def test_calc_avgpool(self):
image_data = self._image_data()
net = self._network('avgpool')
input_bounds = naive_bounds.input_bounds(image_data.image, delta=.1)
dual_obj, dual_var_lists = self._build_objective(
net, input_bounds, image_data.label)
# Explicitly build the expected TensorFlow graph for calculating objective.
(
conv2d_0,
relu_1, # pylint:disable=unused-variable
avgpool_2,
relu_3, # pylint:disable=unused-variable
linear_obj) = self._verifiable_layer_builder(net).build_layers()
(mu_0, ), (lam_1, ), (mu_2, ), _ = dual_var_lists
# Expected input bounds for each layer.
conv2d_0_lb, conv2d_0_ub = self._expected_input_bounds(
image_data.image, .1)
relu_1_lb, relu_1_ub = ibp.IntervalBounds(
conv2d_0_lb, conv2d_0_ub).apply_conv2d(None, conv2d_0.module.w,
conv2d_0.module.b, 'SAME',
(1, 1))
avgpool_2_lb = tf.nn.relu(relu_1_lb)
avgpool_2_ub = tf.nn.relu(relu_1_ub)
relu_3_lb = tf.nn.avg_pool(avgpool_2_lb,
ksize=[2, 2],
padding='VALID',
strides=(1, 1))
relu_3_ub = tf.nn.avg_pool(avgpool_2_ub,
ksize=[2, 2],
padding='VALID',
strides=(1, 1))
# Expected objective value.
objective = 0
act_coeffs_0 = -common.conv_transpose(
mu_0, conv2d_0.module.w, conv2d_0.input_shape, 'SAME', (1, 1))
obj_0 = -tf.reduce_sum(mu_0 * conv2d_0.module.b, axis=(2, 3, 4))
objective += standard_layer_calcs.linear_dual_objective(
None, act_coeffs_0, obj_0, conv2d_0_lb, conv2d_0_ub)
objective += standard_layer_calcs.activation_layer_dual_objective(
tf.nn.relu, mu_0, lam_1, relu_1_lb, relu_1_ub)
act_coeffs_2 = -common.avgpool_transpose(
mu_2,
result_shape=relu_1.output_shape,
kernel_shape=(2, 2),
strides=(1, 1))
objective += standard_layer_calcs.linear_dual_objective(
lam_1, act_coeffs_2, 0., avgpool_2_lb, avgpool_2_ub)
objective_w, objective_b = common.targeted_objective(
linear_obj.module.w, linear_obj.module.b, image_data.label)
shaped_objective_w = tf.reshape(
objective_w,
[self._num_classes(), self._batch_size()] + avgpool_2.output_shape)
objective += standard_layer_calcs.activation_layer_dual_objective(
tf.nn.relu, mu_2, -shaped_objective_w, relu_3_lb, relu_3_ub)
objective += objective_b
self._assert_dual_objective_close(objective, dual_obj, image_data)
def test_calc_conv_batchnorm(self):
image_data = self._image_data()
net = self._network('conv_batchnorm')
input_bounds = naive_bounds.input_bounds(image_data.image, delta=.1)
dual_obj, dual_var_lists = self._build_objective(
net, input_bounds, image_data.label)
# Explicitly build the expected TensorFlow graph for calculating objective.
(
conv2d_0,
relu_1, # pylint:disable=unused-variable
linear_2,
relu_3, # pylint:disable=unused-variable
linear_obj) = self._verifiable_layer_builder(net).build_layers()
(mu_0, ), (lam_1, ), (mu_2, ), _ = dual_var_lists
# Expected input bounds for each layer.
conv2d_0_lb, conv2d_0_ub = self._expected_input_bounds(
image_data.image, .1)
conv2d_0_w, conv2d_0_b = layer_utils.combine_with_batchnorm(
conv2d_0.module.w, None, conv2d_0.batch_norm)
relu_1_lb, relu_1_ub = ibp.IntervalBounds(
conv2d_0_lb, conv2d_0_ub).apply_conv2d(None, conv2d_0_w,
conv2d_0_b, 'VALID', (1, 1))
linear_2_lb = snt.BatchFlatten()(tf.nn.relu(relu_1_lb))
linear_2_ub = snt.BatchFlatten()(tf.nn.relu(relu_1_ub))
linear_2_w, linear_2_b = layer_utils.combine_with_batchnorm(
linear_2.module.w, None, linear_2.batch_norm)
relu_3_lb, relu_3_ub = ibp.IntervalBounds(linear_2_lb,
linear_2_ub).apply_linear(
None, linear_2_w,
linear_2_b)
