def construct_batchnorm_fprop_pattern(self):
"""
Generate graph op that represents a pattern for batchnorm fprop operation.
self.gamma * ((in_obj - xmean) * ng.reciprocal(ng.sqrt(xvar + self.eps))) + self.beta
Returns:
Single pattern that matches batchnorm fprop op
"""
self.batchnorm_fprop_input_tensor_label = "in_obj"
self.batchnorm_fprop_gamma_label = "gamma"
self.batchnorm_fprop_beta_label = "beta"
self.batchnorm_fprop_variance_label = "variance"
self.batchnorm_fprop_epsilon_label = "epsilon"
self.batchnorm_fprop_mean_label = "mean"
# bind the label to the op's which needed to be updated in the dict
in_obj = PatternLabelOp(self.batchnorm_fprop_input_tensor_label,
(lambda op: isinstance(op, ContiguousOp)))
flatten_tensor = PatternSkipOp(in_obj,
(lambda op: isinstance(op, Flatten)))
gamma = PatternLabelOp(self.batchnorm_fprop_gamma_label,
(lambda op: isinstance(op, BroadcastOp)))
beta = PatternLabelOp(self.batchnorm_fprop_beta_label,
(lambda op: isinstance(op, BroadcastOp)))
variance = PatternLabelOp(self.batchnorm_fprop_variance_label,
(lambda op: isinstance(op, Divide)))
epsilon = PatternLabelOp(self.batchnorm_fprop_epsilon_label,
(lambda op: isinstance(op, BroadcastOp)))
mean = PatternLabelOp(self.batchnorm_fprop_mean_label,
(lambda op: isinstance(op, Divide)))
# construct the fprop batchnorm pattern matching the computation graph
# ng.sqrt(xvar + self.eps)
SqrtofVarianceAndEps = ng.sqrt(ng.add(variance, epsilon))
# ng.reciprocal(ng.sqrt(xvar + self.eps))
reciprocal_op = ng.reciprocal(SqrtofVarianceAndEps)
reciprocal_op_w_braodcast = ng.PatternSkipOp(reciprocal_op,
lambda op: isinstance(op, BroadcastOp))
mean_bcast = ng.PatternSkipOp(mean, lambda op: isinstance(op, BroadcastOp))
# (in_obj - xmean) * ng.reciprocal(ng.sqrt(xvar + self.eps))
mul_op_1 = ng.multiply(ng.subtract(flatten_tensor, mean_bcast), reciprocal_op_w_braodcast)
# "self.gamma * ((in_obj - xmean) * ng.reciprocal(ng.sqrt(xvar + self.eps)))
MultiplyGamma = ng.multiply(mul_op_1, gamma)
# self.gamma * ((in_obj - xmean) * ng.reciprocal(ng.sqrt(xvar + self.eps))) + self.beta
AddBeta = ng.Unflatten(ng.Add(MultiplyGamma, beta))
return AddBeta
def construct_relu_bprop_pattern(self):
"""
Generate graph op that represents a pattern for Relu backprop operation.
delta * greater(x, 0) + delta * slope * less(x, 0)
Returns:
Single pattern that matches Relu bprop op
"""
# We want to match x tensor, slope and delta for Relu.
self.relu_bwd_slope_label = "S"
self.relu_bwd_x_label = "X"
self.relu_bwd_delta_label = "D"
# construct 1st operand of Add
zero = ng.constant(0)
zero_w_broadcast = ng.PatternSkipOp(
zero, (lambda op: isinstance(op, BroadcastOp)))
x = ng.PatternLabelOp(
self.relu_bwd_x_label,
(lambda op: not op.is_scalar)) # X is not scalar.
greater_op = Greater(x, zero_w_broadcast)
delta = PatternLabelOp(
self.relu_bwd_delta_label,
(lambda op: not op.is_scalar)) # delta is not scalar.
mul_greater_delta_op = Multiply(greater_op, delta)
# Construct 2nd operand of Add
# We bind slope op to S only if it is scalar.
slope = PatternLabelOp(self.relu_bwd_slope_label,
(lambda op: op.is_scalar))
less_op = Less(x, zero_w_broadcast)
mul_slope_delta_op = Multiply(slope, delta)
mul_slope_delta_less_op = Multiply(less_op, mul_slope_delta_op)
add_op = Add(mul_greater_delta_op, mul_slope_delta_less_op)
return add_op
def construct_batchnorm_bprop_pattern(self):
"""
Generate graph op that represents a pattern for batchnorm backprop operation.
dgamma = np.sum(delta * xhat)
dbeta = np.sum(delta)
dx = gamma_scale * (delta - (xhat * dgamma + dbeta) / m)
In this pattern we are only generating the pattern for dx.
