I'm using tf.nn.bidirectional_rnn with the sequence_length parameter for variable input size, and I can't figure out how to get the final output for each sample in the minibatch:
output, _, _ = tf.nn.bidirectional_rnn(forward1,backward1,input,dtype=tf.float32,sequence_length=input_lengths)
Now, if I had constant sequence lengths, I would simply use output[-1] and get the final output. In my case I have variable sequences (their lengths are known).
Also, is this output the output of both forward and backward LSTMs?
Thanks.
This question can be answered by looking at the source code rnn.py.
For sequences with dynamic length, the source code says:
If the sequence_length vector is provided, dynamic calculation is
performed. This method of calculation does not compute the RNN steps
past the maximum sequence length of the minibatch (thus saving
computational time), and properly propagates the state at an
example's sequence length to the final state output.
Therefore, in order to get the actual last output, you should slice the resulting output.
For bidirectional_rnn, the source code says:
A tuple (outputs, output_state_fw, output_state_bw) where:
outputs is a length T list of outputs (one for each input), which
are depth-concatenated forward and backward outputs.
output_state_fw is the final state of the forward rnn.
output_state_bw is the final state of the backward rnn.
Therefore, the output is a tuple rather than a tensor.
You can concatenate this tuple into a vector if you wish.
Related
How about this thought experiment. You have an LSTM network to encode a sequence of integers (inputs are x_t). For each cell, the weights, biases and outputs of the gates, as well as the previous states (C_t-1, h_t-1) are calculated and stored for the forward pass. Each cell has, thus, a certain hard-coded pattern. We'll use this image for a visualization aid (from Wikipedia).
I now want to take a cell with all its calculated values, and switch the input with the output. The new input is a new value that gets entered into h_t, let's call it h'_t. The computation is inverted to arrive at a new value for x_t that we'll call x'_t. Does the cell keep its properties so that there is a (non-linear) relationship between the output of a cell and the input, regardless of what the output value I enter into it is? This calculation would then be performed for the whole sequence of LSTM cells, but each cell would get a different h'_t value as an input.
Furthermore, would it be enough to only calculate it backwards for the output gate, since one can arrive at x'_t either through the output gate, the input gate, or the forget gate?
In tf.contrib.seq2seq.BasicDecoder document, it says output_layer: (Optional) An instance of tf.layers.Layer, i.e., tf.layers.Dense. Optional layer to apply to the RNN output prior to storing the result or sampling.
In tf.contrib.rnn.OutputProjectionWrapper is Operator adding an output projection to the given cell
I assume these are same?
So I had a specific question with setting up the input in Keras.
I understand that the sequence length refers to the window length of the longest sequence that you are looking to model with the rest being padded by 0's.
However, how do I set up something that is already in a time series array?
For example, right now I have an array that is 550k x 28. So there are 550k rows each with 28 columns (27 features and 1 target). Do I have to manually split the array into (550k- sequence length) different arrays and feed all of those to the network?
Assuming that I want to the first layer to be equivalent to the number of features per row, and looking at the past 50 rows, how do I size the input layer?
Is that simply input_size = (50,27), and again do I have to manually split the dataset up or would Keras automatically do that for me?
RNN inputs are like: (NumberOfSequences, TimeSteps, ElementsPerStep)
Each sequence is a row in your input array. This is also called "batch size", number of examples, samples, etc.
Time steps are the amount of steps for each sequence
Elements per step is how much info you have in each step of a sequence
I'm assuming the 27 features are inputs and relate to ElementsPerStep, while the 1 target is the expected output having 1 output per step.
So I'm also assuming that your output is a sequence with also 550k steps.
Shaping the array:
Since you have only one sequence in the array, and this sequence has 550k steps, then you must reshape your array like this:
(1, 550000, 28)
#1 sequence
#550000 steps per sequence
#28 data elements per step
#PS: this sequence is too long, if it creates memory problems to you, maybe it will be a good idea to use a `stateful=True` RNN, but I'm explaining the non stateful method first.
Now you must split this array for inputs and targets:
X_train = thisArray[:, :, :27] #inputs
Y_train = thisArray[:, :, 27] #targets
Shaping the keras layers:
Keras layers will ignore the batch size (number of sequences) when you define them, so you will use input_shape=(550000,27).
