Why is ans not 3?

#1

Let us assume neuron which aggregates the input and makes a decision on the basis of this aggregation. If sum of all inputs is greater than the given threshold đťšą then output of this neuron is 1 else it is 0. We can implement a boolean function with this neuron if output of this neuron is consistent with the truth table of the boolean function. In other words if the given input configuration for the boolean function outputs 1 then neuron should also give 1 to the same configuration. Consider the following boolean function (x1 And x2) AND (!x3 And !x4)

if I take the wts w1=1, w2=1, w3=1, w4=1 then if inputs are e.g x1=0, x2=1, x3=1, x4=1, o/p of boolean function should be 0. => 1.0 + 1.1 + 1.1 + 1.1 < threshold
=> threshold > 3

#2

Hey @debjanihome, “Note that circle at the end of x3 and x4 input n the diagram depicts it is an inhibitory input i.e. if this input is 1 then the output will be 0 for sure irrespective of other inputs)”

It doesn’t mean that x3 and x4 will be negated and than given to perceptron. The statement means whenever x3 = 1 or x4 = 1 the final output of perceptron will be 0 no matter what are the other inputs.

by this case only these four cases are left

x1 x2 x3 x4 output
0 0 0 0 0
0 1 0 0 0
1 0 0 0 0
1 1 0 0 1

For all rest cases output will be directly zero no need to worry about them. From here you can see that threshold value must be 2.

Hope this resolved your doubt.
Plz mark the doubt as resolved in my doubts section. :blush:

Boolean perceptron 2
Q4. Partial Derivative