def testSimplePredicateOptimization(self): nr_samples=100 ltnw.variable("?data_A",numpy.random.uniform([0.,0.],[.1,1.],(nr_samples,2)).astype("float32")) ltnw.variable("?data_not_A",numpy.random.uniform([2.,0],[3.,1.],(nr_samples,2)).astype("float32")) ltnw.predicate("A",2) ltnw.axiom("forall ?data_A: A(?data_A)") ltnw.axiom("forall ?data_not_A: ~A(?data_not_A)") ltnw.initialize_knowledgebase(initial_sat_level_threshold=.1) sat_level=ltnw.train(track_sat_levels=10000,sat_level_epsilon=.99) self.assertGreater(sat_level,.8) ltnw.constant("a",[0.5,0.5]) ltnw.constant("b",[2.5,0.5]) self.assertGreater(ltnw.ask("A(a)")[0],.8) self.assertGreater(ltnw.ask("~A(b)")[0],.8) result=ltnw.ask_m(["A(a)","~A(b)"]) for r in result: self.assertGreater(r[0],.8) self.assertGreater(r[0],.8)
# define the language, we translate every training example into constants [ltnw.constant("x_%s" % i, [x]) for i, x in enumerate(train_X)] [ltnw.constant("y_%s" % i, [y]) for i, y in enumerate(train_Y)] # define the function f as a linear regressor W = tf.Variable(np.random.randn(), name="weight") b = tf.Variable(np.random.randn(), name="bias") ltnw.function("f", 1, 1, fun_definition=lambda X: tf.add(tf.multiply(X, W), b)) # defining an equal predicate based on the euclidian distance of two vectors ltnw.predicate("eq", 2, ltnl.equal_euclidian) # defining the theory for f in ["eq(f(x_%s),y_%s)" % (i, i) for i in range(len(train_X))]: ltnw.axiom(f) print("\n".join(sorted(ltnw.AXIOMS.keys()))) # initializing knowledgebase and optimizing ltnw.initialize_knowledgebase(optimizer=tf.train.GradientDescentOptimizer( learning_rate=learning_rate)) ltnw.train(max_epochs=epochs) # visualize results on training data ltnw.variable("?x", 1) prediction = ltnw.ask("f(?x)", feed_dict={"?x": train_X.reshape(len(train_X), 1)}) plt.figure(figsize=(12, 5)) plt.subplot(1, 2, 1) plt.plot(train_X, train_Y, 'bo', label='Training data', color="black") plt.plot(train_X,
for j in range(len(data)) if np.sum(np.square(data[i] - data[j])) > np.square(1.) ]) # defining the language ltnw.variable("?x", data) ltnw.variable("?y", data) ltnw.variable("?close_x_y", close_data) ltnw.variable("?distant_x_y", distant_data) [ltnw.predicate("C_" + str(i), 2) for i in range(nr_of_clusters)] ltnw.function("first", 2, fun_definition=lambda d: d[:, :2]) ltnw.function("second", 2, fun_definition=lambda d: d[:, 2:]) print("defining the theory T") ltnw.axiom("forall ?x: %s" % "|".join(["C_%s(?x)" % i for i in range(nr_of_clusters)])) for i in range(nr_of_clusters): ltnw.axiom("exists ?x: C_%s(?x)" % i) ltnw.axiom( "forall ?close_x_y: C_%s(first(?close_x_y)) %% C_%s(second(?close_x_y))" % (i, i)) ltnw.axiom( "forall ?distant_x_y: C_%s(first(?distant_x_y)) %% C_%s(second(?distant_x_y))" % (i, i)) for j in range(i + 1, nr_of_clusters): ltnw.axiom("forall ?x: ~(C_%s(?x) & C_%s(?x))" % (i, j)) print("%s" % "\n".join(ltnw.AXIOMS.keys())) # initialize the knowledgebase and train ltnw.initialize_knowledgebase(optimizer=torch.optim.RMSprop, initial_sat_level_threshold=.5)
names_of_classes=cat_horizontal, device=device) cat_vertical = ['Front', 'Behind'] Category_Vertical = ltnw.class_category(class_label='Vertical', number_of_features=2 * num_of_features, names_of_classes=cat_vertical, device=device) # Object Variables Placeholders ltnw.variable('?obj', torch.zeros(1, num_of_features)) ltnw.variable('?obj_2', torch.zeros(1, num_of_features)) for i, feat in enumerate(obj_colors): ltnw.mlp_predicate(label=feat.capitalize(), class_category=Category_Color) ltnw.variable('?is_' + feat, torch.zeros(1, num_of_features, device=device)) ltnw.axiom('forall ?is_' + feat + ' : ' + feat.capitalize() + '(?is_' + feat + ')') ltnw.variable('?isnot_' + feat, torch.zeros(1, num_of_features, device=device)) ltnw.axiom('forall ?isnot_' + feat + ' : ~' + feat.capitalize() + '(?isnot_' + feat + ')') for i, feat in enumerate(obj_sizes): ltnw.mlp_predicate(label=feat.capitalize(), class_category=Category_Size) ltnw.variable('?is_' + feat, torch.zeros(1, num_of_features, device=device)) ltnw.axiom('forall ?is_' + feat + ' : ' + feat.capitalize() + '(?is_' + feat + ')') ltnw.variable('?isnot_' + feat, torch.zeros(1, num_of_features, device=device)) ltnw.axiom('forall ?isnot_' + feat + ' : ~' + feat.capitalize() + '(?isnot_' + feat + ')') for i, feat in enumerate(obj_shapes):
clusters.append( np.random.multivariate_normal(mean=mean, cov=cov, size=nr_of_points_x_cluster).astype( np.float32)) data = np.concatenate(clusters) # define the language ltnw.variable("?x", data) ltnw.variable("?y", data) ltnw.predicate("close", 2, ltnl.equal_euclidian) [ltnw.predicate("C_" + str(i), 2) for i in range(nr_of_clusters)] ## define the theory print("defining the theory T") ltnw.axiom("forall ?x: %s" % "|".join(["C_%s(?x)" % i for i in range(nr_of_clusters)])) for i in range(nr_of_clusters): ltnw.axiom("exists ?x: C_%s(?x)" % i) ltnw.axiom("forall ?x,?y: (C_%s(?x) & close(?x,?y)) -> C_%s(?y)" % (i, i)) ltnw.axiom( "forall ?x,?y: (C_%s(?x) & ~close(?x,?y)) -> (%s)" % (i, "|".join(["C_%s(?y)" % j for j in range(nr_of_clusters) if i != j]))) for j in range(i + 1, nr_of_clusters): ltnw.axiom("forall ?x: ~(C_%s(?x) & C_%s(?x))" % (i, j)) print("\n".join(sorted(ltnw.AXIOMS.keys()))) ## initialize and optimize ltnw.initialize_knowledgebase(optimizer=tf.train.RMSPropOptimizer( learning_rate=0.1, decay=.9),
import logictensornetworks_wrapper as ltnw nr_samples=500 data=np.random.uniform([0,0],[1.,1.],(nr_samples,2)).astype(np.float32) data_A=data[np.where(np.sum(np.square(data-[.5,.5]),axis=1)<.09)] data_not_A=data[np.where(np.sum(np.square(data-[.5,.5]),axis=1)>=.09)] ltnw.variable("?data_A",data_A) ltnw.variable("?data_not_A",data_not_A) ltnw.variable("?data",data) ltnw.predicate("A",2) ltnw.axiom("forall ?data_A: A(?data_A)") ltnw.axiom("forall ?data_not_A: ~A(?data_not_A)") ltnw.initialize_knowledgebase(initial_sat_level_threshold=.1) sat_level=ltnw.train(track_sat_levels=1000,sat_level_epsilon=.99) plt.figure(figsize=(12,8)) result=ltnw.ask("A(?data)") plt.subplot(2,2,1) plt.scatter(data[:,0],data[:,1],c=result.squeeze()) plt.colorbar() plt.title("A(x) - training data") result=ltnw.ask("~A(?data)") plt.subplot(2,2,2) plt.scatter(data[:,0],data[:,1],c=result.squeeze())
import matplotlib.pyplot as plt import numpy as np import logictensornetworks_wrapper as ltnw import spatial_relations_data # generate artificial data nr_examples = 50 # positive and negative examples for each predicate nr_test_examples=400 # 1) define the language and examples ltnw.predicate("Left",8) ltnw.variable("?left_xy",8) ltnw.variable("?not_left_xy", 8) ltnw.axiom("forall ?left_xy: Left(?left_xy)") ltnw.axiom("forall ?not_left_xy: ~Left(?not_left_xy)") ltnw.predicate("Right",8) ltnw.variable("?right_xy",8) ltnw.variable("?not_right_xy",8) ltnw.axiom("forall ?right_xy: Right(?right_xy)") ltnw.axiom("forall ?not_right_xy: ~Right(?not_right_xy)") ltnw.predicate("Below",8) ltnw.variable("?below_xy",8) ltnw.variable("?not_below_xy",8) ltnw.axiom("forall ?below_xy: Below(?below_xy)") ltnw.axiom("forall ?not_below_xy: ~Below(?not_below_xy)")
