Learning a simple sequence with RNN (Keras) I am trying to learn a very simple sequence using an RNN (implemented in Keras)

The input sequence is randomly generated integers between 0 to 100:

x=np.random.randint(0,100, size=2000)


while the expected output value for time t is the (t-2)th input term i.e:

yt=xt-2

such that an example dataset looks like this:


+------+------+
|  X   |  Y   |
+------+------+
|    0 |   NA |
|   24 |   NA |
|   33 |    0 |
|    6 |   24 |
|   78 |   33 |
|   11 |    6 |
|    . |    . |
|    . |    . |
+------+------+


Note: I drop the NA rows before training.

I am trying to train a simple RNN to learn this sequence as below:

xtrain=np.reshape(df['X'], (df.shape[0], 1, 1))
#to match dimension of input shape for SimpleRNN layer.  

model=Sequential()
model.SimpleRNN(2, input_shape=(None,1)))
model.add(Dense(1))
model.compile(optimizer='adam', loss='mse')
model.fit(x=xtrain, y=df['Y'], epochs=200, batch_size=5)


however, I find that this implementation results in a local minima which predicts constant value(~50) for all test observations.

Could anyone help me with the right way of implementing a basic RNN in Keras to learn this sequence?
Using the raw integers as inputs and targets will make this a very difficult task. A better approach would be to come up with a vector for each number. You can simply encode each number directly as a vector, use a "onehot" representation, or use an Embedding layer. You can see an example of embeddings in conx that is built on Keras here: 

http://conx.readthedocs.io/en/latest/Predicting%20and%20Generating%20Texts.html?highlight=embeddinglayer 

and and example without embeddings using onehot representations here:

http://conx.readthedocs.io/en/latest/AliceInWonderland.html