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whitebox.py
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whitebox.py
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"""
Collection of functions and parameters for analysing a Deep Neural Network
(DNN) as a white box.
"""
import numpy as np
from keras import Model
from .blackbox import getHiddenVector,getLocalMatrixAndBias
def getWeightsAndBiases(model, layers):
weights = []
biases = []
for l in layers:
w, b = model.get_layer(index=l).get_weights()
weights.append(np.copy(w))
biases.append(np.copy(b))
return weights, biases
def getRealSigns(model, layerID):
weights, biases = getWeightsAndBiases(model, range(1, layerID + 1))
signsLayer = np.sign(weights[-1][0])
return signsLayer
def getSignatures(model, layerID):
"""Simulates the signature recovery and returns the corresponding weights, biases."""
weights, biases = getWeightsAndBiases(model, range(1, layerID + 1))
signsLayer = np.sign(weights[-1][0])
weights[-1] = signsLayer[np.newaxis, :] * weights[-1]
biases[-1] = signsLayer * biases[-1]
return weights, biases
def signIsCorrect(neuronID, w, w0):
return (w[:,neuronID]==w0[:,neuronID]).all()
def getScrambledSigns(w, b):
w = w.copy()
b = b.copy()
nNeurons = w.shape[-1]
#------------------------------
# my sign guess and starting point
#------------------------------
# as a starting point, we assume that half of the signatures have wrong signs
for nID in range(nNeurons):
sign = np.random.choice([+1, -1])
w[:,nID] = sign * w[:,nID]
b[nID] = sign * b[nID]
return w, b
def toggleSign(neuronID, w, b):
w[:,neuronID] = (-1) * w[:,neuronID]
b[neuronID] = (-1) * b[neuronID]
return w, b
def getTogglingPoints(model, layerID, neuronID, funcEps):
"""Find at which `epsilon` values a function of epsilon `funcEps` leads to the toggling of a specific neuron
`neuronID` in layer `layerID` of a TensorFlow model `model`.
For example:
>>> funcEps = lambda x: deti.interpol.linearMorphEps(myfrog, mycar, x)
>>> getTogglingPoints(model, layerID, neuronID, funcEps)
"""
import scipy.optimize
weights, bias = getNeuronWeightBias(model, layerID, neuronID)
func = lambda x: getLiEquation(x, funcEps, weights, bias) # the neuron will be toggled when this equation is equal to zero.
epsilons = scipy.optimize.fsolve(func, 0)
return epsilons
def getLiEquation(epsilon, funcMorphEpsilon, weights, bias):
"""Given the neurons `weights` w1...wn and `bias` b, return the equation
w1 * p1 + ... + wn * pn + b,
where the values of `p` are given by a morph function dependent on `epsilon`
(p1, ..., pn) = funcMorphEpsilon(epsilon).
"""
pvec = funcMorphEpsilon(epsilon) # morphed image at position epsilon
pvec = pvec.flatten() # flattened morphed image
LiEquation = np.dot(weights, pvec.flatten()) + bias
return LiEquation
def getNeuronWeightBias(model, layerID, neuronID):
"""Get the neuron weights and bias of neuron `neuronID` in layer `layerID` of a TensorFlow model.
"""
weightsAndBiases = model.layers[layerID].weights
weights = weightsAndBiases[0]
weightsOfNeuron = weights.numpy()[:, neuronID]
bias = weightsAndBiases[1]
biasOfNeuron = bias.numpy()[neuronID]
return weightsOfNeuron, biasOfNeuron
def getNeuronSignature(model, layerID, neuronID):
"""
Get the neuron signature of neuron `neuronID` in layer `layerID` of a TensorFlow model.
The neuron signature is obtained by dividing the weight of each incoming connection `w1...wn` by the weight of the
first connection `w1`, i.e.
(w1/w1, w2/w1, ..., wn/w1).
To obtain the weights and biases themselves, please use getNeuronWeightBias.
