def testOneHotDiffEquivalence():
inputs = [3, 5, 7]
weights = [[0, 1, 0], [0, 0, 1], [1, 0, 0], [0, 0, 0]]
layers = [('relu', 3, weights)]
return encode_equivalence(layers[:], layers[:], inputs, inputs,
'one_hot_diff', 'one_hot_diff')
def testOneHotPartialEquivalence():
inputs = [3, 5, 7]
weights = [[0, 1, 0], [0, 0, 1], [1, 0, 0], [0, 0, 0]]
layers = [('relu', 3, weights)]
return encode_equivalence(layers[:], layers[:], inputs, inputs,
'one_hot_partial_top_2', 'one_hot_partial_top_2')
def testRankingTopK():
inputs = [3, 5, 7]
weights = [[0, 1, 0], [0, 0, 1], [1, 0, 0], [0, 0, 0]]
layers = [('relu', 3, weights)]
# passing layers[:] (copy of layers) is important, because ranking layer is appended to layers
return encode_equivalence(layers[:], layers[:], inputs, inputs,
'ranking_top_2', 'ranking_top_2')
def testEpsilonEquivalence(desired='equivalent'):
if desired == 'equivalent':
weights1 = [[0, 1, 0], [0, 0, 1], [1, 0, 0], [0, 0, 0]]
weights2 = [[0, 1, 0], [0, 0, 1], [1, 0, 0], [-0.4, 0.2, -0.1]]
elif desired == 'different':
weights1 = [[0, 1, 0], [0, 0, 1], [1, 0, 0], [0, 0, 0]]
weights2 = [[0, 1, 0], [0, 0, 1], [1, 0, 0], [-0.6, 0.6, -0.1]]
inputs = [3, 5, 7]
layers1 = [('relu', 3, weights1)]
layers2 = [('relu', 3, weights2)]
return encode_equivalence(layers1[:], layers2[:], inputs, inputs,
'outputs', 'epsilon_0.5')
def encodeEquivalenceExample():
inputs = [-3 / 2, 0]
weights1 = [[1, 4], [2, 5], [3, 6]]
weights2 = [[1, 5], [2, 5], [3, 6]]
layers1 = [('relu', 2, weights1)]
layers2 = [('relu', 2, weights2)]
vars, constraints = encode_equivalence(layers1, layers2, inputs, inputs)
pretty_print(vars, constraints)
print('\n### now smtlib ###\n')
print(print_to_smtlib(vars, constraints))
def testOneMatrixRanking(desired='equivalent'):
ins = [3, 5, 7]
# identity matrix, no biases
weights1 = [[1, 0, 0], [0, 1, 0], [0, 0, 1], [0, 0, 0]]
layers1 = [('linear', 3, weights1)]
if desired == 'equivalent':
# output for ins: [9,8,17]
weights2 = [[1, 0, 0], [0, 1, 0], [0, 0, 1], [6, 3, 10]]
layers2 = [('linear', 3, weights2)]
else:
# output for ins: [17,9,8]
weights2 = [[1, 0, 0], [0, 1, 0], [0, 0, 1], [14, 4, 1]]
layers2 = [('linear', 3, weights2)]
return encode_equivalence(layers1[:],
layers2[:],
ins,
ins,
compared='one_ranking_top_2',
comparator='one_ranking_top_2')
def encodeEquivalenceWithModes(desired='equivalent',
compared='ranking_one_hot',
comparator='diff_one_hot'):
'''
:param desired: Desired result of the equivalence check for ranking_one_hot and diff_one_hot
the NNs are equivalent under these settings for
i_0, i_1 in [-1/4, 1/4] and i_3 in (-9/4, -6/4)
Keywords:
equivalent - yields input bounds s.t. NNs are equivalent
critical - yields input bounds s.t. NNs might be equivalent depending on treatment of interval bounds
different - yields input bounds s.t. NNs are different
if no keyword is entered, the NNs are compared on the fixed input [2,3,5]
:param compared:
:param comparator:
:return: an encoding of the NNs as vars and constraints, s.t. the outcome is as desired
'''
if desired == 'equivalent':
input_los = [-9.5002, 4.75002, -1]
input_his = [-7.5002, 6.75002, 1]
elif desired == 'critical':
input_los = [-1 / 4, -1 / 4, -9 / 4]
input_his = [1 / 4, 1 / 4, -6 / 4]
elif desired == 'different':
input_los = [-1 / 4, -1 / 4, -10 / 4]
input_his = [1 / 4, 1 / 4, -5 / 4]
else:
input_los = [2, 3, 5]
input_his = input_los
weights1 = [[1, 5], [2, 6], [3, 7], [4, 8]]
weights2 = [[1, 5], [2, 6], [3, 7], [4, 15]]
layers1 = [('relu', 2, weights1)]
layers2 = [('relu', 2, weights2)]
vars, constraints = encode_equivalence(layers1, layers2, input_los,
input_his, compared, comparator)
return vars, constraints