def batchNorm(self, node, makeEquations):
"""Function to generate equations for a BatchNormalization
Args:
node (node): ONNX node representing the BatchNormalization operation
:meta private
"""
nodeName = node.output[0]
inputName = node.input[0]
self.shapeMap[nodeName] = self.shapeMap[inputName]
# Get attributes
epsilon = None
for attr in node.attribute:
if attr.name == "epsilon":
epsilon = get_attribute_value(attr)
# Get inputs
scales = self.constantMap[node.input[1]].reshape(-1)
biases = self.constantMap[node.input[2]].reshape(-1)
input_means = self.constantMap[node.input[3]].reshape(-1)
input_variances = self.constantMap[node.input[4]].reshape(-1)
if not makeEquations:
return
numChannels = len(scales)
# Get variables
inputVars = self.varMap[inputName].reshape(numChannels, -1)
outputVars = self.makeNewVariables(nodeName).reshape(numChannels, -1)
assert (inputVars.shape == outputVars.shape)
numInputs = inputVars.shape[1]
for i in range(numChannels):
for j in range(numInputs):
# Add equation
# To know this computation,
# refer to https://github.com/onnx/onnx/blob/master/docs/Operators.md#batchnormalization.
e = MarabouUtils.Equation()
e.addAddend(-1, outputVars[i][j])
e.addAddend(
1 / np.sqrt(input_variances[i] + epsilon) * scales[i],
inputVars[i][j])
e.setScalar(input_means[i] /
np.sqrt(input_variances[i] + epsilon) * scales[i] -
biases[i])
self.addEquation(e)