Since your desired result is a sequence with same length, we will use return_sequences=True. (Else, you'd get only one result).
LSTM(numberOfCells, input_shape=(550000,27), return_sequences=True)
This will output a shape of (BatchSize, 550000, numberOfCells)
You may use a single layer with 1 cell to achieve your output, or you could stack more layers, considering that the last one should have 1 cell to match the shape of your output. (If you're using only recurrent layers, of course)
stateful = True:
When you have sequences so long that your memory can't handle them well, you must define the layer with stateful=True.
In that case, you will have to divide X_train in smaller length sequences*. The system will understand that every new batch is a sequel of the previous batches.
Then you will need to define batch_input_shape=(BatchSize,ReducedTimeSteps,Elements). In this case, the batch size should not be ignored like in the other case.
* Unfortunately I have no experience with stateful=True. I'm not sure about whether you must manually divide your array (less likely, I guess), or if the system automatically divides it internally (more likely).
The sliding window case:
In this case, what I often see is people dividing the input data like this:
From the 550k steps, get smaller arrays with 50 steps:
X = []
for i in range(550000-49):
X.append(originalX[i:i+50]) #then take care of the 28th element
Y = #it seems you just exclude the first 49 ones from the original
In tensorflow.contrib.seq2seq's AttentionWrapper, what does "depth" refer to as stated in the attention_layer_size documentation? When the documentation says to "use the context as attention" if the value is None, what is meant by "the context"?
In Neural Machine Translation by Jointly Learning to Align and Translate they give a description of the (Bahdanau) attention mechanism; essentially what happens is that you compute scalar "alignment scores" a_1, a_2, ..., a_n that indicate how important each element of your encoded input sequence is at a given moment in time (i.e. which part of the input sentence you should pay attention to right now in the current timestep).
Assuming your (encoded) input sequence that you want to "pay attention"/"attend over" is a sequence of vectors denoted as e_1, e_2, ..., e_n, the context vector at a given timestep is the weighted sum over all of these as determined by your alignment scores:
context = c := (a_1*e_1) + (a_2*e_2) + ... + (a_n*e_n)
(Remember that the a_k's are scalars; you can think of this as an "averaged-out" letter/word in your sentence --- so ideally if your model is trained well, the context looks most similar to the e_i you want to pay attention to the most, but bears a little bit of resemblance to e_{i-1}, e_{i+1}, etc. Intuitively, think of a "smeared-out" input element, if that makes any sense...)
Anyway, if attention_layer_size is not None, then it specifies the number of hidden units in a feedforward layer within your decoder that is used to mix this context vector with the output of the decoder's internal RNN cell to get the attention value. If attention_layer_size == None, it just uses the context vector above as the attention value, and no mixing of the internal RNN cell's output is done. (When I say "mixing", I mean that the context vector and the RNN cell's output are concatenated and then projected to the dimensionality that you specify by setting attention_layer_size.)
The relevant part of the implementation is at this line and has a description of how it's computed.
Hope that helps!
I'm trying to implement the paper "End-to-End memory networks" (http://arxiv.org/abs/1503.08895)
Each training example consists of a number of phrases, a question and then the answer. The number of sentences is variable, as is the number of words in each sentence and the question. Each word is encoded as an integer. So my input would have the form [batch size, # of sentences, # words in sentence].
Now my problem is that the second and third dimension are unknown for each mini-batch. Can I still somehow represent this input as a single tensor or do I have to use lists of tensors, so that I have a list of length batch_size, and then a sublist of length number of sentences and then for each sentence a tensor, whose size is also not known in advance, corresponding to the words encoded as integers.
Can I use this second approach or will tensorflow then not be able to backpropagate, e.g. I have an operation where I have to calculate the following sum: \sum_i tf.scalar_mul(p_i, c_i), where p_i is a scalar and c_i is an embedding vector that was previously calculated. The tensors for the p and c values are then stored in a list, so I would have to sum over the elements in the two lists in a loop. I'm assuming that tensorflow would not be able to incoorporate this loop in the computation graph, correct? I'm sceptical since theano has a special scan function that allows one to loop over input, so I'm assuming that a regular loop would cause problems in the computation graph. How does tensorflow handle this?
Moving Yaroslav's comment to an answer:
TensorFlow has tf.scan. Dimensions may also be dynamic as in Theano.