In short

Don’t use softmax.

Use sigmoid for activation of your output layer.

Use binary_crossentropy for loss function.

Use predict for evaluation.

Why

In softmax when increasing score for one label, all others are lowered (it’s a probability distribution). You don’t want that when you have multiple labels.

Complete Code

from tensorflow.keras.models import Sequential
from tensorflow.keras.layers import Dense, Dropout, Activation
from tensorflow.keras.optimizers import SGD

model = Sequential()
model.add(Dense(5000, activation='relu', input_dim=X_train.shape[1]))
model.add(Dropout(0.1))
model.add(Dense(600, activation='relu'))
model.add(Dropout(0.1))
model.add(Dense(y_train.shape[1], activation='sigmoid'))

sgd = SGD(lr=0.01, decay=1e-6, momentum=0.9, nesterov=True)
model.compile(loss="binary_crossentropy",
              optimizer=sgd)

model.fit(X_train, y_train, epochs=5, batch_size=2000)

preds = model.predict(X_test)
preds[preds>=0.5] = 1
preds[preds<0.5] = 0
# score = compare preds and y_test