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Introduction to tensor slicing

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When working on ML applications such as object detection and NLP, it is sometimes necessary to work with sub-sections (slices) of tensors. For example, if your model architecture includes routing, where one layer might control which training example gets routed to the next layer. In this case, you could use tensor slicing ops to split the tensors up and put them back together in the right order.

In NLP applications, you can use tensor slicing to perform word masking while training. For example, you can generate training data from a list of sentences by choosing a word index to mask in each sentence, taking the word out as a label, and then replacing the chosen word with a mask token.

In this guide, you will learn how to use the TensorFlow APIs to:

  • Extract slices from a tensor
  • Insert data at specific indices in a tensor

This guide assumes familiarity with tensor indexing. Read the indexing sections of the Tensor and TensorFlow NumPy guides before getting started with this guide.

Setup

import tensorflow as tf
import numpy as np

Extract tensor slices

Perform NumPy-like tensor slicing using tf.slice.

t1 = tf.constant([0, 1, 2, 3, 4, 5, 6, 7])

print(tf.slice(t1,
               begin=[1],
               size=[3]))
tf.Tensor([1 2 3], shape=(3,), dtype=int32)

Alternatively, you can use a more Pythonic syntax. Note that tensor slices are evenly spaced over a start-stop range.

print(t1[1:4])
tf.Tensor([1 2 3], shape=(3,), dtype=int32)

print(t1[-3:])
tf.Tensor([5 6 7], shape=(3,), dtype=int32)

For 2-dimensional tensors,you can use something like:

t2 = tf.constant([[0, 1, 2, 3, 4],
                  [5, 6, 7, 8, 9],
                  [10, 11, 12, 13, 14],
                  [15, 16, 17, 18, 19]])

print(t2[:-1, 1:3])
tf.Tensor(
[[ 1  2]
 [ 6  7]
 [11 12]], shape=(3, 2), dtype=int32)

You can use tf.slice on higher dimensional tensors as well.

t3 = tf.constant([[[1, 3, 5, 7],
                   [9, 11, 13, 15]],
                  [[17, 19, 21, 23],
                   [25, 27, 29, 31]]
                  ])

print(tf.slice(t3,
               begin=[1, 1, 0],
               size=[1, 1, 2]))
tf.Tensor([[[25 27]]], shape=(1, 1, 2), dtype=int32)

You can also use tf.strided_slice to extract slices of tensors by 'striding' over the tensor dimensions.

Use tf.gather to extract specific indices from a single axis of a tensor.

print(tf.gather(t1,
                indices=[0, 3, 6]))

# This is similar to doing

t1[::3]
tf.Tensor([0 3 6], shape=(3,), dtype=int32)
<tf.Tensor: shape=(3,), dtype=int32, numpy=array([0, 3, 6], dtype=int32)>

tf.gather does not require indices to be evenly spaced.

alphabet = tf.constant(list('abcdefghijklmnopqrstuvwxyz'))

print(tf.gather(alphabet,
                indices=[2, 0, 19, 18]))
tf.Tensor([b'c' b'a' b't' b's'], shape=(4,), dtype=string)

To extract slices from multiple axes of a tensor, use tf.gather_nd. This is useful when you want to gather the elements of a matrix as opposed to just its rows or columns.

t4 = tf.constant([[0, 5],
                  [1, 6],
                  [2, 7],
                  [3, 8],
                  [4, 9]])

print(tf.gather_nd(t4,
                   indices=[[2], [3], [0]]))
tf.Tensor(
[[2 7]
 [3 8]
 [0 5]], shape=(3, 2), dtype=int32)

t5 = np.reshape(np.arange(18), [2, 3, 3])

print(tf.gather_nd(t5,
                   indices=[[0, 0, 0], [1, 2, 1]]))
tf.Tensor([ 0 16], shape=(2,), dtype=int64)
# Return a list of two matrices

print(tf.gather_nd(t5,
                   indices=[[[0, 0], [0, 2]], [[1, 0], [1, 2]]]))
tf.Tensor(
[[[ 0  1  2]
  [ 6  7  8]]

 [[ 9 10 11]
  [15 16 17]]], shape=(2, 2, 3), dtype=int64)
# Return one matrix

print(tf.gather_nd(t5,
                   indices=[[0, 0], [0, 2], [1, 0], [1, 2]]))
tf.Tensor(
[[ 0  1  2]
 [ 6  7  8]
 [ 9 10 11]
 [15 16 17]], shape=(4, 3), dtype=int64)

Insert data into tensors

Use tf.scatter_nd to insert data at specific slices/indices of a tensor. Note that the tensor into which you insert values is zero-initialized.

t6 = tf.constant([10])
indices = tf.constant([[1], [3], [5], [7], [9]])
data = tf.constant([2, 4, 6, 8, 10])

print(tf.scatter_nd(indices=indices,
                    updates=data,
                    shape=t6))
tf.Tensor([ 0  2  0  4  0  6  0  8  0 10], shape=(10,), dtype=int32)

Methods like tf.scatter_nd which require zero-initialized tensors are similar to sparse tensor initializers. You can use tf.gather_nd and tf.scatter_nd to mimic the behavior of sparse tensor ops.

Consider an example where you construct a sparse tensor using these two methods in conjunction.

# Gather values from one tensor by specifying indices

new_indices = tf.constant([[0, 2], [2, 1], [3, 3]])
t7 = tf.gather_nd(t2, indices=new_indices)

# Add these values into a new tensor

t8 = tf.scatter_nd(indices=new_indices, updates=t7, shape=tf.constant([4, 5]))

print(t8)
tf.Tensor(
[[ 0  0  2  0  0]
 [ 0  0  0  0  0]
 [ 0 11  0  0  0]
 [ 0  0  0 18  0]], shape=(4, 5), dtype=int32)

This is similar to:

t9 = tf.SparseTensor(indices=[[0, 2], [2, 1], [3, 3]],
                     values=[2, 11, 18],
                     dense_shape=[4, 5])

print(t9)
SparseTensor(indices=tf.Tensor(
[[0 2]
 [2 1]
 [3 3]], shape=(3, 2), dtype=int64), values=tf.Tensor([ 2 11 18], shape=(3,), dtype=int32), dense_shape=tf.Tensor([4 5], shape=(2,), dtype=int64))
# Convert the sparse tensor into a dense tensor

t10 = tf.sparse.to_dense(t9)

print(t10)
tf.Tensor(
[[ 0  0  2  0  0]
 [ 0  0  0  0  0]
 [ 0 11  0  0  0]
 [ 0  0  0 18  0]], shape=(4, 5), dtype=int32)

To insert data into a tensor with pre-existing values, use tf.tensor_scatter_nd_add.

t11 = tf.constant([[2, 7, 0],
                   [9, 0, 1],
                   [0, 3, 8]])

# Convert the tensor into a magic square by inserting numbers at appropriate indices

t12 = tf.tensor_scatter_nd_add(t11,
                               indices=[[0, 2], [1, 1], [2, 0]],
                               updates=[6, 5, 4])

print(t12)
tf.Tensor(
[[2 7 6]
 [9 5 1]
 [4 3 8]], shape=(3, 3), dtype=int32)

Similarly, use tf.tensor_scatter_nd_sub to subtract values from a tensor with pre-existing values.

# Convert the tensor into an identity matrix

t13 = tf.tensor_scatter_nd_sub(t11,
                               indices=[[0, 0], [0, 1], [1, 0], [1, 1], [1, 2], [2, 1], [2, 2]],
                               updates=[1, 7, 9, -1, 1, 3, 7])

print(t13)
tf.Tensor(
[[1 0 0]
 [0 1 0]
 [0 0 1]], shape=(3, 3), dtype=int32)

Use tf.tensor_scatter_nd_min to copy element-wise minimum values from one tensor to another.

t14 = tf.constant([[-2, -7, 0],
                   [-9, 0, 1],
                   [0, -3, -8]])

t15 = tf.tensor_scatter_nd_min(t14,
                               indices=[[0, 2], [1, 1], [2, 0]],
                               updates=[-6, -5, -4])

print(t15)
tf.Tensor(
[[-2 -7 -6]
 [-9 -5  1]
 [-4 -3 -8]], shape=(3, 3), dtype=int32)

Similarly, use tf.tensor_scatter_nd_max to copy element-wise maximum values from one tensor to another.

t16 = tf.tensor_scatter_nd_max(t14,
                               indices=[[0, 2], [1, 1], [2, 0]],
                               updates=[6, 5, 4])

print(t16)
tf.Tensor(
[[-2 -7  6]
 [-9  5  1]
 [ 4 -3 -8]], shape=(3, 3), dtype=int32)

Further reading and resources

In this guide, you learned how to use the tensor slicing ops available with TensorFlow to exert finer control over the elements in your tensors.