# Expected objective value.
objective = 0
act_coeffs_0 = -common.conv_transpose(
mu_0, conv2d_0_w, conv2d_0.input_shape, 'VALID', (1, 1))
obj_0 = -tf.reduce_sum(mu_0 * conv2d_0_b, axis=(2, 3, 4))
objective += standard_layer_calcs.linear_dual_objective(
None, act_coeffs_0, obj_0, conv2d_0_lb, conv2d_0_ub)
objective += standard_layer_calcs.activation_layer_dual_objective(
tf.nn.relu, mu_0, lam_1, relu_1_lb, relu_1_ub)
act_coeffs_2 = -tf.tensordot(mu_2, tf.transpose(linear_2_w), axes=1)
obj_2 = -tf.tensordot(mu_2, linear_2_b, axes=1)
objective += standard_layer_calcs.linear_dual_objective(
snt.BatchFlatten(preserve_dims=2)(lam_1), act_coeffs_2, obj_2,
linear_2_lb, linear_2_ub)
objective_w, objective_b = common.targeted_objective(
linear_obj.module.w, linear_obj.module.b, image_data.label)
objective += standard_layer_calcs.activation_layer_dual_objective(
tf.nn.relu, mu_2, -objective_w, relu_3_lb, relu_3_ub)
objective += objective_b
self._assert_dual_objective_close(objective, dual_obj, image_data)
def _materialised_conv_layer_dual_objective(w, b, padding, strides, lam_in,
mu_out, lb, ub):
"""Materialised version of `conv_layer_dual_objective`."""
# Flatten the inputs, as the materialised convolution will have no
# spatial structure.
mu_out_flat = snt.BatchFlatten(preserve_dims=2)(mu_out)
# Materialise the convolution as a (sparse) fully connected linear layer.
w_flat, b_flat = layer_utils.materialise_conv(w,
b,
lb.shape[1:].as_list(),
padding=padding,
strides=strides)
activation_coeffs = -tf.tensordot(
mu_out_flat, tf.transpose(w_flat), axes=1)
dual_obj_bias = -tf.tensordot(mu_out_flat, b_flat, axes=1)
# Flatten the inputs, as the materialised convolution will have no
# spatial structure.
if lam_in is not None:
lam_in = snt.FlattenTrailingDimensions(2)(lam_in)
lb = snt.BatchFlatten()(lb)
ub = snt.BatchFlatten()(ub)
return standard_layer_calcs.linear_dual_objective(lam_in,
activation_coeffs,
dual_obj_bias, lb, ub)
def test_conv2d_layer_dual_objective(self, dtype, tol):
num_classes = 5
batch_size = 53
input_height = 17
input_width = 7
kernel_height = 3
kernel_width = 4
input_channels = 3
output_channels = 2
padding = 'VALID'
strides = (2, 1)
# Output dimensions, based on convolution settings.
output_height = 8
output_width = 4
w = tf.random_normal(dtype=dtype,
shape=(kernel_height, kernel_width,
input_channels, output_channels))
b = tf.random_normal(dtype=dtype, shape=(output_channels, ))
lam_in = tf.random_normal(dtype=dtype,
shape=(num_classes, batch_size, input_height,
input_width, input_channels))
mu_out = tf.random_normal(dtype=dtype,
shape=(num_classes, batch_size,
output_height, output_width,
output_channels))
lb = tf.random_normal(dtype=dtype,
shape=(batch_size, input_height, input_width,
input_channels))
ub = tf.random_normal(dtype=dtype,
shape=(batch_size, input_height, input_width,
input_channels))
lb, ub = tf.minimum(lb, ub), tf.maximum(lb, ub)
activation_coeffs = -common.conv_transpose(
mu_out, w, lb.shape[1:].as_list(), padding, strides)
dual_obj_bias = -tf.reduce_sum(mu_out * b, axis=(2, 3, 4))
dual_obj = standard_layer_calcs.linear_dual_objective(
lam_in, activation_coeffs, dual_obj_bias, lb, ub)
# Compare against equivalent linear layer.
dual_obj_lin = _materialised_conv_layer_dual_objective(
w, b, padding, strides, lam_in, mu_out, lb, ub)
with self.test_session() as session:
dual_obj_val, dual_obj_lin_val = session.run(
(dual_obj, dual_obj_lin))
self.assertAllClose(dual_obj_val,
dual_obj_lin_val,
atol=tol,
rtol=tol)
def test_linear_layer_dual_objective(self, dtype, tol):
w = tf.constant([[1.0, 2.0, 3.0], [4.0, -5.0, -6.0]], dtype=dtype)
b = tf.constant([0.1, 0.2, 0.3], dtype=dtype)
lb = tf.constant([[-1.0, -1.0]], dtype=dtype)
ub = tf.constant([[1.0, 1.0]], dtype=dtype)
lam_in = tf.constant([[[-.01, -.02]]], dtype=dtype)
mu_out = tf.constant([[[30.0, 40.0, 50.0]]], dtype=dtype)
# Activation coefficients: -.01 - 260, and -.02 + 380
activation_coeffs = -tf.tensordot(mu_out, tf.transpose(w), axes=1)
dual_obj_bias = -tf.tensordot(mu_out, b, axes=1)
dual_obj = standard_layer_calcs.linear_dual_objective(
lam_in, activation_coeffs, dual_obj_bias, lb, ub)
dual_obj_exp = np.array([[(.01 + 260.0) + (-.02 + 380.0) - 26.0]])
with self.test_session() as session:
dual_obj_act = session.run(dual_obj)
self.assertAllClose(dual_obj_exp, dual_obj_act, atol=tol, rtol=tol)
def test_conv2d_layer_dual_objective_shape(self, dtype):
num_classes = 6
batch_size = 23
input_height = 17
input_width = 7
kernel_height = 3
kernel_width = 4
input_channels = 3
output_channels = 5
padding = 'VALID'
strides = (2, 1)
