Y. LeCun, J. Denker, S. Solla, R. E. Howard, and L. D. Jackel. Optimal brain damage. In D. S. Touretzky, editor, Advances in Neural Information Processing Systems II, San Mateo, CA, 1990. Morgan Kauffman. Home/Search Document Details and Download
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Nonlinear Modelling and Support Vector Machines - Suykens (2001) (Correct)
....optimal How many neurons cost function weight space Fig. 1. Some persistent problems existing for classical neural nets (such as multilayer perceptrons) local minima and choice of the number of hidden units. To a large extent these problems are avoided in SVMs. brain surgeon) 1] 10] [13] involves computing a Hessian matrix or its inverse, in LS SVMs all necessary pruning information follows from the solution vector itself. The second potential drawback is circumvented by applying a weighted least squares version. In this way, the solution can be easily robustified in order to ....
....sparseness can be imposed to LS SVMs by a pruning procedure which is based upon the sorted support value spectrum. This is important in view of an equivalence between SVMs and sparse approximation, shown in [8] An important difference with pruning methods in classical neural networks [1] 10] [13], e.g. optimal brain damage and optimal brain surgeon, is that the LS SVM pruning procedure requires no computation of a Hessian matrix. One immediately gets all necessary pruning information from the solution to the linear system itself. Hence, by plotting the spectrum of the sorted j k j values ....
Le Cun Y., Denker J.S., Solla S.A., "Optimal brain damage," In Touretzky (Ed.) Advances in Neural Information Processing Systems, Vol.2, pp.598-605, San Mateo, CA: Morgan Kaufmann, 1990.
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....training process is the architecture synthesis. An architecturally optimized network supplies structural information about the input field as used by the model, thus giving a qualitative measure of importance. The output of our new procedure is a map quantifying the importance (saliency c.f. [7]) of each individual component of the measurement (i.e. pin, pixel, or voxel) with respect to the obtained empirical relation. Hopefully, this so called saliency map will assist the modeler in interpreting the model and in communicating the interpretation to the end user. In bio medical context it ....
....and data reduction in order to bring down the dimensionality of the neural network. However, we have recently shown that one may cure this extremely ill posed problem using straightforward linear algebra without loss of information [2] 5] The scheme achieves massive weight sharing [7] by projecting the high dimensional data onto a low dimensional basis spanning the so called signal space of the training set input vectors. The saliency map is an attempt to visualize this induced geometry and the specific manner in which this geometry is used by the trained network. As a ....
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Y. Le Cun, J. S. Denker, and S. Solla, "Optimal brain damage," Advances in Neural Information Processing Systems 2, pp. 598--605, 1990.
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....precisely, for the sake of our paper, multi layer feed forward ANNs. On the other hand, finding a good ANNs architecture has been a debatable issue as well in the field of ANNs. Methods for network growing (such as Cascade Correlation [5] and for network pruning (such as Optimal Brain Damage [16]) have been used to overcome the long process for determining a good network architecture. However, all these methods still su#er from their slow convergence and long training time. In addition, they are based on gradient based techniques and therefore can easily stuck in a local minimum. EANNs ....
Y. LeCun, J. Denker, S. Solla, R. E. Howard, and L. D. Jackel. Optimal brain damage. In D. S. Touretzky, editor, Advances in Neural Information Processing Systems II, pages 598--605. Morgan Kau#man, San Mateo, CA, 1990. 20
A Memetic Pareto Evolutionary Approach to Artificial Neural.. - Abbass (2001) (Correct)
....of our paper Multi layer feed forward Artificial Neural Networks (ANNs) On the other hand, finding a good ANNs architecture has been an issue as well in the field of ANNs. Methods for network growing (such as Cascade Correlation [4] and for network pruning (such as Optimal Brain Damage [14]) have been used to overcome the long process for determining a good network architecture. However, all these methods still su#er from their slow convergence and long training time. In addition, they are based on gradient based techniques and therefore can easily stuck in a local minimum. EANNs ....
