Citations
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Journal ArticleDOI
TL;DR: It is demonstrated that finite linear combinations of compositions of a fixed, univariate function and a set of affine functionals can uniformly approximate any continuous function ofn real variables with support in the unit hypercube.
Abstract: In this paper we demonstrate that finite linear combinations of compositions of a fixed, univariate function and a set of affine functionals can uniformly approximate any continuous function ofn real variables with support in the unit hypercube; only mild conditions are imposed on the univariate function. Our results settle an open question about representability in the class of single hidden layer neural networks. In particular, we show that arbitrary decision regions can be arbitrarily well approximated by continuous feedforward neural networks with only a single internal, hidden layer and any continuous sigmoidal nonlinearity. The paper discusses approximation properties of other possible types of nonlinearities that might be implemented by artificial neural networks.

12,286 citations

Christopher M. Bishop1
01 Jan 2006
TL;DR: Probability distributions of linear models for regression and classification are given in this article, along with a discussion of combining models and combining models in the context of machine learning and classification.
Abstract: Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

10,141 citations

Journal ArticleDOI
TL;DR: It is shown that standard multilayer feedforward networks with as few as a single hidden layer and arbitrary bounded and nonconstant activation function are universal approximators with respect to L p (μ) performance criteria, for arbitrary finite input environment measures μ.

5,593 citations

Journal ArticleDOI
TL;DR: In this paper, the authors present a state-of-the-art survey of ANN applications in forecasting and provide a synthesis of published research in this area, insights on ANN modeling issues, and future research directions.

3,680 citations

Journal ArticleDOI
01 Sep 1990
TL;DR: Regularization networks are mathematically related to the radial basis functions, mainly used for strict interpolation tasks as mentioned in this paper, and two extensions of the regularization approach are presented, along with the approach's corrections to splines, regularization, Bayes formulation, and clustering.
Abstract: The problem of the approximation of nonlinear mapping, (especially continuous mappings) is considered. Regularization theory and a theoretical framework for approximation (based on regularization techniques) that leads to a class of three-layer networks called regularization networks are discussed. Regularization networks are mathematically related to the radial basis functions, mainly used for strict interpolation tasks. Learning as approximation and learning as hypersurface reconstruction are discussed. Two extensions of the regularization approach are presented, along with the approach's corrections to splines, regularization, Bayes formulation, and clustering. The theory of regularization networks is generalized to a formulation that includes task-dependent clustering and dimensionality reduction. Applications of regularization networks are discussed. >

3,595 citations

References
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Journal ArticleDOI
TL;DR: In this article, it is shown that many particular choices among possible neurophysiological assumptions are equivalent, in the sense that for every net behaving under one assumption, there exists another net which behaves under another and gives the same results, although perhaps not in the same time.

14,937 citations

Book
03 Jan 1986
TL;DR: In this paper, the problem of the generalized delta rule is discussed and the Generalized Delta Rule is applied to the simulation results of simulation results in terms of the generalized delta rule.
Abstract: This chapter contains sections titled: The Problem, The Generalized Delta Rule, Simulation Results, Some Further Generalizations, Conclusion

13,579 citations

Journal ArticleDOI
TL;DR: This paper provides an introduction to the field of artificial neural nets by reviewing six important neural net models that can be used for pattern classification and exploring how some existing classification and clustering algorithms can be performed using simple neuron-like components.
Abstract: Artificial neural net models have been studied for many years in the hope of achieving human-like performance in the fields of speech and image recognition. These models are composed of many nonlinear computational elements operating in parallel and arranged in patterns reminiscent of biological neural nets. Computational elements or nodes are connected via weights that are typically adapted during use to improve performance. There has been a recent resurgence in the field of artificial neural nets caused by new net topologies and algorithms, analog VLSI implementation techniques, and the belief that massive parallelism is essential for high performance speech and image recognition. This paper provides an introduction to the field of artificial neural nets by reviewing six important neural net models that can be used for pattern classification. These nets are highly parallel building blocks that illustrate neural net components and design principles and can be used to construct more complex systems. In addition to describing these nets, a major emphasis is placed on exploring how some existing classification and clustering algorithms can be performed using simple neuron-like components. Single-layer nets can implement algorithms required by Gaussian maximum-likelihood classifiers and optimum minimum-error classifiers for binary patterns corrupted by noise. More generally, the decision regions required by any classification algorithm can be generated in a straightforward manner by three-layer feed-forward nets.

7,798 citations

Book
01 Jan 1965

2,133 citations

Journal Article
TL;DR: H hierarchical clustering techniques applied to NETtalk reveal that these different networks have similar internal representations of letter-to-sound correspondences within groups of processing units, which suggests that invariant internal representations may be found in assemblies of neurons intermediate in size between highly localized and completely distributed representations.
Abstract: This paper describes NETtalk, a class of massively-parallel network systems that learn to convert English text to speech. The memory representations for pronunciations are learned by practice and are shared among many processing units. The performance of NETtalk has some similarities with observed human performance. (i) The learning follows a power law. (ii) The more words the network learns, the better it is at generalizing and correctly pronouncing new words, (iii) The performance of the network degrades very slowly as connections in the network are damaged: no single link or processing unit is essential. (iv) Relearning after damage is much faster than learning during the original training. (v) Distributed or spaced practice is more effective for long-term retention than massed practice. Network models can be constructed that have the same performance and learning characteristics on a particular task, but differ completely at the levels of synaptic strengths and single-unit responses. However, hierarchical clustering techniques applied to NETtalk reveal that these different networks have similar internal representations of letter-to-sound correspondences within groups of processing units. This suggests that invariant internal representations may be found in assemblies of neurons intermediate in size between highly localized and completely distributed representations.

1,471 citations