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 apply(self, Xs, Ys, Rs, reverse_state):
#this method is correct, but wasteful
grad = ilayers.GradientWRT(len(Xs))
times_alpha = tensorflow.keras.layers.Lambda(lambda x: x * self._alpha)
times_beta = tensorflow.keras.layers.Lambda(lambda x: x * self._beta)
keep_positives = tensorflow.keras.layers.Lambda(
lambda x: x * K.cast(K.greater(x, 0), K.floatx()))
keep_negatives = tensorflow.keras.layers.Lambda(
lambda x: x * K.cast(K.less(x, 0), K.floatx()))
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)
]
# Distinguish postive and negative inputs.
Xs_pos = kutils.apply(keep_positives, Xs)
Xs_neg = kutils.apply(keep_negatives, Xs)
# xpos*wpos + xneg*wneg
activator_relevances = f(self._layer_wo_act_positive,
self._layer_wo_act_negative, Xs_pos, Xs_neg)
if self._beta: #only compute beta-weighted contributions of beta is not zero
# xpos*wneg + xneg*wpos
inhibitor_relevances = f(self._layer_wo_act_negative,
self._layer_wo_act_positive, Xs_pos,
Xs_neg)
return [
tensorflow.keras.layers.Subtract()(
[times_alpha(a), times_beta(b)])
for a, b in zip(activator_relevances, inhibitor_relevances)
]
else:
return activator_relevances
def apply(self, Xs, Ys, Rs, reverse_state):
##print(" in BatchNormalizationReverseLayer.apply:", reverse_state['layer'].__class__.__name__, '(nid: {})'.format(reverse_state['nid']))
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(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 = tensorflow.keras.layers.Lambda(
lambda x: x - K.reshape(self._mean, broadcast_shape))
minus_beta = tensorflow.keras.layers.Lambda(
lambda x: x - K.reshape(self._beta, broadcast_shape))
prepare_div = tensorflow.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 = [
tensorflow.keras.layers.Multiply()([x, ymb, r])
for x, ymb, r in zip(Xs, y_minus_beta, Rs)
]
denominator = [
tensorflow.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))
to_low = tensorflow.keras.layers.Lambda(lambda x: x * 0 + self._low)
to_high = tensorflow.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 = [
tensorflow.keras.layers.Subtract()(
[a, tensorflow.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 = [
tensorflow.keras.layers.Multiply()([a, b])
for a, b in zip(Xs, tmpA)
]
tmpB = [
tensorflow.keras.layers.Multiply()([a, b])
for a, b in zip(low, tmpB)
]
tmpC = [
tensorflow.keras.layers.Multiply()([a, b])
for a, b in zip(high, tmpC)
]
tmp = [
tensorflow.keras.layers.Subtract()(
[a, tensorflow.keras.layers.Add()([b, c])])
for a, b, c in zip(tmpA, tmpB, tmpC)
]
return tmp
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):
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 [
tensorflow.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 = tensorflow.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 [
tensorflow.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))
# The epsilon rule aligns epsilon with the (extended) sign: 0 is considered to be positive
prepare_div = tensorflow.keras.layers.Lambda(lambda x: x + (K.cast(
K.greater_equal(x, 0), K.floatx()) * 2 - 1) * self._epsilon)
# Get activations.
Zs = kutils.apply(self._layer_wo_act, Xs)
# Divide incoming relevance by the activations.
tmp = [ilayers.Divide()([a, prepare_div(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 [
tensorflow.keras.layers.Multiply()([a, b])
for a, b in zip(Xs, 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 [
tensorflow.keras.layers.Multiply()([a, b])
for a, b in zip(Xs, tmp)
]