Deterministic design for neural network learning: an approach based on discrepancy

IEEE Transactions on Neural Networks
Cristiano Cervellera, Marco Muselli

Abstract

The general problem of reconstructing an unknown function from a finite collection of samples is considered, in case the position of each input vector in the training set is not fixed beforehand but is part of the learning process. In particular, the consistency of the empirical risk minimization (ERM) principle is analyzed, when the points in the input space are generated by employing a purely deterministic algorithm (deterministic learning). When the output generation is not subject to noise, classical number-theoretic results, involving discrepancy and variation, enable the establishment of a sufficient condition for the consistency of the ERM principle. In addition, the adoption of low-discrepancy sequences enables the achievement of a learning rate of O(1/L), with L being the size of the training set. An extension to the noisy case is provided, which shows that the good properties of deterministic learning are preserved, if the level of noise at the output is not high. Simulation results confirm the validity of the proposed approach.

References

Aug 1, 1996·Neural Networks : the Official Journal of the International Neural Network Society·David A. Cohn
Feb 6, 2008·IEEE Transactions on Neural Networks·K Fukumizu
Jan 1, 1994·IEEE Transactions on Neural Networks·M T Hagan, M B Menhaj

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Citations

Apr 21, 2010·Neural Networks : the Official Journal of the International Neural Network Society·Cristiano CervelleraMarco Muselli
Oct 21, 2014·IEEE Transactions on Neural Networks and Learning Systems·Cristiano Cervellera, Danilo Macciò
Mar 1, 2013·IEEE Transactions on Neural Networks and Learning Systems·Cristiano Cervellera, Danilo Macciò
Feb 23, 2010·IEEE Transactions on Neural Networks·Cristiano Cervellera
Aug 15, 2008·IEEE Transactions on Neural Networks·Cristiano CervelleraMarco Muselli
Feb 7, 2007·IEEE Transactions on Neural Networks·Angelo AlessandriMarcello Sanguineti
Mar 29, 2006·IEEE Transactions on Neural Networks·Marcin Witczak

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