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relu_to_optimization replaces some linear constraints on variable with variable bounds #278

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relu_to_optimization replaces some linear constraints on variable with variable bounds #278

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45 changes: 29 additions & 16 deletions neural_network_lyapunov/relu_to_optimization.py
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Original file line number Diff line number Diff line change
Expand Up @@ -298,7 +298,7 @@ def _compute_linear_output_bound_by_lp(
) if linear_layer.bias is None else linear_layer.bias[j]
Ain_linear_input, Ain_neuron_output, Ain_neuron_binary,\
rhs_in, Aeq_linear_input, Aeq_neuron_output,\
Aeq_neuron_binary, rhs_eq, _, _ =\
Aeq_neuron_binary, rhs_eq, _, _, _, _ =\
_add_constraint_by_neuron(
linear_layer.weight[j], bij, relu_layer,
torch.tensor(previous_neuron_input_lo[
Expand Down Expand Up @@ -519,8 +519,8 @@ def output_constraint(self, x_lo, x_up,
z_pre_relu_lo, z_pre_relu_up, x_lo, x_up, method)
for layer_count in range(len(self.relu_unit_index)):
Ain_z_curr, Ain_z_next, Ain_binary_layer, rhs_in_layer,\
Aeq_z_curr, Aeq_z_next, Aeq_binary_layer, rhs_eq_layer, _, _ =\
_add_constraint_by_layer(
Aeq_z_curr, Aeq_z_next, Aeq_binary_layer, rhs_eq_layer, _, _,\
_, _ = _add_constraint_by_layer(
self.model[2*layer_count], self.model[2*layer_count+1],
z_pre_relu_lo[self.relu_unit_index[layer_count]],
z_pre_relu_up[self.relu_unit_index[layer_count]])
Expand Down Expand Up @@ -588,7 +588,14 @@ def output_constraint(self, x_lo, x_up,
(self.model[-1].out_features, ), dtype=self.dtype)
else:
mip_constr_return.Cout = self.model[-1].bias.clone()

binary_lo = torch.zeros((self.num_relu_units,), dtype=self.dtype)
binary_up = torch.ones((self.num_relu_units,), dtype=self.dtype)
# If the input to the relu is always >= 0, then the relu will always
# be active.
binary_lo[z_pre_relu_lo >= 0] = 1.
# If the input to the relu is always <= 0, then the relu will always
# be inactive.
binary_up[z_pre_relu_up <= 0] = 0.
mip_constr_return.Ain_input = Ain_input[:ineq_constr_count]
mip_constr_return.Ain_slack = Ain_slack[:ineq_constr_count]
mip_constr_return.Ain_binary = Ain_binary[:ineq_constr_count]
Expand All @@ -597,6 +604,8 @@ def output_constraint(self, x_lo, x_up,
mip_constr_return.Aeq_slack = Aeq_slack[:eq_constr_count]
mip_constr_return.Aeq_binary = Aeq_binary[:eq_constr_count]
mip_constr_return.rhs_eq = rhs_eq[:eq_constr_count]
mip_constr_return.binary_lo = binary_lo
mip_constr_return.binary_up = binary_up
return (mip_constr_return, z_pre_relu_lo, z_pre_relu_up,
z_post_relu_lo, z_post_relu_up, output_lo, output_up)

