sympy_xor_neural_network.py

sympy_xor_neural_network.py

from sympy import *

a, b, c, d, e, f = symbols('a b c d e f')
x1, x2, x3, x4 = symbols('x:4')
y1, y2, y3, y4 = symbols('y:4')
z1, z2, z3, z4 = symbols('z:4')

"""
input = Matrix([
    [x1, y1],
    [x2, y2],
    [x3, y2],
    [x4, y4]
])

output_actual = Matrix([
    z1,
    z2,
    z3,
    z4
])

# weights
w_hidden = Matrix([
    [a, b],  # w0->0, w0->1
    [c, d]  # w1->0, w1->1
])

w_output = Matrix([
    e,
    f
]).transpose()
"""

input = Matrix([
    [0, 0],
    [1, 0],
    [0, 1],
    [1, 1]
])

output_actual = Matrix([
    0,
    1,
    1,
    0
])

w_hidden = Matrix([
    [.1, .2],  # w0->0, w0->1
    [.3, .4]  # w1->0, w1->1
])

w_output = Matrix([
    .5,
    .6
]).transpose()

# apply weights to input
hidden_applied = w_hidden * input.transpose()
# print(latex(w_hidden) + " . " + latex(input.transpose()) + " = " + latex(hidden_applied))
output_applied = w_output * hidden_applied
# print(latex(w_output) + " . " + latex(w_hidden) + " . " + latex(input.transpose()) + " = " + latex(output_applied))

# Apply sigmoid function
sigmoid = lambda x: 1 / (1 + exp(-x))
activated = output_applied.applyfunc(sigmoid)

# Calculate errors

# backprop output -> hidden
output_errors = output_actual.transpose() - activated
# print(latex(w_output.transpose()) + " . " + latex(output_errors))
hidden_errors = w_output.transpose() * output_errors
print(latex(hidden_errors))

# backprop hidden -> input
input_errors = w_hidden.transpose() * hidden_errors
print(latex(w_hidden.transpose()) + " . " + latex(hidden_errors) + " = " + latex(input_errors))