### Demonstrate that the asymptotic behavior of the learn

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In this problem, we revisit the adaptive control of the learning rate discussed in Section 4.10. The issue of interest is to demonstrate that the asymptotic behavior of the learn ingrate parameter η (x) in Eq. (4.85) does not converge to zero as the number of iterations increases to infinity.

#### Use intuitive arguments to justify these four heuristics

When the algebraic sign of the cost function with respect to a particular synaptic weight alternates for several consecutive iterations of the algorithm, the learning-rate p

#### Define the weight-error vector

An alternative to the mean-square error (MSE) formulation of the learning curve that we sometimes find in the literature is the mean-square deviation (MSD) learning curve. D

#### Algorithm for computing a set of synaptic weights

Use the back-propagation algorithm for computing a set of synaptic weights and bias levels for a neural network structured as in Fig. 4.8 to solve the XOR problem. Assume th

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#### Neural network involving a single hidden neuron

Figure P4.1 shows a neural network involving a single hidden neuron for solving the XOR problem; this network may be viewed as an alternative to that considered in Section 4

#### Investigate the difference that would be made

The momentum constant α is normally assigned a positive value in the range 0 α ≤ 1. Investigate the difference that would be made in the behavior of Eq. (4.43) with respect

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