By Grégoire Montavon, Geneviève Orr, Klaus-Robert Müller
The assumption for this ebook dates again to the NIPS'96 workshop "Tips of the alternate" the place, for the 1st time, a scientific try out was once made to make an evaluate and overview of tips for successfully exploiting neural community strategies. prompted by means of the good fortune of this assembly, the amount editors have ready the current entire documentation. in addition to together with chapters constructed from the workshop contributions, they've got commissioned extra chapters to around out the presentation and entire the assurance of proper subareas. this useful reference booklet is geared up in 5 components, each one which includes numerous coherent chapters utilizing constant terminology. The paintings begins with a common advent and every half opens with an advent by way of the quantity editors. A finished topic index permits quick access to person themes. The ebook is a gold mine not just for execs and researchers within the quarter of neural info processing, but in addition for beginners to the sector.
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7. Lines of constant E. x2 x1 Fig. 8. For the LMS algorithm, the eigenvectors and eigenvalues of H measure the spread of the inputs in input space. 8. Using a scalar learning rate is problematic in multiple dimensions. We want η to be large so that convergence is fast along the shallow directions of E (small eigenvalues of H), however, if η is too large the weights will diverge along the steep directions (large eigenvalues of H). To see this more speciﬁcally, let us again expand E, but this time about a minimum 1 E(W ) ≈ E(Wmin ) + (W − Wmin )T H(Wmin ) (W − Wmin ).
Dynamics and Algorithms for Stochastic learning. PhD thesis, Oregon Graduate Institute, 1995. 50 Y. LeCun et al. 31. B. Orr. Removing noise in on-line search using adaptive batch sizes. In Michael C. Mozer, Michael I. Jordan, and Thomas Petsche, editors, Advances in Neural Information Processing Systems, volume 9, page 232. The MIT Press, 1997. 32. L. Orr. Regularization in the selection of radial basis function centers. Neural Computation, 7(3):606–623, 1995. 33. A. Pearlmutter. Fast exact multiplication by the hessian.
40. V. Vapnik. The Nature of Statistical Learning Theory. Springer Verlag, New York, 1995. 41. V. Vapnik. Statistical Learning Theory Wiley, New York, 1998. 42. A. Waibel, T. Hanazawa, G. Hinton, K. Shikano, and K. J. Lang. Phoneme recognition using time-delay neural networks. IEEE Transactions on Acoustics, Speech, and Signal Processing, ASSP-37:328–339, 1989. 43. W. Wiegerinck, A. Komoda, and T. Heskes. Stochastic dynamics of learning with momentum in neural networks. Journal of Physics A, 27:4425–4437, 1994.