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The cross-entropy loss for a single-layer perceptron on a training set D -Kx),j).(x,y2),...(xP.yj is defined as W, X where y (w,x() is the output of
The cross-entropy loss for a single-layer perceptron on a training set D -Kx"),j").(x,y2),...(xP.yj is defined as W, X where y (w,x() is the output of the perceptron. Show that this expression is non- negative for y,y E [0,1] and assumes a minimum (as a function of the perceptron output 9) if9(w, x(u))-y(H) for all ?, i.e. if the neuron output ?(w, xu)) corresponds to the target value y(u) for each training sample ? The cross-entropy loss for a single-layer perceptron on a training set D -Kx"),j").(x,y2),...(xP.yj is defined as W, X where y (w,x() is the output of the perceptron. Show that this expression is non- negative for y,y E [0,1] and assumes a minimum (as a function of the perceptron output 9) if9(w, x(u))-y(H) for all ?, i.e. if the neuron output ?(w, xu)) corresponds to the target value y(u) for each training sample
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