By Grégoire Montavon, Geneviève Orr, Klaus-Robert Müller

The belief for this ebook dates again to the NIPS'96 workshop "Tips of the exchange" the place, for the 1st time, a scientific try out used to be made to make an overview and review of methods for successfully exploiting neural community thoughts. prompted through the luck of this assembly, the amount editors have ready the current finished documentation. along with together with chapters built from the workshop contributions, they've got commissioned additional chapters to around out the presentation and whole the assurance of suitable subareas. this useful reference booklet is geared up in 5 components, every one including a number of coherent chapters utilizing constant terminology. The paintings starts off with a normal creation and every half opens with an creation by way of the amount editors. A accomplished topic index permits easy accessibility to person issues. The publication is a gold mine not just for pros and researchers within the quarter of neural info processing, but additionally for newbies to the sector.

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The bottom graph plots the gradient of E as a function of W . Since E is quadratic, the gradient is simply a straight line with value zero at the minimum and ∂E(Wc ) at the current weight Wc . ∂ 2 E/∂ 2 W is simply the slope of this line and ∂W is computed using the standard slope formula ∂E(Wc )/∂W − 0 . 23). 6(i)d) ηmax = 2ηopt . 23) is only an approximation. In such a case, it may take multiple iterations to locate the minimum even when using ηopt , however, convergence can still be quite fast.

3 0 50 100 150 200 250 300 350 400 450 Fig. 2. A real validation error curve. Vertical: validation set error; horizontal: time (in training epochs). 4 for a rough explanation of this behavior. As we see, the validation error can still go further down after it has begun to increase — plus in a realistic setting we do never know the exact generalization error but estimate it by the validation set error instead. There is no obvious rule for deciding when the minimum of the generalization error is obtained.

Matrix Computations, 2nd ed. Johns Hopkins University Press, Baltimore, 1989. 15. M. Heskes and B. Kappen. On-line learning processes in artificial neural networks. In J. G. Tayler, editor, Mathematical Approaches to Neural Networks, volume 51, pages 199–233. Elsevier, Amsterdam, 1993. 16. Robert A. Jacobs. Increased rates of convergence through learning rate adaptation. Neural Networks, 1:295–307, 1988. 17. A. H. Kramer and A. Sangiovanni-Vincentelli. Efficient parallel learning algorithms for neural networks.

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