def forward_symbolic(self, var, inputs): x = inputs var_coef = var y = var_coef[-1] for i in range(len(inputs)): y += x[i] * var_coef[i] sigmoid = 1 / (1 + dreal.exp(-y)) return [1 - sigmoid, sigmoid]
def forward_symbolic(self, var, inputs): x = inputs layer1_weights, layer2_weights = var layer1 = [] for i in range(self.linear1.weight.size(0)): #in the case where wer have bias. Currently disabled #ex = self.linear1.bias.data[i].item() ex = 0 for j in range(self.linear1.weight.size(1)): ex += inputs[j] * layer1_weights[i][j] layer1.append(dreal.tanh(ex)) layer2 = [] for i in range(self.linear2.weight.size(0)): #ex = self.linear2.bias.data[i].item() ex = 0 for j in range(self.linear2.weight.size(1)): ex += layer1[j] * layer2_weights[i][j] layer2.append(ex) softmax = [ dreal.exp(layer2[0]) / (dreal.exp(layer2[0]) + dreal.exp(layer2[1])), dreal.exp(layer2[1]) / (dreal.exp(layer2[0]) + dreal.exp(layer2[1])) ] return softmax
def forward_symbolic(self, var, inputs): x = inputs layer1_weights, layer2_weights, layer3_weights = var layer1 = [] for i in range(self.linear1.weight.size(0)): ex = 0 for j in range(self.linear1.weight.size(1)): ex += inputs[j] * layer1_weights[i][j] layer1.append(dreal.tanh(ex)) layer2 = [] for i in range(self.linear2.weight.size(0)): ex = 0 for j in range(self.linear2.weight.size(1)): ex += layer1[j] * layer2_weights[i][j] layer2.append(dreal.tanh(ex)) layer3 = [] for i in range(self.linear3.weight.size(0)): ex = 0 for j in range(self.linear3.weight.size(1)): ex += layer2[j] * layer3_weights[i][j] layer3.append(ex) softmax = [ dreal.exp(layer3[0]) / (dreal.exp(layer3[0]) + dreal.exp(layer3[1])), dreal.exp(layer3[1]) / (dreal.exp(layer3[0]) + dreal.exp(layer3[1])) ] return softmax
def test_functions_with_expression(self): self.assertEqual(str(abs(e_x)), "abs(x)") self.assertEqual(str(exp(e_x)), "exp(x)") self.assertEqual(str(sqrt(e_x)), "sqrt(x)") self.assertEqual(str(pow(e_x, e_y)), "pow(x, y)") self.assertEqual(str(sin(e_x)), "sin(x)") self.assertEqual(str(cos(e_x)), "cos(x)") self.assertEqual(str(tan(e_x)), "tan(x)") self.assertEqual(str(asin(e_x)), "asin(x)") self.assertEqual(str(acos(e_x)), "acos(x)") self.assertEqual(str(atan(e_x)), "atan(x)") self.assertEqual(str(atan2(e_x, e_y)), "atan2(x, y)") self.assertEqual(str(sinh(e_x)), "sinh(x)") self.assertEqual(str(cosh(e_x)), "cosh(x)") self.assertEqual(str(tanh(e_x)), "tanh(x)") self.assertEqual(str(min(e_x, e_y)), "min(x, y)") self.assertEqual(str(max(e_x, e_y)), "max(x, y)") self.assertEqual(str(if_then_else(e_x > e_y, e_x, e_y)), "(if (x > y) then x else y)")
def test_functions_with_variable(self): self.assertEqual(str(abs(x)), "abs(x)") self.assertEqual(str(exp(x)), "exp(x)") self.assertEqual(str(sqrt(x)), "sqrt(x)") self.assertEqual(str(pow(x, y)), "pow(x, y)") self.assertEqual(str(sin(x)), "sin(x)") self.assertEqual(str(cos(x)), "cos(x)") self.assertEqual(str(tan(x)), "tan(x)") self.assertEqual(str(asin(x)), "asin(x)") self.assertEqual(str(acos(x)), "acos(x)") self.assertEqual(str(atan(x)), "atan(x)") self.assertEqual(str(atan2(x, y)), "atan2(x, y)") self.assertEqual(str(sinh(x)), "sinh(x)") self.assertEqual(str(cosh(x)), "cosh(x)") self.assertEqual(str(tanh(x)), "tanh(x)") self.assertEqual(str(min(x, y)), "min(x, y)") self.assertEqual(str(max(x, y)), "max(x, y)") self.assertEqual(str(if_then_else(x > y, x, y)), "(if (x > y) then x else y)")