"""
weightsOfNeuron, _ = getNeuronWeightBias(model, layerID, neuronID)
w1 = weightsOfNeuron[0]
return [w/w1 for w in weightsOfNeuron]
def getLayerOutputs(model, testInput, onlyLayerID=None):
"""
For a neural network model, collect the intermediate outputs of all layers* for a test input.
*or only one particular layer identified by its `layerID` in model.layers via the `onlyLayerID` parameter
"""
outputOfAllLayers = []
for layerID, layer in enumerate(model.layers):
if onlyLayerID is not None and layerID != onlyLayerID:
continue
intermediateLayerModel = Model(inputs=model.input, outputs=model.get_layer(layer.name).output)
intermediateOutput = intermediateLayerModel.predict(testInput)
outputOfAllLayers.append(intermediateOutput)
if onlyLayerID is not None: outputOfAllLayers = outputOfAllLayers[0]
return outputOfAllLayers
def findToggledNeuronsInLayer(model, layerID, interpolatedImages, debug=False):
"""
For a given model find the toggled neurons in layer `layer_id` when moving from image x1 to x2
via the interpolatedImages.
Get the `interpolatedImages` by using (for example) the function `getInterpolatedImages`.
Returns:
An array that contains in which of the `n` steps which neuron was toggled.
For example, the following output means that first neuron 12 was toggled in step 3007:
array([[3007, 12],
[6103, 19],
[7742, 4],
[8067, 2],
[9543, 15],
[9556, 15],
[9557, 15]])
"""
#-----------------------------------------------
# Get layer outputs for interpolated images
#-----------------------------------------------
outputLayer = getLayerOutputs(model, interpolatedImages, onlyLayerID=layerID)
#-----------------------------------------------
# Analyze activity and toggling
#-----------------------------------------------
activeInLayer = (outputLayer > 0).astype(int) # find if the neuron was active or not
toggled = np.diff(activeInLayer, axis=0) # find toggling points for each neuron (axis=0)
if debug:
print(toggled)
#-----------------------------------------------
# Return which neuron was toggled in which step
#-----------------------------------------------
toggledStepNeuron = np.argwhere((toggled == 1) | (toggled == -1))
return toggledStepNeuron
"""
A simple linear interpolation between two input images x1 and x2
"""
linearMorph = lambda x1, x2, i, steps: x1 + (x2 - x1) / steps * i
def getInterpolatedImages(x1, x2, morph=linearMorph, n=10_000):
"""
Get the interpolated images between x1 and x2.
morph: morph function to move from x1 to x2. Required functional form is morph(x1, x2, i, n),
where `n` is the number of steps with which to move x1 into x2 and
`i=0...n-1` is the current step id.
"""
#-----------------------------------------------
# Interpolate between x1, x2
#-----------------------------------------------
morphX = np.zeros((n,) + x1.shape)
for i in range(n):
morphX[i] = morph(x1, x2, i, n)
return morphX
def collectWeightAndBiasLists(model, layerID):
"""Helper function: Collect lists of all previous layers weight and biases matrices up to (not including) layer `layerID`.
Returns: Ws, Bs (list of all numpy array weight matrices before layerID, list of all numpy array bias vectors before layerID)
"""
Ws = []
Bs = []
# for all previous layers, collect the weights and biases:
for pID in range(0, layerID):
weightsAndBiases = model.layers[pID].weights
if len(weightsAndBiases) == 0:
continue
w = weightsAndBiases[0]
w = w.numpy()
b = weightsAndBiases[1].numpy()
Ws += [w]
Bs += [b]
return Ws, Bs
def getOutputMatrixWhitebox(x, model, layerId, ReLUInOutFunc=False):
weights, biases = getWeightsAndBiases(model, range(1, layerId + 1))
# Output of layer layerId before ReLus
y = getHiddenVector(weights, biases, layerId, x, relu=False)
weights, biases = getWeightsAndBiases(model, range(layerId + 1, len(model.layers)))
if ReLUInOutFunc:
weights[0][y < 0] = 0
else:
y[y < 0] = 0
o, b = getLocalMatrixAndBias(weights, biases, y)