def f(cls, x, params, do_alter, do_shift_x=True):
w1, w2, b = params
if do_alter:
b *= 2.
w1 += 5.
w2 /= 0.9
if do_shift_x:
x = x * 2 + 1.
return 0.5 * np.dot(np.dot(x.T, w1), x) + np.dot(w2, x) + b
def f_lin_exact(cls, x0, x, params, do_alter, do_shift_x=True):
w1, w2, b = params
f0 = EmpiricalTest.f(x0, params, do_alter, do_shift_x)
if do_shift_x:
x0 = x0 * 2 + 1.
x = x * 2 + 1.
dx = x - x0
if do_alter:
b *= 2.
w1 += 5.
w2 /= 0.9
return f0 + np.dot(np.dot(x0.T, w1) + w2, dx)
def f_2_exact(x0, x, params, do_alter, do_shift_x=True):
w1, w2, b = params
f_lin = EmpiricalTest.f_lin_exact(x0, x, params, do_alter,
do_shift_x)
if do_shift_x:
x0 = x0 * 2 + 1.
x = x * 2 + 1.
if do_alter:
b *= 2.
w1 += 5.
w2 /= 0.9
dx = x - x0
return f_lin + 0.5 * np.dot(np.dot(dx.T, w1), dx)
def forward(self, x):
"""Performs the forward pass.
Args:
x: 2-d array of size batch_size x image_size.
Returns:
A 2-d array of size batch_size x num_classes.
"""
for l in self.layers:
w = l.weights
b = l.biases
x = self.sigmoid(np.dot(x, w) + b)
return x
def apply_fun(params, inputs, **kwargs):
W, b = params
return tfnp.dot(inputs, W) + b