How to concatenate two layers in keras?

You’re getting the error because result defined as Sequential() is just a container for the model and you have not defined an input for it.

Given what you’re trying to build set result to take the third input x3.

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

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

third = Sequential()
# of course you must provide the input to result which will be your x3
third.add(Dense(1, input_shape=(1,), activation='sigmoid'))

# lets say you 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'])

However, my preferred way of building a model that has this type of input structure would be to use the functional api.

Here is an implementation of your requirements to get you started:

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'])

To answer the question in the comments:

1. How are result and merged connected? Assuming you mean how are they concatenated.

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. Now, x1 is input to first, x2 is input into second and x3 input into third.