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Besides, the network itself may be viewed simply as a nonlinear input–output mapping. In this sense, we can regard generalization as the effect of a good nonlinear interpolation of the input data. The network performs useful interpolation primarily because multi­ layer perceptrons with continuous activation functions lead to output functions that are also continuous. 5 describes how generalization may occur in a hypothetical network. ” The generalization point is seen as the result of interpolation performed by the network.

60. Calculate the slope of the logistic function at origin. Then point out what the logistic function will be when the slope parameter approaches infinity. 3. The limiting values of the algebraic sigmoid function ϕ…v† ˆ p are v 1 ‡ v2 1 and ‡1. 4. Calculate the value of the derivative at the origin. 4. 24 and is called the piecewise-linear function. Here, the amplification factor inside the linear region of operation is assumed to be unity. 26 and, and study the following problems, respectively. 4 (case 1).

This implies that the single-layer perceptron cannot solve the XOR problem. 7. 8. Notice that the following two assumptions are required. • Each neuron is represented by a McCulloch–Pitts model, which utilizes the threshold function as activation function. 7 Architectural graph of network for solving the XOR problem. 8 Signal flow graph of network for solving the XOR problem. • Bits 0 and 1 are represented by the levels 0 and ‡1, respectively. 9. 10. 7. 7. 7. The function of the output neuron is to construct a linear combination of the decision boundaries formed by the two hidden neurons.

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