As I can understand your problem, the main reason for this error is the result defined as Sequential() is just a container for the model and you have not defined input for it.

It looks like you’re trying to build a set result to take the third input x3.

**Improvised code for your problem:**

first = Sequential()

first.add(Dense(1, input_shape=(2,), activation='sigmoid'))

second = Sequential()

second.add(Dense(1, input_shape=(1,), activation='sigmoid'))

third = Sequential()

# provide the input to result with will be your x3

third.add(Dense(1, input_shape=(1,), activation='sigmoid'))

#then add a few more layers to first and second.

# concatenate them

merged = Concatenate([first, second])

# then concatenate the two outputs

result = Concatenate([merged, third])

ada_grad = Adagrad(lr=0.1, epsilon=1e-08, decay=0.0)

result.compile(optimizer=ada_grad, loss='binary_crossentropy',

metrics=['accuracy'])

You can try another way of building a model that this type of input structure would be to use the functional API.

**For example:**

from keras.models import Model

from keras.layers import Concatenate, Dense, LSTM, Input, concatenate

from keras.optimizers import Adagrad

first_input = Input(shape=(2, ))

first_dense = Dense(1, )(first_input)

second_input = Input(shape=(2, ))

second_dense = Dense(1, )(second_input)

merge_one = concatenate([first_dense, second_dense])

third_input = Input(shape=(1, ))

merge_two = concatenate([merge_one, third_input])

model = Model(inputs=[first_input, second_input, third_input], outputs=merge_two)

ada_grad = Adagrad(lr=0.1, epsilon=1e-08, decay=0.0)

model.compile(optimizer=ada_grad, loss='binary_crossentropy',

metrics=['accuracy'])

**Concatenation works like this:**

a b c

a b c g h i a b c g h i

d e f j k l d e f j k l

i.e rows are just joined.

2) You can say that x1 is input to first, x2 is input into second and x3 input into third.

I hope this solution solved your problem.

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