7.10: Quantitative Problems

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Suppose that a neural network has been trained to classify students as likely to graduate or not likely to graduate based on various input parameters. There is a single output neuron having four inputs,

x_1,x_2,x_3,

and one output,

y

. The output

y

is used to make the classification. The weights of the three inputs of this neuron are

w_1=0.25

w_2=0.09

, and

w_3=-0.31

. The bias of the neuron is

b=-0.23

. Find the output

y

{(x_1,x_2,x_3)}=(0.4,-1.2,0.6)

and if the activation function is:

ReLU
Leaky ReLU defined by max⁡ (0.2x,x)
Sigmoid
Softplus

Which of the four activation functions, applied at the output layer, would be best suited for this classification task? Using this activation function, how would the neural network classify the student?

The output of a neural network on data points are given in the table.

Table 7.4
Data point	Predicted $\widehat y$	Actual(target) $y$
1	$(0.043,1.169,1.019)$	$(0,1,1)$
2	$(-0.149,0.927,-0.136)$	$(0,1,0)$
3	$(0.96,0.237,-0.109)$	$(1,0,0)$
4	$(0.842,-0.148,-0.218)$	$(1,0,0)$
5	$(0.942,0.838,1.011)$	$(1,1,1)$

Compute the average loss using the following loss functions.

MSE

Hinge loss

Search

Text Color

Text Size

Margin Size

Font Type