Many to one and many to many LSTM examples in Keras

So:

1. One-to-one: you could use a Dense layer as you are not processing sequences:

   model.add(Dense(output_size, input_shape=input_shape))
   

2. One-to-many: this option is not supported well as chaining models is not very easy in Keras, so the following version is the easiest one:

   model.add(RepeatVector(number_of_times, input_shape=input_shape))
   model.add(LSTM(output_size, return_sequences=True))
   

3. Many-to-one: actually, your code snippet is (almost) an example of this approach:

   model = Sequential()
   model.add(LSTM(1, input_shape=(timesteps, data_dim)))
   

4. Many-to-many: This is the easiest snippet when the length of the input and output matches the number of recurrent steps:

   model = Sequential()
   model.add(LSTM(1, input_shape=(timesteps, data_dim), return_sequences=True))
   

5. Many-to-many when number of steps differ from input/output length: this is freaky hard in Keras. There are no easy code snippets to code that.

EDIT: Ad 5

In one of my recent applications, we implemented something which might be similar to many-to-many from the 4th image. In case you want to have a network with the following architecture (when an input is longer than the output):

                                        O O O
                                        | | |
                                  O O O O O O
                                  | | | | | | 
                                  O O O O O O

You could achieve this in the following manner:

model = Sequential()
model.add(LSTM(1, input_shape=(timesteps, data_dim), return_sequences=True))
model.add(Lambda(lambda x: x[:, -N:, :])) #Select last N from output

Where N is the number of last steps you want to cover (on image N = 3).

From this point getting to:

                                        O O O
                                        | | |
                                  O O O O O O
                                  | | | 
                                  O O O 

is as simple as artificial padding sequence of length N using e.g. with 0 vectors, in order to adjust it to an appropriate size.

Great Answer by @Marcin Możejko

I would add the following to NR.5 (many to many with different in/out length):

A) as Vanilla LSTM

model = Sequential()
model.add(LSTM(N_BLOCKS, input_shape=(N_INPUTS, N_FEATURES)))
model.add(Dense(N_OUTPUTS))

B) as Encoder-Decoder LSTM

model.add(LSTM(N_BLOCKS, input_shape=(N_INPUTS, N_FEATURES))  
model.add(RepeatVector(N_OUTPUTS))
model.add(LSTM(N_BLOCKS, return_sequences=True))  
model.add(TimeDistributed(Dense(1)))
model.add(Activation('linear'))