By Grégoire Montavon, Geneviève Orr, Klaus-Robert Müller
The assumption for this booklet dates again to the NIPS'96 workshop "Tips of the alternate" the place, for the 1st time, a scientific test used to be made to make an overview and overview of tips for successfully exploiting neural community concepts. inspired by means of the luck of this assembly, the quantity editors have ready the current accomplished documentation. along with together with chapters constructed from the workshop contributions, they've got commissioned extra chapters to around out the presentation and entire the insurance of correct subareas. this convenient reference ebook is equipped in 5 elements, each one inclusive of numerous coherent chapters utilizing constant terminology. The paintings starts off with a basic creation and every half opens with an advent through the amount editors. A accomplished topic index permits easy accessibility to person themes. The e-book is a gold mine not just for execs and researchers within the zone of neural info processing, but additionally for newbies to the sphere.
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The assumption for this booklet dates again to the NIPS'96 workshop "Tips of the exchange" the place, for the 1st time, a scientific try out was once made to make an evaluation and overview of methods for successfully exploiting neural community recommendations. inspired through the luck of this assembly, the quantity editors have ready the current accomplished documentation.
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Additional info for Neural Networks: Tricks of the Trade
This can be implemented with a simple recipe: (1) compute the total gradient by multiple forward and backward propagation steps. (2) Add δ to the k-th parameter and compute again the gradient, and ﬁnally (3) subtract both results and divide by δ. Due to numerical errors in this computation scheme the resulting Hessian might not be perfectly symmetric. In this case it should be symmetrized as described below. 49) and the Hessian follows as T H(w) = p ∂f (w, xp ) ∂f (w, xp ) + ∂w ∂w (dp − f (w, xp ))T p ∂ 2 f (w, xp ) .
In D. S. Touretzky, editor, Advances in Neural Information Processing Systems 2, pages 650–657, San Mateo, CA, 1990. Morgan Kaufmann. 8. D. J. C. McKay. A practical Bayesian framework for backpropagation networks. Neural Computation, 4:448–472, 1992. 9. R. M. Neal. Bayesian Learning for Neural Networks. Number 118 in Lecture Notes in Statistics. Springer, New York, 1996. 10. M. P. Perrone. Improving Regression Estimation: Averaging Methods for Variance Reduction with Extensions to General Convex Measure Optimization.
59) using only two gradient computations (at point w and w + αΨ respectively), which can be readily computed with backprop (α is a small constant). This method can be applied to compute the principal eigenvector and eigenvalue of H by the power method. 60) the vector Ψ (t) will converge to the largest eigenvector of H and Ψ (t) to the corresponding eigenvalue [23, 14, 10]. See also  for an even more accurate method that (1) does not use ﬁnite diﬀerences and (2) has similar complexity. e. how does the Hessian change with architecture and details of the implementation.
Neural Networks: Tricks of the Trade by Grégoire Montavon, Geneviève Orr, Klaus-Robert Müller