Y. LeCun, J.J. Denker, and S.A. Solla. Optimal brain damage. In D. Touretzky, editor, Advances in Neural Information Processing Systems. Morgan Kaufmann, 1990.
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.... the size and complexity of the minimized agent may stand as an estimate for the complexity of the task it solves (while the size of the original agent is arbitrary) Most pruning algorithms in the neural networks literature, such as pruning by the weights magnitude, Optimal Brain Damage (OBD) [2], Optimal Brain Surgeon (OBS) 3] and contribution based pruning [4, 5] are non evolutionary methods. OBD and OBS analytically predict the e#ect of a weight removal on the error function and all algorithms allow for retraining after the elimination of weights . However, in the case of EAA no ....
LeCun, Y., Denker, J., Solla, S., Howard, R.E., Jackel, L.D.: Optimal brain damage. In Touretzky, D.S., ed.: Advances in Neural Information Processing Systems. Volume 2., San Mateo, CA, Morgan Kau#man (1990) 598--605
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.... the size and complexity of the minimized agent may stand as an estimate for the complexity of the task it solves (while the size of the original agent is arbitrary) Most pruning algorithms in the neural networks literature, such as pruning by the weights magnitude, Optimal Brain Damage (OBD) [2], Optimal Brain Surgeon (OBS) 3] and contribution based pruning [4, 5] are non evolutionary methods. OBD and OBS analytically predict the effect of a weight removal on the error function and all algorithms allow for retraining after the elimination of weights 3. However, in the case of EAA no ....
LeCun, Y., Denker, J., Solla, S., Howard, R.E., Jackel, L.D.: Optimal brain damage. In Touretzky, D.S., ed.: Advances in Neural Information Processing Systems. Volume 2., San Mateo, CA, Morgan Kauffman (1990) 598-605
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....A ground truth map containing 35 land cover classes as the result of a ground data collection campaign is available. II. EVOLUTION OF ARTIFICIAL NEURAL NETWORKS Various methods have been suggested for the automatic construction of ANN topologies. Among these are Network Growing (OBS [8] OBD [9], etc. Network Pruning (Cascade Correlation [10] etc. and Evolutionary Design of networks. In the netGEN system we chose the latter approach by employing Genetic Algorithms. We restricted the genetic search to Feed Forward Networks which are trained by standard Error Back Propagation ....
Y.L. Le Cun, J.S. Denker, and S.A. Solla. Optimal Brain Damage. In D. Touretzky, editor, Advances in Neural Information Processing Systems, Vol. 2, volume 2, pages 599--605. Morgan Kaufmann, 1990.
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.... weight values [9] Second order functions which use the second derivatives of weight values [5] Considering the influence of the perturbation of weight w jk on the change of energy function E (j is the index of the neurons in hidden layer) we choose the saliency measure defined as follows [10], s jk # # # # # # And our C function will be, j # # # # # # # The second derivative term, can be easily calculated by chain rule. In our particularly case, we choose a two layer feed forward neural network with 40 hidden neurons and 1 output neuron. The ....
Y. LeCun, J. S. Denker, and S. A. Solla, "Optimal brain damage," in Advances in Neural Information Processing Systems,D.S.Touretzky,Ed., San Mateo, CA, 1990, vol. 2, pp. 598--605, Morgan Kaufmann Publishers.
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Y. LeCun, J. Denker, S. Solla, R. E. Howard, and L. D. Jackel. Optimal brain damage. In D. S. Touretzky, editor, Advances in Neural Information Processing Systems II, San Mateo, CA, 1990. Morgan Kauffman.
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Y. LeCun, J. S. Denker, and S. A. Solla, "Optimal brain damage, " in Advances in Neural Information Processing Systems 2, D. S. Touretzky, Ed. San Mateo, CA: Morgan Kaufmann, 1990, pp. 598--605.
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