relu_to_optimization replaces some linear constraints on variable with variable bounds.

Author: hongkai-dai

neural_network_lyapunov/relu_to_optimization.py

@@ -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[
@@ -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]
@@ -597,6 +604,10 @@ 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.input_lo = x_lo
+        mip_constr_return.input_up = x_up
+        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)
 
@@ -994,6 +1005,8 @@ 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,
@@ -1004,18 +1017,17 @@ 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 = 1
+        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)
@@ -1024,7 +1036,7 @@ 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,
@@ -1057,10 +1069,13 @@ 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)
@@ -1089,4 +1104,4 @@ 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

neural_network_lyapunov/test/test_relu_to_optimization.py

@@ -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))
@@ -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_up)
+                if mip_constr_return.binary_up is not None:
+                    con.append(beta_var >= mip_constr_return.binary_lo)
                 objective = cp.Minimize(0.)
                 prob = cp.Problem(objective, con)
                 prob.solve(solver=cp.GUROBI)

neural_network_lyapunov/test/test_relu_to_optimization_utils.py

@@ -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)
 
@@ -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],
@@ -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(
@@ -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)],
@@ -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)
 
@@ -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)