def apply(self, Xs, Ys, Rs, reverse_state):
grad = ilayers.GradientWRT(len(Xs))
to_low = keras.layers.Lambda(lambda x: x * 0 + self._low)
to_high = keras.layers.Lambda(lambda x: x * 0 + self._high)
low = [to_low(x) for x in Xs]
high = [to_high(x) for x in Xs]
# Get values for the division.
A = kutils.apply(self._layer_wo_act, Xs)
B = kutils.apply(self._layer_wo_act_positive, low)
C = kutils.apply(self._layer_wo_act_negative, high)
Zs = [
keras.layers.Subtract()([a, keras.layers.Add()([b, c])])
for a, b, c in zip(A, B, C)
]
# Divide relevances with the value.
tmp = [ilayers.SafeDivide()([a, b]) for a, b in zip(Rs, Zs)]
# Distribute along the gradient.
tmpA = iutils.to_list(grad(Xs + A + tmp))
tmpB = iutils.to_list(grad(low + B + tmp))
tmpC = iutils.to_list(grad(high + C + tmp))
tmpA = [keras.layers.Multiply()([a, b]) for a, b in zip(Xs, tmpA)]
tmpB = [keras.layers.Multiply()([a, b]) for a, b in zip(low, tmpB)]
tmpC = [keras.layers.Multiply()([a, b]) for a, b in zip(high, tmpC)]
tmp = [
keras.layers.Subtract()([a, keras.layers.Add()([b, c])])
for a, b, c in zip(tmpA, tmpB, tmpC)
]
return tmp
def f(layer1, layer2, X1, X2):
# Get activations of full positive or negative part.
Z1 = kutils.apply(layer1, X1)
Z2 = kutils.apply(layer2, X2)
Zs = [
tensorflow.keras.layers.Add()([a, b]) for a, b in zip(Z1, Z2)
]
# Divide incoming relevance by the activations.
tmp = [ilayers.SafeDivide()([a, b]) for a, b in zip(Rs, Zs)]
# Propagate the relevance to the input neurons
# using the gradient
tmp1 = iutils.to_list(grad(X1 + Z1 + tmp))
tmp2 = iutils.to_list(grad(X2 + Z2 + tmp))
# Re-weight relevance with the input values.
tmp1 = [
tensorflow.keras.layers.Multiply()([a, b])
for a, b in zip(X1, tmp1)
]
tmp2 = [
tensorflow.keras.layers.Multiply()([a, b])
for a, b in zip(X2, tmp2)
]
#combine and return
return [
tensorflow.keras.layers.Add()([a, b])
for a, b in zip(tmp1, tmp2)
]
def f(layer, X):
Zs = kutils.apply(layer, X)
# Divide incoming relevance by the activations.
tmp = [ilayers.SafeDivide()([a, b]) for a, b in zip(Rs, Zs)]
# Propagate the relevance to the input neurons
# using the gradient
tmp = iutils.to_list(grad(X + Zs + tmp))
# Re-weight relevance with the input values.
tmp = [keras.layers.Multiply()([a, b]) for a, b in zip(X, tmp)]
return tmp
def apply(self, Xs, Ys, Rs, reverse_state):
grad = ilayers.GradientWRT(len(Xs))
# Get activations.
Zs = kutils.apply(self._layer_wo_act, Xs)
# Divide incoming relevance by the activations.
tmp = [ilayers.SafeDivide()([a, b]) for a, b in zip(Rs, Zs)]
# Propagate the relevance to input neurons
# using the gradient.
tmp = iutils.to_list(grad(Xs + Zs + tmp))
# Re-weight relevance with the input values.
return [keras.layers.Multiply()([a, b]) for a, b in zip(Xs, tmp)]
def apply(self, Xs, Ys, Rs, _reverse_state: Dict):
input_shape = [K.int_shape(x) for x in Xs]
if len(input_shape) != 1:
