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barcode generator in vb.net The BACKPROPAGATION Algorithm in Software
452 The BACKPROPAGATION Algorithm QR Code JIS X 0510 Encoder In None Using Barcode generator for Software Control to generate, create QR Code image in Software applications. QR Code Scanner In None Using Barcode reader for Software Control to read, scan read, scan image in Software applications. The BACKPROPAGATION algorithm learns the weights for a multilayer network, given a network with a fixed set of units and interconnections It employs gradient descent to attempt to minimize the squared error between the network output values and the target values for these outputs This section presents the BACKPROPAGATION algorithm, and the following section gives the derivation for the gradient descent weight update rule used by BACKPROPAGATION Because we are considering networks with multiple output units rather than single units as before, we begin by redefining E to sum the errors over all of the network output units Quick Response Code Printer In Visual C# Using Barcode generator for .NET framework Control to generate, create QR Code image in .NET applications. Print QR Code In Visual Studio .NET Using Barcode printer for ASP.NET Control to generate, create QR image in ASP.NET applications. where outputs is the set of output units in the network, and tkd and OM are the target and output values associated with the kth output unit and training example d The learning problem faced by BACKPROPAGATION is to search a large hypothesis space defined by all possible weight values for all the units in the network The situation can be visualized in terms of an error surface similar to that shown for linear units in Figure 44 The error in that diagram is replaced by our new definition of E, and the other dimensions of the space correspond now to all of the weights associated with all of the units in the network As in the case of training a single unit, gradient descent can be used to attempt to find a hypothesis to minimize E Drawing QR Code In .NET Framework Using Barcode encoder for VS .NET Control to generate, create QR image in .NET framework applications. Create Denso QR Bar Code In VB.NET Using Barcode creator for Visual Studio .NET Control to generate, create Quick Response Code image in Visual Studio .NET applications. B ~ c ~ ~ ~ o ~ ~ G A T I O ~ ( t r a i n i n g a x ani,p,~ e s,nhidden) q, m no,, , DataMatrix Drawer In None Using Barcode generator for Software Control to generate, create Data Matrix ECC200 image in Software applications. Draw Code 39 In None Using Barcode maker for Software Control to generate, create USS Code 39 image in Software applications. Each training example is a pair of the form (2,i ), where x' is the vector of network input values, and is the vector of target network output values q is the learning rate (eg, O5) ni, is the number of network inputs, nhidden the number of units in the hidden layer, and no,, the number of output units The inputfiom unit i into unit j is denoted xji, and the weightfrom unit i to unit j is denoted wji a Create a feedforward network with ni, inputs, m i d d e n hidden units, and nour output units a Initialize all network weights to small random numbers (eg, between 05 and 5 0) r Until the termination condition is met, Do Bar Code Generator In None Using Barcode creator for Software Control to generate, create bar code image in Software applications. GTIN  128 Maker In None Using Barcode drawer for Software Control to generate, create UCC128 image in Software applications. a For each (2,i ) in trainingaxamples, Do
EAN13 Maker In None Using Barcode printer for Software Control to generate, create EAN 13 image in Software applications. Print Bar Code In None Using Barcode printer for Software Control to generate, create bar code image in Software applications. Propagate the input forward through the network: Making Leitcode In None Using Barcode drawer for Software Control to generate, create Leitcode image in Software applications. UCC  12 Generator In ObjectiveC Using Barcode creator for iPad Control to generate, create UPC Symbol image in iPad applications. 1, Input the instance x' to the network and compute the output o, of every unit the network
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Draw Barcode In None Using Barcode generator for Word Control to generate, create barcode image in Office Word applications. Bar Code Reader In Java Using Barcode reader for Java Control to read, scan read, scan image in Java applications. 6k 4 ok(l  ok)(tk  0 k ) 3 For each hidden unit h, calculate its error term 6h
4 Update each network weight
where
Aw J l
I 1 1 TABLE 42 The stochastic gradient descent version of the BACKPROPAGATION algorithm for feedforward networks containing two layers of sigmoid units One major difference in the case of multilayer networks is that the error surface can have multiple local minima, in contrast to the singleminimum parabolic error surface shown in Figure 44 Unfortunately, this means that gradient descent is guaranteed only to converge toward some local minimum, and not necessarily the global minimum error Despite this obstacle, in practice BACKPROPAGATION has been found to produce excellent results in many realworld applications algorithm is presented in Table 42 The algorithm as The BACKPROPAGATION described here applies to layered feedforward networks containing two layers of sigmoid units, with units at each layer connected to all units from the preceding layer This is the incremental, or stochastic, gradient descent version of BACKPROPAGATION The notation used here is the same as that used in earlier sections, with the following extensions: CHAPTER 4 ARTIFICIAL NEURAL NETWORKS
An index (eg, an integer) is assigned to each node in the network,where a "node" is either an input to the network or the output of some unit in the network xji denotes the input from node i to unit j , and wji denotes the corresponding weight 6, denotes the error term associated with unit n It plays a role analogous to the quantity (t  o ) in our earlier discussion of the delta training rule As we shall see later, 6, =  Notice the algorithm in Table 42 begins by constructing a network with the desired number of hidden and output units and initializing all network weights to small random values Given this fixed network structure, the main loop of the algorithm then repeatedly iterates over the training examples For each training example, it applies the network to the example, calculates the error of the network output for this example, computes the gradient with respect to the error on this example, then updates all weights in the network This gradient descent step is iterated (often thousands of times, using the same training examples multiple times) until the network performs acceptably well The gradient descent weightupdate rule (Equation [T45] in Table 42) is similar to the delta training rule (Equation [410]) Like the delta rule, it updates each weight in proportion to the learning rate r ] , the input value xji to which the weight is applied, and the error in the output of the unit The only difference is that the error ( t  o ) in the delta rule is replaced by a more complex error term, aj The exact form of aj follows from the derivation of the weighttuning rule given in Section 453 To understand it intuitively, first consider how ak is computed for each network output unit k (Equation [T43] in the algorithm) ak is simply the familiar (tk  ok) from the delta rule, multiplied by the factor o k ( l  ok), which is the derivative of the sigmoid squashing function The ah value for each hidden unit h has a similar form (Equation [T44] in the algorithm) However, since training examples provide target values tk only for network outputs, no target values are directly available to indicate the error of hidden units' values Instead, the error term for hidden unit h is calculated by summing the error terms Jk for each output unit influenced by h, weighting each of the ak's by wkh,the weight from hidden unit h to output unit k This weight characterizes the degree to which hidden unit h is "responsible for" the error in output unit k The algorithm in Table 42 updates weights incrementally, following the Presentation of each training example This corresponds to a stochastic approximation to gradient descent To obtain the true gradient of E one would sum the 6, x,, values over all training examples before altering weight values The weightupdate loop in BACKPROPAGATIONbe iterated thousands of may times in a typical application A variety of termination conditions can be used to halt the procedure One may choose to halt after a fixed number of iterations through the loop, or once the error on the training examples falls below some threshold, or once the error on a separate validation set of examples meets some