def test_functions_with_float(self): v_x = 1.0 v_y = 1.0 self.assertEqual(abs(v_x), math.fabs(v_x)) self.assertEqual(exp(v_x), math.exp(v_x)) self.assertEqual(sqrt(v_x), math.sqrt(v_x)) self.assertEqual(pow(v_x, v_y), v_x**v_y) self.assertEqual(sin(v_x), math.sin(v_x)) self.assertEqual(cos(v_x), math.cos(v_x)) self.assertEqual(tan(v_x), math.tan(v_x)) self.assertEqual(asin(v_x), math.asin(v_x)) self.assertEqual(acos(v_x), math.acos(v_x)) self.assertEqual(atan(v_x), math.atan(v_x)) self.assertEqual(atan2(v_x, v_y), math.atan2(v_x, v_y)) self.assertEqual(sinh(v_x), math.sinh(v_x)) self.assertEqual(cosh(v_x), math.cosh(v_x)) self.assertEqual(tanh(v_x), math.tanh(v_x)) self.assertEqual(min(v_x, v_y), min(v_x, v_y)) self.assertEqual(max(v_x, v_y), max(v_x, v_y)) self.assertEqual( if_then_else(Expression(v_x) > Expression(v_y), v_x, v_y), v_x if v_x > v_y else v_y)
def sigm_dr(x): # sigmoid is f(x) = 1/(1+e^-x) y = x.copy() for idx in range(len(y)): y[idx, 0] = 1 / (1 + dr.exp(-y[idx, 0])) return y
def _sympy_converter(var_map, exp, target, expand_pow=False): rv = None assert isinstance(exp, sp.Expr) and target is not None if isinstance(exp, sp.Symbol): rv = var_map.get(exp.name, None) elif isinstance(exp, sp.Number): try: rv = RealVal(exp) if isinstance(target, Z3Verifier) else sp.RealNumber(exp) except: # Z3 parser error rep = sp.Float(exp, len(str(exp))) rv = RealVal(rep) elif isinstance(exp, sp.Add): # Add(exp_0, ...) rv = _sympy_converter(var_map, exp.args[0], target, expand_pow=expand_pow) # eval this expression for e in exp.args[1:]: # add it to all other remaining expressions rv += _sympy_converter(var_map, e, target, expand_pow=expand_pow) elif isinstance(exp, sp.Mul): rv = _sympy_converter(var_map, exp.args[0], target, expand_pow=expand_pow) for e in exp.args[1:]: rv *= _sympy_converter(var_map, e, target, expand_pow=expand_pow) elif isinstance(exp, sp.Pow): x = _sympy_converter(var_map, exp.args[0], target, expand_pow=expand_pow) e = _sympy_converter(var_map, exp.args[1], target, expand_pow=expand_pow) if expand_pow: try: i = float(e.sexpr()) assert i.is_integer() i = int(i) - 1 rv = x for _ in range(i): rv *= x except: # fallback rv = _sympy_converter(var_map, exp, target, expand_pow=False) else: rv = x ** e elif isinstance(exp, sp.Max): x = _sympy_converter(var_map, exp.args[1], target, expand_pow=expand_pow) zero = exp.args[0] if target == Z3Verifier: rv = z3.If(x >= 0.0, x, 0.0) else: rv = dr.max(x, 0.0) elif isinstance(exp, sp.Heaviside): x = _sympy_converter(var_map, exp.args[0], target, expand_pow=False) if target == Z3Verifier: rv = z3.If(x > 0.0, 1.0, 0.0) else: rv = dr.if_then_else(x>0.0, 1.0, 0.0) elif isinstance(exp, sp.Function): # check various activation types ONLY FOR DREAL if isinstance(exp, sp.tanh): rv = dr.tanh(_sympy_converter(var_map, exp.args[0], target, expand_pow=expand_pow)) elif isinstance(exp, sp.sin): rv = dr.sin(_sympy_converter(var_map, exp.args[0], target, expand_pow=expand_pow)) elif isinstance(exp, sp.cos): rv = dr.cos(_sympy_converter(var_map, exp.args[0], target, expand_pow=expand_pow)) elif isinstance(exp, sp.exp): rv = dr.exp(_sympy_converter(var_map, exp.args[0], target, expand_pow=expand_pow)) else: ValueError('Term ' + str(exp) + ' not recognised') assert rv is not None return rv