Using simple weights (-1, -1) and bias (2) for NAND perceptron

Question

In most study material about perceptrons, a perceptron is defined like this.

output = 1 if w . x + b > 0 output = 0 if w . x + b <= 0

(The dot '.' in the above formulas represent the dot product.)

In most examples of NAND perceptron I have seen, the NAND perceptron is defined like these:

• w = [-2, -2], b = 3 (source: http://neuralnetworksanddeeplearning.com/chap1.html)
• w = [-1, -1], b = 1.5 (source: http://users.monash.edu/~app/CSE5301/Lnts/LbD.pdf)
• w = [-0.6, -0.6], b = 1 (source: http://toritris.weebly.com/perceptron-2-logical-operations.html)

I am defining my NAND perceptron as follows.

• w = [-1, -1], b = 2

Here is the proof that it works like a NAND perceptron.

x0 x1 | w0 * x0 + w1 * x1 + b | output
------+-----------------------+-------
0  0  | 2                     | 1
0  1  | 1                     | 1
1  0  | 1                     | 1
1  1  | 0                     | 0

It this a valid NAND perceptron? Is there any specific reason why existing text do not use a simple NAND perceptron like this?

Answer 1

Because it is not a good practice to draw the discriminative boundary near the sample data: