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 apply(self, Xs, Ys, Rs, reverse_state):
#this method is correct, but wasteful
grad = ilayers.GradientWRT(len(Xs))
times_alpha0 = tensorflow.keras.layers.Lambda(
lambda x: x * self._alpha[0])
times_alpha1 = tensorflow.keras.layers.Lambda(
lambda x: x * self._alpha[1])
times_beta0 = tensorflow.keras.layers.Lambda(
lambda x: x * self._beta[0])
times_beta1 = tensorflow.keras.layers.Lambda(
lambda x: x * self._beta[1])
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(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 = [
tensorflow.keras.layers.Multiply()([a, b])
for a, b in zip(X, tmp)
]
return tmp
# Distinguish postive and negative inputs.
Xs_pos = kutils.apply(keep_positives, Xs)
Xs_neg = kutils.apply(keep_negatives, Xs)
# xpos*wpos
r_pp = f(self._layer_wo_act_positive, Xs_pos)
# xneg*wneg
r_nn = f(self._layer_wo_act_negative, Xs_neg)
# a0 * r_pp + a1 * r_nn
r_pos = [
tensorflow.keras.layers.Add()([times_alpha0(pp),
times_beta1(nn)])
for pp, nn in zip(r_pp, r_nn)
]
# xpos*wneg
r_pn = f(self._layer_wo_act_negative, Xs_pos)
# xneg*wpos
r_np = f(self._layer_wo_act_positive, Xs_neg)
# b0 * r_pn + b1 * r_np
r_neg = [
tensorflow.keras.layers.Add()([times_beta0(pn),
times_beta1(np)])
for pn, np in zip(r_pn, r_np)
]
return [
tensorflow.keras.layers.Subtract()([a, b])
for a, b in zip(r_pos, r_neg)
]
def apply(self, Xs, Ys, reversed_Ys, reverse_state: Dict):
# Apply relus conditioned on backpropagated values.
reversed_Ys = kutils.apply(self._activation, reversed_Ys)
# Apply gradient of forward pass without relus.
Ys_wo_relu = kutils.apply(self._layer_wo_relu, Xs)
return ilayers.GradientWRT(len(Xs))(Xs + Ys_wo_relu + reversed_Ys)
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 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)
]
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 GuidedBackpropReverseReLULayer(Xs, Ys, reversed_Ys, reverse_state: Dict):
activation = keras.layers.Activation("relu")
# Apply relus conditioned on backpropagated values.
reversed_Ys = kutils.apply(activation, reversed_Ys)
# Apply gradient of forward pass.
return ilayers.GradientWRT(len(Xs))(Xs + Ys + reversed_Ys)
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, reversed_Ys, _reverse_state: Dict):
# Reapply the prepared layers.
act_Xs = kutils.apply(self._filter_layer, Xs)
act_Ys = kutils.apply(self._act_layer, act_Xs)
pattern_Ys = kutils.apply(self._pattern_layer, Xs)
# Layers that apply the backward pass.
grad_act = ilayers.GradientWRT(len(act_Xs))
grad_pattern = ilayers.GradientWRT(len(Xs))
# First step: propagate through the activation layer.
# Workaround for linear activations.
linear_activations = [None, keras.activations.get("linear")]
if self._act_layer.activation in linear_activations:
tmp = reversed_Ys
else:
# if linear activation this behaves strange
tmp = iutils.to_list(grad_act(act_Xs + act_Ys + reversed_Ys))
# Second step: propagate through the pattern layer.
return grad_pattern(Xs + pattern_Ys + 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):
# 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))
# The epsilon rule aligns epsilon with the (extended) sign: 0 is considered to be positive
prepare_div = 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 [keras.layers.Multiply()([a, b]) for a, b in zip(Xs, tmp)]