# extend below lambda layers towards multiple parameters.
raise ValueError(
"BatchNormalizationReverseLayer expects Xs with len(Xs) = 1, but was len(Xs) = {}".format( # noqa
len(Xs)
)
)
input_shape = input_shape[0]
# prepare broadcasting shape for layer parameters
broadcast_shape = [1] * len(input_shape)
broadcast_shape[self._axis] = input_shape[self._axis]
broadcast_shape[0] = -1
# reweight relevances as
# x * (y - beta) R
# Rin = ---------------- * ----
# x - mu y
# batch norm can be considered as 3 distinct layers of subtraction,
# multiplication and then addition. The multiplicative scaling layer
# has no effect on LRP and functions as a linear activation layer
minus_mu = keras.layers.Lambda(
lambda x: x - K.reshape(self._mean, broadcast_shape)
)
minus_beta = keras.layers.Lambda(
lambda x: x - K.reshape(self._beta, broadcast_shape)
)
prepare_div = keras.layers.Lambda(
lambda x: x
+ (K.cast(K.greater_equal(x, 0), K.floatx()) * 2 - 1) * K.epsilon()
)
x_minus_mu = kutils.apply(minus_mu, Xs)
if self._center:
y_minus_beta = kutils.apply(minus_beta, Ys)
else:
y_minus_beta = Ys
numerator = [
keras.layers.Multiply()([x, ymb, r])
for x, ymb, r in zip(Xs, y_minus_beta, Rs)
]
denominator = [
keras.layers.Multiply()([xmm, y]) for xmm, y in zip(x_minus_mu, Ys)
]
return [
ilayers.SafeDivide()([n, prepare_div(d)])
for n, d in zip(numerator, denominator)
]
def apply(self, Xs, Ys, Rs, reverse_state):
grad = ilayers.GradientWRT(len(Xs))
# Create dummy forward path to take the derivative below.
Ys = kutils.apply(self._layer_wo_act_b, Xs)
# Compute the sum of the weights.
ones = ilayers.OnesLike()(Xs)
Zs = iutils.to_list(self._layer_wo_act_b(ones))
# Weight the incoming relevance.
tmp = [ilayers.SafeDivide()([a, b]) for a, b in zip(Rs, Zs)]
# Redistribute the relevances along the gradient.
tmp = iutils.to_list(grad(Xs + Ys + tmp))
return tmp
def apply(self, Xs, Ys, Rs, reverse_state):
# the outputs of the pooling operation at each location is the sum of its inputs.
# the forward message must be known in this case, and are the inputs for each pooling thing.
# the gradient is 1 for each output-to-input connection, which corresponds to the "weights"
# of the layer. It should thus be sufficient to reweight the relevances and and do a gradient_wrt
grad = ilayers.GradientWRT(len(Xs))
# Get activations.
Zs = kutils.apply(self._layer_wo_act, Xs)
# Divide incoming relevance by the activations.
tmp = [ilayers.SafeDivide()([a, b]) for a, b in zip(Rs, Zs)]
# Propagate the relevance to input neurons
# using the gradient.
tmp = iutils.to_list(grad(Xs + Zs + tmp))
# Re-weight relevance with the input values.
return [keras.layers.Multiply()([a, b]) for a, b in zip(Xs, tmp)]
def apply(self, Xs, Ys, Rs, reverse_state):
grad = ilayers.GradientWRT(len(Xs))
#TODO: assert all inputs are positive, instead of only keeping the positives.
#keep_positives = keras.layers.Lambda(lambda x: x * K.cast(K.greater(x,0), K.floatx()))
#Xs = kutils.apply(keep_positives, Xs)
# Get activations.
Zs = kutils.apply(self._layer_wo_act_b_positive, Xs)
# Divide incoming relevance by the activations.
tmp = [ilayers.SafeDivide()([a, b]) for a, b in zip(Rs, Zs)]
# Propagate the relevance to input neurons
# using the gradient.
tmp = iutils.to_list(grad(Xs + Zs + tmp))
# Re-weight relevance with the input values.
return [keras.layers.Multiply()([a, b]) for a, b in zip(Xs, tmp)]
def apply(self, Xs, Ys, Rs, reverse_state):
grad = ilayers.GradientWRT(len(Xs))
to_low = keras.layers.Lambda(lambda x: x * 0 + self._low)
to_high = keras.layers.Lambda(lambda x: x * 0 + self._high)
def f(Xs):
low = [to_low(x) for x in Xs]
high = [to_high(x) for x in Xs]
A = kutils.apply(self._layer_wo_act, Xs)
B = kutils.apply(self._layer_wo_act_positive, low)
C = kutils.apply(self._layer_wo_act_negative, high)
return [
keras.layers.Subtract()([a, keras.layers.Add()([b, c])])
for a, b, c in zip(A, B, C)
]
# Get values for the division.
Zs = f(Xs)
# Divide relevances with the value.
tmp = [ilayers.SafeDivide()([a, b]) for a, b in zip(Rs, Zs)]
# Distribute along the gradient.
tmp = iutils.to_list(grad(Xs + Zs + tmp))
return tmp
def norm(x, count):
return ilayers.SafeDivide(factor=1)([x, count])