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)
def testSimplePredicate(self): import tensorflow nr_samples=100 ltnw.constant("a",[2.,3.]) ltnw.variable("?data_A",numpy.random.uniform([0.,0.],[.1,1.],(nr_samples,2)).astype("float32")) mu=tensorflow.constant([2.,3.]) ltnw.predicate("A",2,pred_definition=lambda x: tensorflow.exp(-tensorflow.norm(tensorflow.subtract(x,mu),axis=1))); self.assertEqual(ltnw.ask("A(a)"),1.) self.assertGreater(ltnw.ask("forall ?data_A: A(?data_A)"),0.)
# 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, ltnw.SESSION.run(W) * train_X + ltnw.SESSION.run(b), label='Fitted line') plt.plot(train_X, prediction, 'bo', label='prediction', color="red") plt.legend() # generate test data and visualize regressor results test_X = np.random.uniform(start, end, (testing_size)).astype("float32") prediction = ltnw.ask("f(?x)", feed_dict={"?x": test_X.reshape(len(test_X), 1)}) test_Y = slope * test_X + np.random.normal(scale=var, size=len(train_X)) plt.subplot(1, 2, 2)
"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) ltnw.train(max_epochs=200) # retrieve the truth values for all samples and all clusters, i.e. check membership prC = [ltnw.ask("C_%s(?x)" % i) for i in range(nr_of_clusters)] n = 2 m = (nr_of_clusters + 1) // n + 1 fig = plt.figure(figsize=(3 * 3, m * 3)) fig.add_subplot(m, n, 1) plt.title("groundtruth") for c in clusters: plt.scatter(c[:, 0], c[:, 1]) data = np.concatenate(clusters) x0 = data[:, 0] x1 = data[:, 1] for i in range(nr_of_clusters): fig.add_subplot(m, n, i + 2) plt.title("C" + str(i) + "(?x)")
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()) plt.colorbar() plt.title("~A(x) - training data") data_test=np.random.uniform([0,0],[1.,1.],(500,2)).astype(np.float32) ltnw.variable("?data_test",data_test) result=ltnw.ask("A(?data_test)") plt.subplot(2,2,3)
"?z" : spatial_relations_data.generate_rectangles(nr_examples)} # 4) train the model ltnw.initialize_knowledgebase(feed_dict=feed_dict, optimizer=tf.train.AdamOptimizer(0.05), formula_aggregator=lambda *x: tf.reduce_min(tf.concat(x,axis=0))) ltnw.train(feed_dict=feed_dict,max_epochs=10000) # 5) evaluate the truth of formulas not given directly to the model for f in ["forall ?x,?y,?z: Contained_in(?x,?y) -> (Left(?y,?z)->Left(?x,?z))", "forall ?x,?y,?z: Contained_in(?x,?y) -> (Right(?y,?z)->Right(?x,?z))", "forall ?x,?y,?z: Contained_in(?x,?y) -> (Above(?y,?z)->Above(?x,?z))", "forall ?x,?y,?z: Contained_in(?x,?y) -> (Below(?y,?z)->Below(?x,?z))", "forall ?x,?y,?z: Contained_in(?x,?y) -> (Contains(?y,?z)->Contains(?x,?z))", "forall ?x,?y,?z: Contained_in(?x,?y) -> (Contained_in(?y,?z)->Contained_in(?x,?z))"]: print("%s: %s" % (f,ltnw.ask(f,feed_dict=feed_dict))) # 6) plot some examples truth values of P(ct,t) where ct is a central rectangle, and # t is a set of randomly generated rectangles ltnw.constant("ct",[.5,.5,.3,.3]) test_data=spatial_relations_data.generate_rectangles(nr_test_examples) ltnw.variable("?t",test_data) fig = plt.figure(figsize=(12,8)) jet = cm = plt.get_cmap('jet') cbbst = test_data[:,:2] + 0.5*test_data[:,2:] for j,p in enumerate(["Left","Right","Above","Below","Contains","Contained_in"]): plt.subplot(2, 3, j + 1) formula="%s(ct,?t)" % p plt.title(formula) results=ltnw.ask(formula,feed_dict=feed_dict)
