Gather and Scatter

Gather(), Scatter()

Shorten or lengthen a data sequence based on a mask.

BS.Sequences.Gather  (maskSequence, dataSequence)
BS.Sequences.Scatter (maskSequence, dataSequence)

Parameters

• maskSequence: a sequence of 0 or 1 (static tensor dimension [1]), where 1 indicate samples to keep. (Any other value gives rise to undefined behavior and may change in the future.)
• dataSequence: the data sequence to process. For Gather(), its length must be the same as that of maskSequence, while for Scatter(), it must be equal to the number of ones in maskSequence.

Return value

For Gather(), a sequence that contains a subset of dataSequence, with some samples dropped. The length of the result sequence will be equal to the number of ones in maskSequence.

For Scatter(), a sequence that contains samples of dataSequence and inserted zeroes. The result sequence will have the same length as maskSequence.

Description

Gather() and Scatter() allow you to shorten or lengthen an input sequence, such as a sequence of words, based on a mask sequence.

Gather() returns the sub-sequence of those samples dataSequence[n] for which maskSequence[n] is 1, while those for which the mask is 0 will be dropped.

Scatter() takes elements of a sub-sequence and places them in a longer sequence, inserting zeroes.

For example:

g = Gather  (m, d)
s = Scatter (m, g)

d = A B C D E F G H I J K L M N O P Q R S T U V W X Y Z  # data
m = 1 1 0 1 0 0 1 0 1 1 0 0 1 0 0 1 1 0 0 1 0 0 1 1 0 1  # mask
g = A B D G I J M P Q T W X Z
s = A B 0 D 0 0 G 0 I J 0 0 M 0 0 P Q 0 0 T 0 0 W X 0 Z

Gather() is often used indirectly through Slice(..., axis=-1), BS.Sequences.First(), and BS.Sequences.Last().

Examples

Recurrent language model

Given a word sequence of the form <s> A B C ... </s>, a language model takes the input of the form <s> A B C ... to predict labels of the form A B C ... </s>. Gather() allows a single word sequence to be read from file, and then create the input and labels by dropping the trailing </s> and leading <s>, respectively:

words  = Input {inputDim}
inputMask  = !BS.Sequences.IsFirst (words)
labelsMask = !BS.Sequences.IsLast  (words)
input  =                       Gather (inputMask,  words)          # drop trailing </s>
labels = ReconcileDynamicAxis (Gather (labelsMask, words), input)  # drop leading <s>

lstmLM = Sequential
(
    EmbeddingLayer {300} :
    RecurrentLSTMLayer {512} :
    DenseLayer {inputDim, activation=LogSoftmax}
)

logP = lstmLM (input)
ce = -TransposeTimes (labels, logP)
criterionNodes = (ce)

Note: The Gather() operation can more conveniently be written as follows, which under the hood calls Gather():

input  =                       Slice (0, -1, words, axis=-1)          # strip trailing </s>
labels = ReconcileDynamicAxis (Slice (1,  0, words, axis=-1), input)  # strip leading <s>

Thought vector

The following selects the last sample of a hidden-state sequence:

h = RecurrentLSTMLayer {} (x)       # sequence of hidden states
lastMask = BS.Sequences.IsLast (h)  # mask to denote the last step
thoughtVector = BS.Sequences.Gather (lastMask, h)  # select the last

IsFirst(), IsLast()

Create a mask for use with Gather() to select the first and last sample of a sequence, respectively.

BS.Sequences.IsFirst (dataSequence)
BS.Sequences.IsLast  (dataSequence)

Parameters

• dataSequence: any sequence, e.g. a word sequence

Return value

A mask for use with Gather() that will select the first or last item, respectively, while dropping all other samples.

Description

IsFirst() and IsLast() create a mask for use with Gather() to select the first and last sample of a sequence, respectively, which is typically needed in sequence-to-sequence models to extract the "thought vector" (the last hidden state of a recurrence).

Examples

See here.