Weights and biases

Learning in the context of a neural network is the process of adjusting the weights and biases in such a manner that for given inputs, the correct responses, or outputs are achieved. Learning algorithms include ... 

The neural network shown in Figure 10.24 is in the proeess of being trained using a BPA. The eurrent inputs x and 2 have values of 0.2 and 0.6 respeetively, and the desired output dj = 1. The existing weights and biases are Hidden layer... 

Calculate the output jy and hence the new values for the weights and biases. Assume a learning rate of 0.5. 

In Example 10.9(b), if the target values for the outputs are d 2 = 0 and 1 22 = 1, ealeulate new values for the weights and biases using the baek-propagation algorithm. Assume a learning rate of 0.5 with no momentum term. 

To obtain a successful learning process, the ANN has to update all weights and biases to minimise the overall average quadratic error. 

The simplest way to stop the iterative process by which the weights and biases are updated is to fix in advance a threshold error. When the average error [considering the calibration standards, see eqn (5.8)] is lower than the threshold value, the net stops training and the last set of weights and biases are stored [41]. In some publications it is said that the ANN converged. 

Guha R, Stanton DT, Jurs PC (2005) Interpreting computational neural network QSAR models a detailed interpretation of the weights and biases. J Chem Inf Model 45 1109-1121... 

Training the network is nothing more than an optimization problem. When a large data set is used, or when the network has a large number of weights and biases, this task can... 

Figure 4. A representation of a distribution of rms errors fh)m numerous neural networks starting fo>m different weights and biases.

The five descriptors found in this model were then fed to a computational neural network in an attempt to improve the predictive ability. The program ANN was used to optimize the starting weights and biases. The quality of the model was assessed by calculating the residuals [actual-predicted values of -logCLCso)] of the prediction set compounds. 

After the weights and biases have been adjusted, the activation and error terms are reset to zero for the next trial. The only carryover from trial to trial is contained in the weights, the biases, and their delta values (co(/, (5, Aco, , and AJ, ). 

The interpretability of the derived NN model may be difficult to understand even though the influences of the descriptors on the derived model can be simulated. Guha and coworkers [87] have developed a two-step method for understanding the weights and biases in neural networks, in which first the neuron transform is linearized followed by a ranking scheme for the neurons. 

Guha, R., Stanton, D.T and Jurs, P.C. (2005) Interpreting computational neural network quantitative structure-activity relationship models a detailed interpretation ofthe weights and biases./. Chem. Inf. Model., 45, 1109-1121. 

After the learning step, the ANN is used to estimate output values for actual input data. ANN weights and biases are fixed during this process, and the ANN acts as an open-loop feedforward estimator. 

The components of the matrix and the vector are called the weights and biases of the layer. Here the hidden layer is denoted as layer 1 and the output layer is denoted as layer 2. Then, the output of the hidden layer is calculated from the transfer function which is chosen to be the hyperbolic tangent sigmoid function in this study ... 

SO the total number of parameters is Isl + 1. At the initial step, the parameter vector is initialized with random weights and biases. Then, the error vector e is given by the difference between the measurements and the network predicted values ... 

The ANN training is an optimization process in which an error function is minimized by adjusting the ANN parameters (weights and biases). When an input training pattern is introduced to the ANN, it calculates an output. Output is compared with the real output (experimental data) provided by the user. 

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