) # initialize knowledge base ltnw.initialize_knowledgebase( optimizer=tf.train.RMSPropOptimizer(learning_rate=0.01, decay=.9), formula_aggregator=lambda *x: 1. / tf.reduce_mean(1. / tf.concat(x, axis=0) )) # Train the KB ltnw.train(max_epochs=10000) # query the KB and display the results df_smokes_cancer = pd.DataFrame(np.concatenate( [ltnw.ask("Smokes(p)"), ltnw.ask("Cancer(p)")], axis=1), columns=["Smokes", "Cancer"], index=list('abcdefghijklmn')) df_friends_ah = pd.DataFrame(np.squeeze(ltnw.ask("Friends(p1,q1)")), index=list('abcdefgh'), columns=list('abcdefgh')) df_friends_in = pd.DataFrame(np.squeeze(ltnw.ask("Friends(p2,q2)")), index=list('ijklmn'), columns=list('ijklmn')) print(df_smokes_cancer) print(df_friends_ah) print(df_friends_in) plt.figure(figsize=(15, 4)) plt.subplot(131) plt_heatmap(df_smokes_cancer)
ltnw.axiom("forall ?data, ?data_2: (A(?data) & B(?data_2)) -> R_A_B(?data,?data_2)") ltnw.axiom("forall ?data, ?data_2: R_A_B(?data,?data_2) -> (A(?data) & B(?data_2))") ltnw.initialize_knowledgebase(initial_sat_level_threshold=.99) sat_level=ltnw.train(track_sat_levels=1000,sat_level_epsilon=.01,max_epochs=epochs) plt.figure(figsize=(12,8)) plt.subplot(2,2,1) plt.title("data A/B") plt.scatter(data_A[:,0],data_A[:,1],c="red",alpha=1.,label="A") plt.scatter(data_B[:,0],data_B[:,1],c="blue",alpha=1.,label="B") plt.legend() idx=2 for pred in ["R_A_A","R_A_B","R_B_B"]: result_A_A=ltnw.ask("%s(?data_A,?data_A_2)" % pred) result_A_B=ltnw.ask("%s(?data_A,?data_B)" % pred) result_B_B=ltnw.ask("%s(?data_B,?data_B_2)" % pred) plt.subplot(2,2,idx) idx+=1 plt.title(pred) for i1,d1 in enumerate(data_A): for i2,d2 in enumerate(data_A): plt.plot([d1[0],d2[0]],[d1[1],d2[1]],alpha=result_A_A[i1,i2,0],c="black") for i1,d1 in enumerate(data_A): for i2,d2 in enumerate(data_B): plt.plot([d1[0],d2[0]],[d1[1],d2[1]],alpha=result_A_B[i1,i2,0],c="black") for i1,d1 in enumerate(data_B): for i2,d2 in enumerate(data_B): plt.plot([d1[0],d2[0]],[d1[1],d2[1]],alpha=result_B_B[i1,i2,0],c="black")
torch.stack([ torch.cat([full_obj_set[p[0]], full_obj_set[p[1]]]) for p in front_pairs ]).to(device), verbose=False) ltnw.variable('?behind_pair', torch.stack([ torch.cat([full_obj_set[p[0]], full_obj_set[p[1]]]) for p in behind_pairs ]).to(device), verbose=False) ## Test the axioms on the freshly declared variables with torch.no_grad(): for a in axioms.keys(): axioms[a].append(ltnw.ask(a)) axioms_mean = {k: sum(axioms[k]) / len(axioms[k]) for k in axioms.keys()} all_axioms_mean = np.array([axioms_mean[k] for k in axioms_mean.keys() ]).sum() / len(axioms_mean) pbar.set_description("Current Mean : %f" % (all_axioms_mean)) pbar.update(1) axioms_mean = {k: sum(axioms[k]) / len(axioms[k]) for k in axioms.keys()} axioms_min = {k: min(axioms[k]) for k in axioms.keys()} axioms_max = {k: max(axioms[k]) for k in axioms.keys()} all_axioms_mean = np.array([axioms_mean[k] for k in axioms_mean.keys() ]).sum() / len(axioms_mean) for k in axioms_mean: