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Problem 8. Consider the XOR problem (0,1) (0,0) (1,1) It's impossible for a single hyperplane to classify the above data with 0 error. Recall that in a hidden layer network we perform several linear transformations of the data to obtain a new feature representation. Each output in the new feature space is converted to a non- linear form using the sigmoid function or the sign function. These new outputs are then combined linearly again. If the hidden outputs are not converted to non-linear then we just get another linear classifier and cannot solve XOR. We will use a one-layer network with two hidden nodes to classify XOR with 0 error. In the first plane we will separate (0,0) from the other points as shown in the figure. We will convert the output of each classifier with the sign function that simply returns the sign of a number. The first plane above shown in dotted line is given by $w_1 = 1.17$ and $w_0 = -0.5$ and the feature output is $sign(w_1x + w_0)$. Write down the output of the four data points as given by this transformation (4 pts)

          Problem 8. Consider the XOR problem
(0,1)
(0,0)
(1,1)
It's impossible for a single hyperplane to classify the above data with 0 error. Recall that
in a hidden layer network we perform several linear transformations of the data to obtain
a new feature representation. Each output in the new feature space is converted to a non-
linear form using the sigmoid function or the sign function. These new outputs are then
combined linearly again. If the hidden outputs are not converted to non-linear then we
just get another linear classifier and cannot solve XOR.
We will use a one-layer network with two hidden nodes to classify XOR with 0 error. In
the first plane we will separate (0,0) from the other points as shown in the figure. We will
convert the output of each classifier with the sign function that simply returns the sign of
a number.
The first plane above shown in dotted line is given by $w_1 = 1.17$ and $w_0 = -0.5$ and
the feature output is $sign(w_1x + w_0)$. Write down the output of the four data points
as given by this transformation (4 pts)

Problem 8. Consider the XOR problem
(0,1)
(0,0)
(1,1)
It's impossible for a single hyperplane to classify the above data with 0 error. Recall that
in a hidden layer network we perform several linear transformations of the data to obtain
a new feature representation. Each output in the new feature space is converted to a non-
linear form using the sigmoid function or the sign function. These new outputs are then
combined linearly again. If the hidden outputs are not converted to non-linear then we
just get another linear classifier and cannot solve XOR.
We will use a one-layer network with two hidden nodes to classify XOR with 0 error. In
the first plane we will separate (0,0) from the other points as shown in the figure. We will
convert the output of each classifier with the sign function that simply returns the sign of
a number.
The first plane above shown in dotted line is given by w1 = 1.17 and w0 = -0.5 and
the feature output is sign(w1x + w0). Write down the output of the four data points
as given by this transformation (4 pts)

Added by Ashley G.

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