2. Consider the neuron on the left with three inputs. The plot of the activation function...

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2. Consider the neuron on the left with three inputs. The plot of the activation function of the neuron is given on the right. More precisely, -{₁+ f(v) = 0, v +0.5, 1, v < -0.5 -0.5 ≤ v ≤ 0.5 v> 0.5 (a) Suppose the error at the output is defined as E = (t-o)² where t is the target output. Derive the weight update equations for this neuron using the gradient descent method. (b) Write a program to train this neuron such that it evaluates the function (21 AND 22) OR 23. Note that in this problem you are not restricted to use the McCulloch-Pitts neuron. In fact, you will train the network to find the weights. In your program, you should i. initialize the weights randomly, ii. use the weight update equations you derived in part (a), iii. stop the iterations when the error drops below the "machine epsilon" (in MATLAB, it is denoted by the constant eps.). Report the resulting values of the weights. How does the learning rate affect the convergence? Try different values and discuss. (c) Since there are three inputs, they can be visualized in 3D space. Plot the input points and the discriminant corresponding to the weights you found in part (b), and explain how this problem can be interpreted as a linear discriminant problem separating two sets of points. 2. Consider the neuron on the left with three inputs. The plot of the activation function of the neuron is given on the right. More precisely, -{₁+ f(v) = 0, v +0.5, 1, v < -0.5 -0.5 ≤ v ≤ 0.5 v> 0.5 (a) Suppose the error at the output is defined as E = (t-o)² where t is the target output. Derive the weight update equations for this neuron using the gradient descent method. (b) Write a program to train this neuron such that it evaluates the function (21 AND 22) OR 23. Note that in this problem you are not restricted to use the McCulloch-Pitts neuron. In fact, you will train the network to find the weights. In your program, you should i. initialize the weights randomly, ii. use the weight update equations you derived in part (a), iii. stop the iterations when the error drops below the "machine epsilon" (in MATLAB, it is denoted by the constant eps.). Report the resulting values of the weights. How does the learning rate affect the convergence? Try different values and discuss. (c) Since there are three inputs, they can be visualized in 3D space. Plot the input points and the discriminant corresponding to the weights you found in part (b), and explain how this problem can be interpreted as a linear discriminant problem separating two sets of points.

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a Weight update equations for the neuron using the gradient descent method The gradient of the error function with respect to the weights is given by ... View the full answer