Expand Down Expand Up @@ -994,6 +1003,8 @@ def _add_constraint_by_neuron(
Aeq_neuron_output = torch.empty((0, 1), dtype=dtype)
Aeq_binary = torch.empty((0, 1), dtype=dtype)
rhs_eq = torch.empty((0, ), dtype=dtype)
binary_lo = 0
binary_up = 1
else:
# The (leaky) ReLU is always active, or always inactive. If
# the lower bound output_lo[j] >= 0, then it is always active,
Expand All @@ -1004,18 +1015,17 @@ def _add_constraint_by_neuron(
# zᵢ₊₁(j) = c*((Wᵢzᵢ)(j) + bᵢ(j)) and βᵢ(j) = 0
if neuron_input_lo >= 0:
slope = 1.
binary_value = 1
binary_lo = 1
binary_up = 1
elif neuron_input_up <= 0:
slope = relu_layer.negative_slope if isinstance(
relu_layer, nn.LeakyReLU) else 0.
binary_value = 0.
Aeq_linear_input = torch.cat((-slope * Wij.reshape(
(1, -1)), torch.zeros((1, Wij.numel()), dtype=dtype)),
dim=0)
Aeq_neuron_output = torch.tensor([[1.], [0]], dtype=dtype)
Aeq_binary = torch.tensor([[0.], [1.]], dtype=dtype)
rhs_eq = torch.stack(
(slope * bij, torch.tensor(binary_value, dtype=dtype)))
binary_lo = 0
binary_up = 0
Aeq_linear_input = -slope * Wij.reshape((1, -1))
Aeq_neuron_output = torch.tensor([[1.]], dtype=dtype)
Aeq_binary = torch.tensor([[0.]], dtype=dtype)
rhs_eq = slope * bij.reshape((1,))
Ain_linear_input = torch.empty((0, Wij.numel()), dtype=dtype)
Ain_neuron_output = torch.empty((0, 1), dtype=dtype)
Ain_binary = torch.empty((0, 1), dtype=dtype)
Expand All @@ -1024,7 +1034,7 @@ def _add_constraint_by_neuron(
relu_layer, neuron_input_lo, neuron_input_up)
return Ain_linear_input, Ain_neuron_output, Ain_binary, rhs_in,\
Aeq_linear_input, Aeq_neuron_output, Aeq_binary, rhs_eq,\
neuron_output_lo, neuron_output_up
neuron_output_lo, neuron_output_up, binary_lo, binary_up


def _add_constraint_by_layer(linear_layer, relu_layer,
Expand Down Expand Up @@ -1057,10 +1067,13 @@ def _add_constraint_by_layer(linear_layer, relu_layer,
z_next_up = []
bias = linear_layer.bias if linear_layer.bias is not None else \
torch.zeros((linear_layer.out_features,), dtype=dtype)
binary_lo = torch.zeros((linear_layer.out_features,), dtype=dtype)
binary_up = torch.ones((linear_layer.out_features,), dtype=dtype)
for j in range(linear_layer.out_features):
Ain_linear_input, Ain_neuron_output, Ain_binary_j, rhs_in_j,\
Aeq_linear_input, Aeq_neuron_output, Aeq_binary_j, rhs_eq_j,\
neuron_output_lo, neuron_output_up = _add_constraint_by_neuron(
neuron_output_lo, neuron_output_up, binary_lo[j], binary_up[j] =\
_add_constraint_by_neuron(
linear_layer.weight[j], bias[j], relu_layer,
linear_output_lo[j], linear_output_up[j])
Ain_z_curr.append(Ain_linear_input)
Expand Down Expand Up @@ -1089,4 +1102,4 @@ def _add_constraint_by_layer(linear_layer, relu_layer,
torch.cat(Ain_binary, dim=0), torch.cat(rhs_in, dim=0),\
torch.cat(Aeq_z_curr, dim=0), torch.cat(Aeq_z_next, dim=0),\
torch.cat(Aeq_binary, dim=0), torch.cat(rhs_eq, dim=0),\
torch.stack(z_next_lo), torch.stack(z_next_up)
torch.stack(z_next_lo), torch.stack(z_next_up), binary_lo, binary_up
7 changes: 5 additions & 2 deletions neural_network_lyapunov/test/test_relu_to_optimization.py
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Original file line number Diff line number Diff line change
Expand Up @@ -297,8 +297,7 @@ def test_model(model, method):
num_ineq = (relu_free_pattern.num_relu_units -
num_z_pre_relu_lo_positive -
num_z_pre_relu_up_negative) * 4 + 4
num_eq = (num_z_pre_relu_lo_positive + num_z_pre_relu_up_negative)\
* 2
num_eq = num_z_pre_relu_lo_positive + num_z_pre_relu_up_negative
self.assertEqual(mip_constr_return.Ain_input.shape, (num_ineq, 2))
self.assertEqual(mip_constr_return.Ain_slack.shape,
(num_ineq, relu_free_pattern.num_relu_units))
Expand Down Expand Up @@ -345,6 +344,10 @@ def test_input_output(x):
mip_constr_return.Aeq_binary.detach().numpy() @
beta_var
== mip_constr_return.rhs_eq.squeeze().detach().numpy())
if mip_constr_return.binary_lo is not None:
con.append(beta_var >= mip_constr_return.binary_lo)
if mip_constr_return.binary_up is not None:
con.append(beta_var <= mip_constr_return.binary_up)
objective = cp.Minimize(0.)
prob = cp.Problem(objective, con)
prob.solve(solver=cp.GUROBI)
Expand Down
16 changes: 11 additions & 5 deletions neural_network_lyapunov/test/test_relu_to_optimization_utils.py
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Original file line number Diff line number Diff line change
Expand Up @@ -15,7 +15,7 @@ def constraint_test(self, Wij, bij, relu_layer, neuron_input_lo,
neuron_input_up):
Ain_linear_input, Ain_neuron_output, Ain_binary, rhs_in,\
Aeq_linear_input, Aeq_neuron_output, Aeq_binary, rhs_eq,\
neuron_output_lo, neuron_output_up = \
neuron_output_lo, neuron_output_up, binary_lo, binary_up = \
relu_to_optimization._add_constraint_by_neuron(
Wij, bij, relu_layer, neuron_input_lo, neuron_input_up)

Expand All @@ -35,7 +35,10 @@ def constraint_test(self, Wij, bij, relu_layer, neuron_input_lo,
linear_input = model.addVars(Wij.numel(),
lb=-gurobipy.GRB.INFINITY)
neuron_output = model.addVars(1, lb=-gurobipy.GRB.INFINITY)
binary = model.addVars(1, vtype=gurobipy.GRB.BINARY)
binary = model.addVars(1,
lb=binary_lo,
ub=binary_up,
vtype=gurobipy.GRB.BINARY)
model.addMConstrs(
[Ain_linear_input, Ain_neuron_output, Ain_binary],
[linear_input, neuron_output, binary],
Expand Down Expand Up @@ -107,7 +110,7 @@ def constraint_test(self, linear_layer, relu_layer, z_curr_lo, z_curr_up):
linear_output_lo, linear_output_up = mip_utils.propagate_bounds(
linear_layer, z_curr_lo, z_curr_up)
Ain_z_curr, Ain_z_next, Ain_binary, rhs_in, Aeq_z_curr, Aeq_z_next,\
Aeq_binary, rhs_eq, z_next_lo, z_next_up = \
Aeq_binary, rhs_eq, z_next_lo, z_next_up, binary_lo, binary_up = \
relu_to_optimization._add_constraint_by_layer(
linear_layer, relu_layer, linear_output_lo, linear_output_up)
z_next_lo_expected, z_next_up_expected = mip_utils.propagate_bounds(
Expand All @@ -130,6 +133,8 @@ def constraint_test(self, linear_layer, relu_layer, z_curr_lo, z_curr_up):
z_next = model.addVars(linear_layer.out_features,
lb=-gurobipy.GRB.INFINITY)
beta = model.addVars(linear_layer.out_features,
lb=binary_lo,
ub=binary_up,
vtype=gurobipy.GRB.BINARY)
model.addMConstrs(
[torch.eye(linear_layer.in_features, dtype=self.dtype)],
Expand Down Expand Up @@ -185,7 +190,7 @@ def constraint_gradient_test(self, linear_layer, relu_layer, z_curr_lo,
linear_output_lo, linear_output_up = mip_utils.propagate_bounds(
linear_layer, z_curr_lo, z_curr_up)
Ain_z_curr, Ain_z_next, Ain_binary, rhs_in, Aeq_z_curr, Aeq_z_next,\
Aeq_binary, rhs_eq, z_next_lo, z_next_up =\
Aeq_binary, rhs_eq, z_next_lo, z_next_up, binary_lo, binary_up =\
relu_to_optimization._add_constraint_by_layer(
linear_layer, relu_layer, linear_output_lo, linear_output_up)

Expand Down Expand Up @@ -213,7 +218,8 @@ def eval_fun(linear_layer_weight, linear_layer_bias, input_lo_np,
linear_layer, torch.from_numpy(input_lo_np),
torch.from_numpy(input_up_np))
Ain_z_curr, Ain_z_next, Ain_binary, rhs_in, Aeq_z_curr,\
Aeq_z_next, Aeq_binary, rhs_eq, z_next_lo, z_next_up =\
Aeq_z_next, Aeq_binary, rhs_eq, z_next_lo, z_next_up,\
binary_lo, binary_up =\
relu_to_optimization._add_constraint_by_layer(
linear_layer, relu_layer, linear_output_lo,
linear_output_up)
Expand Down