# Output dimensions, based on convolution settings.
output_height = 8
output_width = 4
w = tf.placeholder(dtype=dtype,
shape=(kernel_height, kernel_width, input_channels,
output_channels))
b = tf.placeholder(dtype=dtype, shape=(output_channels, ))
lam_in = tf.placeholder(dtype=dtype,
shape=(num_classes, batch_size, input_height,
input_width, input_channels))
mu_out = tf.placeholder(dtype=dtype,
shape=(num_classes, batch_size, output_height,
output_width, output_channels))
lb = tf.placeholder(dtype=dtype,
shape=(batch_size, input_height, input_width,
input_channels))
ub = tf.placeholder(dtype=dtype,
shape=(batch_size, input_height, input_width,
input_channels))
activation_coeffs = -common.conv_transpose(
mu_out, w, lb.shape[1:].as_list(), padding, strides)
dual_obj_bias = -tf.reduce_sum(mu_out * b, axis=(2, 3, 4))
dual_obj = standard_layer_calcs.linear_dual_objective(
lam_in, activation_coeffs, dual_obj_bias, lb, ub)
self.assertEqual(dtype, dual_obj.dtype)
self.assertEqual((num_classes, batch_size), dual_obj.shape)
def test_linear_layer_dual_objective_shape(self, dtype):
num_classes = 3
batch_size = 11
input_size = 7
output_size = 5
w = tf.placeholder(dtype=dtype, shape=(input_size, output_size))
b = tf.placeholder(dtype=dtype, shape=(output_size, ))
lam_in = tf.placeholder(dtype=dtype,
shape=(num_classes, batch_size, input_size))
mu_out = tf.placeholder(dtype=dtype,
shape=(num_classes, batch_size, output_size))
lb = tf.placeholder(dtype=dtype, shape=(batch_size, input_size))
ub = tf.placeholder(dtype=dtype, shape=(batch_size, input_size))
activation_coeffs = -tf.tensordot(mu_out, tf.transpose(w), axes=1)
dual_obj_bias = -tf.tensordot(mu_out, b, axes=1)
dual_obj = standard_layer_calcs.linear_dual_objective(
lam_in, activation_coeffs, dual_obj_bias, lb, ub)
self.assertEqual(dtype, dual_obj.dtype)
self.assertEqual((num_classes, batch_size), dual_obj.shape)
def test_calc_linear(self):
image_data = self._image_data()
net = self._network('linear')
input_bounds = naive_bounds.input_bounds(image_data.image, delta=.1)
dual_obj, dual_var_lists = self._build_objective(
net, input_bounds, image_data.label)
# Explicitly build the expected TensorFlow graph for calculating objective.
(
linear_0,
relu_1, # pylint:disable=unused-variable
linear_obj) = self._verifiable_layer_builder(net).build_layers()
(mu_0, ), _ = dual_var_lists
# Expected input bounds for each layer.
linear_0_lb, linear_0_ub = self._expected_input_bounds(
image_data.image, .1)
linear_0_lb = snt.BatchFlatten()(linear_0_lb)
linear_0_ub = snt.BatchFlatten()(linear_0_ub)
relu_1_lb, relu_1_ub = ibp.IntervalBounds(linear_0_lb,
linear_0_ub).apply_linear(
None, linear_0.module.w,
linear_0.module.b)
# Expected objective value.
objective = 0
act_coeffs_0 = -tf.tensordot(
mu_0, tf.transpose(linear_0.module.w), axes=1)
obj_0 = -tf.tensordot(mu_0, linear_0.module.b, axes=1)
objective += standard_layer_calcs.linear_dual_objective(
None, act_coeffs_0, obj_0, linear_0_lb, linear_0_ub)
objective_w, objective_b = common.targeted_objective(
linear_obj.module.w, linear_obj.module.b, image_data.label)
objective += standard_layer_calcs.activation_layer_dual_objective(
tf.nn.relu, mu_0, -objective_w, relu_1_lb, relu_1_ub)
objective += objective_b
self._assert_dual_objective_close(objective, dual_obj, image_data)
def affine_layer_contrib(self, layer, dual_vars_lm1, activation_coeffs,
dual_obj_bias):
"""Computes the contribution of an affine layer to the dual objective.
Compute the term::
max_x (lam_{l-1}^T x - mu_l^T (W_l x + b_l))
where W_l, b_l is the affine mapping for layer l.
Args:
layer: affine (linear/conv) layer.
dual_vars_lm1: lam_{l-1}, or None for the first layer.
activation_coeffs: mu_l^T W_l
dual_obj_bias: mu_l^T b_l
Returns:
Dual objective contribution.
"""
return standard_layer_calcs.linear_dual_objective(
dual_vars_lm1,
activation_coeffs,
dual_obj_bias,
layer.input_bounds.lower_offset,
layer.input_bounds.upper_offset,
inverse_temperature=self._inverse_temperature)
