Use graphical illustration to demonstrate neural network training algorithms

Draw the contour plot of the E(w) in the 2-dimensional space

 

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The purpose of this exercise is to use graphical illustration to demonstrate neural network training algorithms.It is suggested that a ruler(or a graph paper with grids) is used to draw the graphs.

 

Let E(w) represent the training error as a function of neural network internal weights,where is a vector of neural network internal weights.For convenience of graphical explanation,we assume that we consider only two variables for neural network training,and the function E(w) is simplified using 2nd order Taylor series.

More specifically,let E(w) for batch mode training be described as

ew

 

 

where is a vector of two variables

w1

 

 

and superscript T denotes the transpose of the vector.

Suppose the initial value of for neural network training is :

w=[0.5  1.0]T

 

Use graphical illustration to carry out two epochs of neural network training with batch mode backpropagation(part 2a) and conjugate gradient (part 2b) methods.

 

Part 2(a): You are required  to:

1.Draw the contour plot of the E(w) in the 2-dimensional space.

2.On the contour plot indicate the initial point of w

3.On the contour plot,show the gradient direction 9

4.On the contour plot,show the direction for the batch mode backpropagation method assuming the momentum factor is zero.

5.On the contour plot,show the new location of w after one epoch of training is finished,assuming we have used line minimization to determine the optimal step size η

6.Repeat 3-5 above for one more epoch.Indicate the new location of at end of the 2nd epoch.

 

Part 2(b): Suppose that we use Conjugate Gradient method to do the training where E(w), w and initial values of are defined as in (1)-(3).

 

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