tf / where

TensorFlow 1 version

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Return the elements where condition is True (multiplexing x and y).

tf.where(
    condition, x=None, y=None, name=None
)

Used in the notebooks

This operator has two modes: in one mode both x and y are provided, in another mode neither are provided. condition is always expected to be a tf.Tensor of type bool.

Retrieving indices of True elements

If x and y are not provided (both are None):

tf.where will return the indices of condition that are True, in the form of a 2-D tensor with shape (n, d). (Where n is the number of matching indices in condition, and d is the number of dimensions in condition).

Indices are output in row-major order.

tf.where([True, False, False, True])
<tf.Tensor: shape=(2, 1), dtype=int64, numpy=
array([[0],
       [3]])>

tf.where([[True, False], [False, True]])
<tf.Tensor: shape=(2, 2), dtype=int64, numpy=
array([[0, 0],
       [1, 1]])>

tf.where([[[True, False], [False, True], [True, True]]])
<tf.Tensor: shape=(4, 3), dtype=int64, numpy=
array([[0, 0, 0],
       [0, 1, 1],
       [0, 2, 0],
       [0, 2, 1]])>

Multiplexing between x and y

If x and y are provided (both have non-None values):

tf.where will choose an output shape from the shapes of condition, x, and y that all three shapes are broadcastable to.

The condition tensor acts as a mask that chooses whether the corresponding element / row in the output should be taken from x (if the element in condition is True) or y (if it is false).

tf.where([True, False, False, True], [1,2,3,4], [100,200,300,400])
<tf.Tensor: shape=(4,), dtype=int32, numpy=array([  1, 200, 300,   4],
dtype=int32)>
tf.where([True, False, False, True], [1,2,3,4], [100])
<tf.Tensor: shape=(4,), dtype=int32, numpy=array([  1, 100, 100,   4],
dtype=int32)>
tf.where([True, False, False, True], [1,2,3,4], 100)
<tf.Tensor: shape=(4,), dtype=int32, numpy=array([  1, 100, 100,   4],
dtype=int32)>
tf.where([True, False, False, True], 1, 100)
<tf.Tensor: shape=(4,), dtype=int32, numpy=array([  1, 100, 100,   1],
dtype=int32)>

tf.where(True, [1,2,3,4], 100)
<tf.Tensor: shape=(4,), dtype=int32, numpy=array([1, 2, 3, 4],
dtype=int32)>
tf.where(False, [1,2,3,4], 100)
<tf.Tensor: shape=(4,), dtype=int32, numpy=array([100, 100, 100, 100],
dtype=int32)>

Note that if the gradient of either branch of the tf.where generates a NaN, then the gradient of the entire tf.where will be NaN. A workaround is to use an inner tf.where to ensure the function has no asymptote, and to avoid computing a value whose gradient is NaN by replacing dangerous inputs with safe inputs.

Instead of this,

y = tf.constant(-1, dtype=tf.float32)
tf.where(y > 0, tf.sqrt(y), y)
<tf.Tensor: shape=(), dtype=float32, numpy=-1.0>

Use this

tf.where(y > 0, tf.sqrt(tf.where(y > 0, y, 1)), y)
<tf.Tensor: shape=(), dtype=float32, numpy=-1.0>