ltnw.variable('?behind_pair', [full_obj_set[p[0]] + full_obj_set[p[1]] for p in behind_pairs]) time_diff = time.time() - start_time print('Time to complete : ', time_diff) start_time = time.time() print('******* Predicate/Axioms for Object Features ******') # Object Features for feat in obj_feat: ltnw.predicate(label=feat.capitalize(), number_of_features_or_vars=num_of_features, layers=num_of_layers) for i, feat in enumerate(obj_feat): ltnw.axiom('forall ?is_' + feat + ' : ' + feat.capitalize() + '(?is_' + feat + ')') ltnw.axiom('forall ?isnot_' + feat + ' : ~' + feat.capitalize() + '(?isnot_' + feat + ')') # Implicit axioms about object features ## objects can only be one color for c in obj_colors: is_color = '' is_not_color = '' for not_c in obj_colors: if not_c == c: is_color = c.capitalize() + '(?obj)' if not_c != c: is_not_color += '~' + not_c.capitalize() + '(?obj) &' ltnw.axiom('forall ?obj: ' + is_color + ' -> ' + is_not_color[:-1]) ltnw.axiom('forall ?obj: ' + is_not_color[:-1] + ' -> ' + is_color) ## objects can only be one size for s in obj_sizes:
import logictensornetworks_wrapper as ltnw nr_samples=500 data=np.random.uniform([0,0],[1.,1.],(nr_samples,2)).astype(np.float32) data_A=data[np.where(np.sum(np.square(data-[.5,.5]),axis=1)<.09)] data_B=data[np.where(np.sum(np.square(data-[.5,.5]),axis=1)>=.09)] ltnw.variable("?data",data) ltnw.variable("?data_A",data_A) ltnw.variable("?data_B",data_B) ltnw.predicate("A",2) ltnw.predicate("B",2) ltnw.axiom("forall ?data_A: A(?data_A)") ltnw.axiom("forall ?data_B: ~A(?data_B)") ltnw.axiom("forall ?data_B: B(?data_B)") ltnw.axiom("forall ?data_A: ~B(?data_A)") ltnw.axiom("forall ?data: A(?data) -> ~B(?data)") ltnw.axiom("forall ?data: B(?data) -> ~A(?data)") ltnw.initialize_knowledgebase(optimizer=torch.optim.RMSprop, initial_sat_level_threshold=.99) # The number of iterations were dramatically reduced. sat_level=ltnw.train(track_sat_levels=1000,sat_level_epsilon=.01,max_epochs=2000) result=ltnw.ask("A(?data)") plt.figure(figsize=(10,8)) plt.subplot(2,2,1)
ltnw.variable("p", tf.concat(list(ltnw.CONSTANTS.values()), axis=0)) ltnw.variable("q", ltnw.VARIABLES["p"]) ltnw.variable("p1", tf.concat([ltnw.CONSTANTS[l] for l in "abcdefgh"], axis=0)) ltnw.variable("q1", ltnw.VARIABLES["p1"]) ltnw.variable("p2", tf.concat([ltnw.CONSTANTS[l] for l in "ijklmn"], axis=0)) ltnw.variable("q2", ltnw.VARIABLES["p2"]) # declare the predicates ltnw.predicate('Friends', embedding_size * 2) ltnw.predicate('Smokes', embedding_size) ltnw.predicate('Cancer', embedding_size) # add the assertional knowledge in our posses ltnw.axiom("Friends(a,b)") ltnw.axiom("~Friends(a,c)") ltnw.axiom("~Friends(a,d)") ltnw.axiom("Friends(a,e)") ltnw.axiom("Friends(a,f)") ltnw.axiom("Friends(a,g)") ltnw.axiom("~Friends(a,h)") ltnw.axiom("Friends(b,c)") ltnw.axiom("~Friends(b,d)") ltnw.axiom("~Friends(b,e)") ltnw.axiom("~Friends(b,f)") ltnw.axiom("~Friends(b,g)") ltnw.axiom("~Friends(b,h)") ltnw.axiom("Friends(c,d)") ltnw.axiom("~Friends(c,e)") ltnw.axiom("~Friends(c,f)")
data_A=np.random.uniform([0,0],[.25,1.],(nr_samples,2)).astype(np.float32) data_B=np.random.uniform([.75,0],[1.,1.],(nr_samples,2)).astype(np.float32) data=np.concatenate([data_A,data_B]) ltnw.variable("?data_A",data_A) ltnw.variable("?data_A_2",data_A) ltnw.variable("?data_B",data_B) ltnw.variable("?data_B_2",data_B) ltnw.variable("?data",data) ltnw.variable("?data_1",data) ltnw.variable("?data_2",data) ltnw.predicate("A",2) ltnw.predicate("B",2) ltnw.axiom("forall ?data_A: A(?data_A)") ltnw.axiom("forall ?data_B: ~A(?data_B)") ltnw.axiom("forall ?data_B: B(?data_B)") ltnw.axiom("forall ?data_A: ~B(?data_A)") ltnw.predicate("R_A_A",4) ltnw.predicate("R_B_B",4) ltnw.predicate("R_A_B",4) ltnw.axiom("forall ?data, ?data_2: (A(?data) & A(?data_2)) -> R_A_A(?data,?data_2)") ltnw.axiom("forall ?data, ?data_2: R_A_A(?data,?data_2) -> (A(?data) & A(?data_2))") ltnw.axiom("forall ?data, ?data_2: (B(?data) & B(?data_2)) -> R_B_B(?data,?data_2)") ltnw.axiom("forall ?data, ?data_2: R_B_B(?data,?data_2) -> (B(?data) & B(?data_2))")