LSTM Initial state from Dense layer

Question

I am using a lstm on time series data. I have features about the time series that are not time dependent. Imagine company stocks for the series and stuff like company location in the non-time series features. This is not the usecase, but it is the same idea. For this example, let's just predict the next value in the time series.

So a simple example would be:

feature_input = Input(shape=(None, data.training_features.shape[1]))
dense_1 = Dense(4, activation='relu')(feature_input)
dense_2 = Dense(8, activation='relu')(dense_1)

series_input = Input(shape=(None, data.training_series.shape[1]))
lstm = LSTM(8)(series_input, initial_state=dense_2)
out = Dense(1, activation="sigmoid")(lstm)

model = Model(inputs=[feature_input,series_input], outputs=out)
model.compile(loss='mean_squared_error', optimizer='adam', metrics=["mape"])

however, I am just not sure on how to specify the initial state on the list correctly. I get

ValueError: An initial_state was passed that is not compatible with `cell.state_size`. Received `state_spec`=[<keras.engine.topology.InputSpec object at 0x11691d518>]; However `cell.state_size` is (8, 8)

which I can see is caused by the 3d batch dimension. I tried using Flatten, Permutation, and Resize layers but I don't believe that is correct. What am I missing and how can I connect these layers?

Answer 1

The first problem is that an LSTM(8) layer expects two initial states h_0 and c_0, each of dimension (None, 8). That's what it means by "cell.state_size is (8, 8)" in the error message.

If you only have one initial state dense_2, maybe you can switch to GRU (which requires only h_0). Or, you can transform your feature_input into two initial states.

The second problem is that h_0 and c_0 are of shape (batch_size, 8), but your dense_2 is of shape (batch_size, timesteps, 8). You need to deal with the time dimension before using dense_2 as initial states.

So maybe you can change your input shape into (data.training_features.shape[1],) or take average over timesteps with GlobalAveragePooling1D.

A working example would be:

feature_input = Input(shape=(5,))
dense_1_h = Dense(4, activation='relu')(feature_input)
dense_2_h = Dense(8, activation='relu')(dense_1_h)
dense_1_c = Dense(4, activation='relu')(feature_input)
dense_2_c = Dense(8, activation='relu')(dense_1_c)

series_input = Input(shape=(None, 5))
lstm = LSTM(8)(series_input, initial_state=[dense_2_h, dense_2_c])
out = Dense(1, activation="sigmoid")(lstm)
model = Model(inputs=[feature_input,series_input], outputs=out)
model.compile(loss='mean_squared_error', optimizer='adam', metrics=["mape"])