Wendemuth, A., Opper, M., and Kinzel, W. (1993). The effect of correlations in neural networks. Journal of Physics A, 26(13):3165--3185.  Home/Search Document Not in Database Summary Related Articles Check |
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Online Learning From Finite Training Sets - Barber, Sollich (1998) (2 citations) (Correct)
....the directions of w and x are uncorrelated: y 2 = m 2 . As for the case of unbiased inputs, the evolution of the generalization error is largely determined by the eigenvalue spectrum of the input correlation matrix A. This has been determined by a number of authors (LeCun et al. 1991; Wendemuth et al. 1993; Halkjaer and Winther, 1997) and shows the following features: There is a normal part of the spectrum, with eigenvalues which tend to finite values as N 1; the eigenvalues in this part of the spectrum are identical to those for the unbiased input case, expect for a rescaling 12 Barber ....
....therefore successfully exploits the presence of the input bias to achieve better generalization performance 13 . This contrasts markedly with the case of offline learning, where generalization performance (at finite learning times t) deteriorates as soon as an input bias is present 14 . 13 Wendemuth et al. 1993) view the input bias as additional information which leads to improved generalization. In our case, the same conclusion can be arrived at by considering the extreme limit of maximal bias, m 2 = 1: In this case, the distribution of input vectors collapses to the point x = x, and so perfect ....
Wendemuth, A., Opper, M., and Kinzel, W. (1993). The effect of correlations in neural networks. Journal of Physics A, 26(13):3165--3185.
Online Learning From Finite Training Sets and Robustness to.. - Sollich, Barber (1998) (2 citations) (Correct)
....the directions of w and x are uncorrelated: y 2 = m 2 . As for the case of unbiased inputs, the evolution of the generalization error is largely determined by the eigenvalue spectrum of the input correlation matrix A. This has been determined by a number of authors (LeCun et al. 1991; Wendemuth et al. 1993; Halkjaer and Winther, 1997) and shows the following features: There is a normal part of the spectrum, with eigenvalues which tend to finite values as N 1; the eigenvalues in this part of the spectrum are identical to those for the unbiased input case, expect for a rescaling by the factor (1 ....
....from local minima. We have done some exploratory work along those lines for soft committee machine architectures, using a fairly simple minded approximation scheme (Sollich and Barber, 1998) Considerable challenges remain, however, and there is much scope for future work in this direction. 13 Wendemuth et al. 1993) view the input bias as additional information which leads to improved generalization. In our case, the same conclusion can be arrived at by considering the extreme limit of maximal bias, m 2 = 1: In this case, the distribution of input vectors collapses to the point x = x, and so perfect ....
Wendemuth, A., Opper, M., and Kinzel, W. (1993). The effect of correlations in neural networks. Journal of Physics A, 26(13):3165--3185.
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