Last active
August 22, 2019 02:46
-
-
Save michalliu/5962e8e603ee17924ccc5944a2e81280 to your computer and use it in GitHub Desktop.
back propagation expained
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
import math | |
#back propagation expained | |
#http://cs231n.github.io/optimization-2/ | |
def compute(w, x): | |
# forward pass | |
dot = w[0] * x[0] + w[1] * x[1] + w[2] | |
# sigmoid | |
f = 1.0 / (1 + math.exp(-dot)) | |
return f | |
def gradient(f, w, x): | |
ddot = (1-f) * f #gradient on dot variable | |
dw = [x[0] * ddot, x[1] * ddot, 1 * ddot] # chain rule [dw0, dw1, dw2] | |
dx = [w[0] * ddot, w[1] * ddot] # chain rule [dx0, dx1] | |
return dw, dx | |
w0 = [2,-3,-3] | |
x0 = [-1,-2] | |
# throw values to see gradient | |
# forward pass | |
f = compute(w0, x0) | |
print("f=%s" % f) | |
# backward pass check gradient | |
g_w0, g_x0 = gradient (f, w0, x0) | |
print("gw0=%s" % g_w0) | |
print("gx0=%s" % g_x0) | |
def evaluate(w_chg, x_chg): | |
w1 = [w0[0] + w_chg[0], w0[1]+ w_chg[1], w0[2]+ w_chg[2]] | |
x1 = [x0[0]+ x_chg[0], x0[1]+ x_chg[1]] | |
expected_f = f + w_chg[0] * g_w0[0] + w_chg[1] * g_w0[1] + w_chg[2] * g_w0[2] + x_chg[0] * g_x0[0] + x_chg[1] * g_x0[1] | |
print("expectedf=%s" % expected_f) | |
actual_f = compute(w1,x1) | |
print("actual_f=%s" % actual_f) | |
diff = actual_f - expected_f | |
#print("diff=%s" % diff) | |
return diff | |
# should be approximatly zero when those change is very small | |
# according to the gradient at w0,x0 | |
# w_change x_change | |
print(evaluate([0.2,0.1,0.1],[0.1,0.2])) |
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment