Weight Initialization

Java code 128a development on javagenerate, create code 128c none on java projects

Gradient-based optimization methods, for example gradient descent, is very sensitive to the initial weight vectors. If the initial position is close to a local minimum, convergence will be fast. However, if the initial weight vector is on a flat area in the error surface, convergence is slow. Furthermore, large initial weight values have been shown to prematurely saturate units due to extreme output values with associated zero derivatives [Hush et al. 1991]. In the case of optimization algorithms such as

Build barcode in javagenerate, create bar code none with java projects

CHAPTER 7. PERFORMANCE ISSUES (SUPERVISED

decode bar code for javaUsing Barcode recognizer for Java Control to read, scan read, scan image in Java applications.

LEARNING)

Control code 128 code set c image on visual c#.netuse .net framework code128 writer tocreate code-128c on .net c#

PSO and GAs, initialization should be uniformly over the entire search space to ensure that all parts of the search space are covered. A sensible weight initialization strategy is to choose small random weights centered around 0. This will cause net input signals to be close to zero. Activation functions then output midrange values regardless of the values of input units. Hence, there is no bias toward any solution. Wessels and Barnard showed that random weights in the range [-==i=, //* nin ] is a good choice, where fanin is the number of connections leading to a unit [Wessels and Barnard 1992]. Why don't we just initialize all the weights to zero in the case of gradient-based optimization This strategy will work only if the NN has just one hidden unit. For more than one hidden unit, all the units produce the same output, and thus make the same contribution to the approximation error. All the weights are therefore adjusted with the same value. Weights will remain the same irrespective of training time - hence, no learning takes place. Initial weight values of zero for PSO will also fail, since no velocity changes are made; therefore no weight changes. GAs, on the other hand, will work with initial zero weights if mutation is implemented.

Code 128C creator on .netgenerate, create ansi/aim code 128 none with .net projects

Learning Rate and Momentum

.net Vs 2010 uss code 128 encoding with .netusing barcode printing for .net control to generate, create ansi/aim code 128 image in .net applications.

The convergence speed of NNs is directly proportional to the learning rate 77. Considering stochastic GD, the momentum term added to the weight updates also has as its objective improving convergence time. Learning Rate The learning rate controls the size of each step toward the minimum of the objective function. If the learning rate is too small, the weight adjustments are correspondingly small. More learning iterations are then required to reach a local minimum. However, the search path will closely approximate the gradient path. Figure 7.5(a) illustrates the effect of small rj. On the other hand, large n will have large weight updates. Convergence will initially be fast, but the algorithm will eventually oscillate without reaching the minimum. It is also possible that too large a learning rate will cause "jumping" over a good local minimum proceeding toward a bad local minimum. Figure 7.5(b) illustrates the oscillating behavior, while Figure 7.5(c) illustrates how large learning rates may cause the network to overshoot a good minimum and get trapped in a bad local minimum. Small learning rates also have the disadvantage of being trapped in a bad local minimum as illustrated in Figure 7.5(d). The search path goes down the first local minimum, with no mechanism to move out of it toward the next, better minimum. Of course, all depends on the initial starting position. If the second initial point is used, the NN will converge to the better local minimum.

7.3. PERFORMANCE FACTORS

Gs1128 creator for javausing java toadd gs1 barcode on asp.net web,windows application

(a) Small 77

Barcode integrated in javausing barcode development for java control to generate, create barcode image in java applications.

(b) Large n gets stuck

Linear 1d Barcode barcode library with javause java 1d generator togenerate 1d in java

Starting position 1

Control code 128 image with javause java code 128c maker todisplay ansi/aim code 128 for java

(c) Large 77 overshoots

Gs1 Datamatrix Barcode writer with javausing java toprint data matrix barcode on asp.net web,windows application

(d) Small 77 gets stuck

Modified Plessey barcode library on javausing barcode printing for java control to generate, create msi image in java applications.

Figure 7.5: Effect of learning rate

decode ean / ucc - 13 in noneUsing Barcode Control SDK for None Control to generate, create, read, scan barcode image in None applications.

CHAPTER 7. PERFORMANCE ISSUES (SUPERVISED

Develop barcode on javausing barcode encoder for birt control to generate, create bar code image in birt applications.

LEARNING)

Make qr codes in .netuse local reports rdlc qr bidimensional barcode integrated touse qr-codes for .net

But how do we choose the value of the learning rate One approach is to find the optimal value of the learning rate through cross-validation, which is a lengthy process. An alternative is to select a small value (e.g. 0.1) and to increase the value if convergence is too slow, or to decrease it if the error does not decrease fast enough. Plaut et al. proposed that the learning rate should be inversely proportional to the fanin of a neuron [Plaut et al. 1986]. This approach has been theoretically justified through an analysis of the eigenvalue distribution of the Hessian matrix of the objective function [Le Gun et al. 1991]. Several heuristics have been developed to dynamically adjust the learning rate during training. One of the simplest approaches is to assume that each weight has a different learning rate rjkj. The following rule is then applied to each weight before that weight is updated: if the direction in which the error decreases at this weight change is the same as the direction in which it has been decreasing recently, then nkj is increased; if not, nkj is decreased [Jacobs 1988]. The direction in which the error decreases is determined by the sign of the partial derivative of the objective function with respect to the weight. Usually, the average change over a number of pattern presentations is considered and not just the previous adjustment. An alternative is to use an annealing schedule to gradually reduce a large learning rate to a smaller value (refer to equation 4.22). This allows for large initial steps, and ensures small steps in the region of the minimum. Of course more complex adaptive learning rate techniques have been developed, with elaborate theoretical analysis. The interested reader is referred to [Darken and Moody, Magoulas et al. 1997, Salomon and Van Hemmen 1996, Vogl et al. 1988],

Control qrcode size in microsoft wordto build qr-code and qr-code data, size, image with office word barcode sdk

recognizing ecc200 in .netUsing Barcode decoder for VS .NET Control to read, scan read, scan image in VS .NET applications.

Barcode recognizer for .netUsing Barcode scanner for .NET Control to read, scan read, scan image in .NET applications.