Returns:
Single pattern that matches batchnorm bprop op
"""
self.batchnorm_bprop_input_tensor = "input_tensor"
self.batchnorm_bprop_delta = "delta"
self.batchnorm_bprop_gamma_label = "gamma"
self.batchnorm_bprop_var_label = "var"
self.batchnorm_bprop_ivar_label = "ivar"
self.batchnorm_bprop_xmu1_label = "xmu1"
self.batchnorm_bprop_xmu2_label = "xmu2"
self.batchnorm_bprop_negative_inverse_sqrtvar = "negative_inverse_sqrtvar"
self.batchnorm_bprop_inverse_sqrtvar = "inverse_sqrtvar"
self.batchnorm_bprop_sqrtvar_label = "sqrtvar"
self.batchnorm_bprop_sqrsum = "sqrsum"
self.batchnorm_bprop_mean_1 = "mean_1"
self.batchnorm_bprop_mean_2 = "mean_2"
self.batchnorm_bprop_input_sum = "input_sum"
# bind the op's to the label
input_tensor = PatternLabelOp(self.batchnorm_bprop_input_tensor,
(lambda op: isinstance(op, Flatten)))
var = PatternLabelOp(self.batchnorm_bprop_var_label,
(lambda op: isinstance(op, Divide)))
gamma = PatternLabelOp(self.batchnorm_bprop_gamma_label,
(lambda op: isinstance(op, BroadcastOp)))
delta = PatternLabelOp(self.batchnorm_bprop_delta,
(lambda op: isinstance(op, Flatten)))
xmu1 = PatternLabelOp(self.batchnorm_bprop_xmu1_label,
(lambda op: isinstance(op, Subtract)))
xmu2 = PatternLabelOp(self.batchnorm_bprop_xmu2_label,
(lambda op: isinstance(op, Subtract)))
ivar = PatternLabelOp(self.batchnorm_bprop_ivar_label,
(lambda op: isinstance(op, BroadcastOp)))
negative_inverse_sqrtvar = PatternLabelOp(
self.batchnorm_bprop_negative_inverse_sqrtvar,
(lambda op: isinstance(op, NegativeOp)))
inverse_sqrtvar = PatternLabelOp(
self.batchnorm_bprop_inverse_sqrtvar,
(lambda op: isinstance(op, ReciprocalOp)))
sqrtvar = PatternLabelOp(self.batchnorm_bprop_sqrtvar_label,
(lambda op: isinstance(op, SqrtOp)))
sqrsum = PatternLabelOp(self.batchnorm_bprop_sqrsum,
(lambda op: isinstance(op, Sum)))
mean_1 = PatternLabelOp(self.batchnorm_bprop_mean_1,
(lambda op: isinstance(op, Divide)))
mean_2 = PatternLabelOp(self.batchnorm_bprop_mean_2,
(lambda op: isinstance(op, Divide)))
input_sum = PatternLabelOp(self.batchnorm_bprop_input_sum,
(lambda op: isinstance(op, Sum)))
constant_point_5 = ng.constant(0.5)
constant_point_5_w_broadcast = ng.PatternSkipOp(
constant_point_5, lambda op: isinstance(op, BroadcastOp))
constant_two = ng.constant(2)
constant_two_w_broadcast = ng.PatternSkipOp(
constant_two, lambda op: isinstance(op, BroadcastOp))
# construct the pattern
dxhat = Multiply(gamma, delta)
# divar = np.sum(dxhat*xmu, axis=0)
divar = Sum(Multiply(dxhat, xmu1))
# dxmu1 = dxhat * ivar
dxmu1 = Multiply(dxhat, ivar)
# dsqrtvar = -1. /(sqrtvar**2) * divar
dsqrtvar = Multiply(
Multiply(inverse_sqrtvar, negative_inverse_sqrtvar), divar)
# dvar = 0.5 * 1. /np.sqrt(var+eps) * dsqrtvar
dvar = Divide(Multiply(dsqrtvar, constant_point_5_w_broadcast),
sqrtvar)
# dsq = 1. / N * np.ones((N, D)) * dvar
dsq = Divide(Multiply(dvar, var), sqrsum)
dsq_w_broadcast = ng.PatternSkipOp(
dsq, (lambda op: isinstance(op, BroadcastOp)))
# dxmu2 = 2 * xmu * dsq
dxmu2 = Multiply(xmu2,
Multiply(constant_two_w_broadcast, dsq_w_broadcast))
# dx1 = (dxmu1 + dxmu2)
# dmu = -1 * np.sum(dxmu1 + dxmu2, axis=0)
# dx2 = 1. /N * np.ones((N,D)) * dmu
# dx = dx1 + dx2
dxmu2_mul = Multiply(Sum(ng.negative(dxmu2)), mean_2)
dxmu2_div = Divide(dxmu2_mul, input_sum)
dxmu2_div_w_broadcast = ng.PatternSkipOp(
dxmu2_div, (lambda op: isinstance(op, BroadcastOp)))
dxmu2_div_plus_dxmu2 = Add(dxmu2_div_w_broadcast, dxmu2)
dx1 = Add(dxmu1, dxmu2_div_plus_dxmu2)
dxmu1_mul = Multiply(Sum(ng.negative(dxmu1)), mean_1)
dxmu1_div = Divide(dxmu1_mul, Sum(input_tensor))
dxmu1_div_w_broadcast = ng.PatternSkipOp(
dxmu1_div, (lambda op: isinstance(op, BroadcastOp)))
dx = Add(dxmu1_div_w_broadcast, dx1)
return dx
