What are the weights and bias for the AND perceptron?

user_7994074 0
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I am implementing AND Perceptron and facing difficulty in deciding the weights and bias for the combination to match it to AND Truth table.

Here's the Code that I have written:

import pandas as pd

# Set weight1, weight2, and bias
weight1 = 2.0
weight2 = -1.0
bias = -1.0

# Inputs and outputs
test_inputs = [(0, 0), (0, 1), (1, 0), (1, 1)]
correct_outputs = [False, False, False, True]
outputs = []

# Generate and check output
for test_input, correct_output in zip(test_inputs, correct_outputs):
    linear_combination = weight1 * test_input[0] + weight2 * test_input[1] + bias
    output = int(linear_combination >= 0)
    is_correct_string = 'Yes' if output == correct_output else 'No'
    outputs.append([test_input[0], test_input[1], linear_combination, output, is_correct_string])

# Print output
num_wrong = len([output[4] for output in outputs if output[4] == 'No'])
output_frame = pd.DataFrame(outputs, columns=['Input 1', '  Input 2', '  Linear Combination', '  Activation Output', '  Is Correct'])
if not num_wrong:
    print('Nice!  You got it all correct.\n')
else:
    print('You got {} wrong.  Keep trying!\n'.format(num_wrong))
print(output_frame.to_string(index=False))

I have to decide weight1, weight2 and bias and from the mentioned values. I am getting one output wrong when there is 1 and 0 as Input.

Thanks for helping.

pandas neural-network python
4 Answers
  • The equation is symmetric: the two inputs are functionally equivalent.
  • Taking your weights as the variables, you have four (now three) inequalities in three (now two) variables. Where are you stuck on solving that system?

System:

w = weight (same for both inputs)
b = bias

0*w + 0*w + b <= 0
1*w + 0*w + b <= 0
1*w + 1*w + b >  0

This leaves you with

w + b <= 0
2*w + b > 0

You should be able to characterize the possible solutions from there.

user_47851850

AND Perceptron:

weight1 = 1.0
weight2 = 1.0
bias = -2.0

OR Perceptron:

weight1 = 1.0
weight2 = 1.0
bias = -1

NOT Perceptron:

weight1 = 1.0
weight2 = -2.0
bias = 0

The bias acts as an intercept to adjust the linear equation.

user_32640360

Try using relu activation function and see if it solves your problem

relu(weight1 * test_input[0] + weight2 * test_input[1] + bias)

1, 1 and -1.5 should work.

user_78230130

Perceptron algorithm

prediction = 1 if wx+b >=0 and 0 if wx+<0

so the inputs are (0, 0), (0, 1), (1, 0), (1, 1) make sure the number you will input for weight1, weight2 and bias will out put < 0 as false and >=0 as true

  1. for inputs (0,0)

weight1*0+weight2*0+-2

1*0+1*0-2 = -2

  1. for inputs (0,1)

1*0+1*1-2 = -1

  1. for inputs (1,0)

1*1+1*0-2 = -1

  1. for inputs (1,1)

1*1+1*1-2 = 0

Therefore , my weight1 =1, weight2 =1 and bias = -2. I got all the answers as correct

you can use any weight1,weight2 and bias values you want as long as the output states the AND operation. Remember you can apply to OR and other operations

user_27038940
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