tf.gather_nd

Gather slices from params into a Tensor with shape specified by indices.

tf.gather_nd(
    params, indices, batch_dims=0, name=None
)

Used in the notebooks

Used in the guide	Used in the tutorials
Introduction to tensor slicing	Parametrized Quantum Circuits for Reinforcement Learning

indices is a Tensor of indices into params. The index vectors are arranged along the last axis of indices.

This is similar to tf.gather, in which indices defines slices into the first dimension of params. In tf.gather_nd, indices defines slices into the first N dimensions of params, where N = indices.shape[-1].

Gathering scalars

In the simplest case the vectors in indices index the full rank of params:

tf.gather_nd(
    indices=[[0, 0],
             [1, 1]],
    params = [['a', 'b'],
              ['c', 'd']]).numpy()
array([b'a', b'd'], dtype=object)

In this case the result has 1-axis fewer than indices, and each index vector is replaced by the scalar indexed from params.

In this case the shape relationship is:

index_depth = indices.shape[-1]
assert index_depth == params.shape.rank
result_shape = indices.shape[:-1]

If indices has a rank of K, it is helpful to think indices as a (K-1)-dimensional tensor of indices into params.

Gathering slices

If the index vectors do not index the full rank of params then each location in the result contains a slice of params. This example collects rows from a matrix:

tf.gather_nd(
    indices = [[1],
               [0]],
    params = [['a', 'b', 'c'],
              ['d', 'e', 'f']]).numpy()
array([[b'd', b'e', b'f'],
       [b'a', b'b', b'c']], dtype=object)

Here indices contains [2] index vectors, each with a length of 1. The index vectors each refer to rows of the params matrix. Each row has a shape of [3] so the output shape is [2, 3].

In this case, the relationship between the shapes is:

index_depth = indices.shape[-1]
outer_shape = indices.shape[:-1]
assert index_depth <= params.shape.rank
inner_shape = params.shape[index_depth:]
output_shape = outer_shape + inner_shape

It is helpful to think of the results in this case as tensors-of-tensors. The shape of the outer tensor is set by the leading dimensions of indices. While the shape of the inner tensors is the shape of a single slice.

Batches

Additionally, both params and indices can have M leading batch dimensions that exactly match. In this case batch_dims must be set to M.

For example, to collect one row from each of a batch of matrices you could set the leading elements of the index vectors to be their location in the batch:

tf.gather_nd(
    indices = [[0, 1],
               [1, 0],
               [2, 4],
               [3, 2],
               [4, 1]],
    params=tf.zeros([5, 7, 3])).shape.as_list()
[5, 3]

The batch_dims argument lets you omit those leading location dimensions from the index:

tf.gather_nd(
    batch_dims=1,
    indices = [[1],
               [0],
               [4],
               [2],
               [1]],
    params=tf.zeros([5, 7, 3])).shape.as_list()
[5, 3]

This is equivalent to caling a separate gather_nd for each location in the batch dimensions.

params=tf.zeros([5, 7, 3])
indices=tf.zeros([5, 1])
batch_dims = 1

index_depth = indices.shape[-1]
batch_shape = indices.shape[:batch_dims]
assert params.shape[:batch_dims] == batch_shape
outer_shape = indices.shape[batch_dims:-1]
assert index_depth <= params.shape.rank
inner_shape = params.shape[batch_dims + index_depth:]
output_shape = batch_shape + outer_shape + inner_shape
output_shape.as_list()
[5, 3]

More examples

Indexing into a 3-tensor:

tf.gather_nd(
    indices = [[1]],
    params = [[['a0', 'b0'], ['c0', 'd0']],
              [['a1', 'b1'], ['c1', 'd1']]]).numpy()
array([[[b'a1', b'b1'],
        [b'c1', b'd1']]], dtype=object)

tf.gather_nd(
    indices = [[0, 1], [1, 0]],
    params = [[['a0', 'b0'], ['c0', 'd0']],
              [['a1', 'b1'], ['c1', 'd1']]]).numpy()
array([[b'c0', b'd0'],
       [b'a1', b'b1']], dtype=object)

tf.gather_nd(
    indices = [[0, 0, 1], [1, 0, 1]],
    params = [[['a0', 'b0'], ['c0', 'd0']],
              [['a1', 'b1'], ['c1', 'd1']]]).numpy()
array([b'b0', b'b1'], dtype=object)

The examples below are for the case when only indices have leading extra dimensions. If both 'params' and 'indices' have leading batch dimensions, use the 'batch_dims' parameter to run gather_nd in batch mode.

Batched indexing into a matrix:

tf.gather_nd(
    indices = [[[0, 0]], [[0, 1]]],
    params = [['a', 'b'], ['c', 'd']]).numpy()
array([[b'a'],
       [b'b']], dtype=object)

Batched slice indexing into a matrix:

tf.gather_nd(
    indices = [[[1]], [[0]]],
    params = [['a', 'b'], ['c', 'd']]).numpy()
array([[[b'c', b'd']],
       [[b'a', b'b']]], dtype=object)

Batched indexing into a 3-tensor:

tf.gather_nd(
    indices = [[[1]], [[0]]],
    params = [[['a0', 'b0'], ['c0', 'd0']],
              [['a1', 'b1'], ['c1', 'd1']]]).numpy()
array([[[[b'a1', b'b1'],
         [b'c1', b'd1']]],
       [[[b'a0', b'b0'],
         [b'c0', b'd0']]]], dtype=object)

tf.gather_nd(
    indices = [[[0, 1], [1, 0]], [[0, 0], [1, 1]]],
    params = [[['a0', 'b0'], ['c0', 'd0']],
              [['a1', 'b1'], ['c1', 'd1']]]).numpy()
array([[[b'c0', b'd0'],
        [b'a1', b'b1']],
       [[b'a0', b'b0'],
        [b'c1', b'd1']]], dtype=object)

tf.gather_nd(
    indices = [[[0, 0, 1], [1, 0, 1]], [[0, 1, 1], [1, 1, 0]]],
    params = [[['a0', 'b0'], ['c0', 'd0']],
              [['a1', 'b1'], ['c1', 'd1']]]).numpy()
array([[b'b0', b'b1'],
       [b'd0', b'c1']], dtype=object)

Examples with batched 'params' and 'indices':

tf.gather_nd(
    batch_dims = 1,
    indices = [[1],
               [0]],
    params = [[['a0', 'b0'],
               ['c0', 'd0']],
              [['a1', 'b1'],
               ['c1', 'd1']]]).numpy()
array([[b'c0', b'd0'],
       [b'a1', b'b1']], dtype=object)

tf.gather_nd(
    batch_dims = 1,
    indices = [[[1]], [[0]]],
    params = [[['a0', 'b0'], ['c0', 'd0']],
              [['a1', 'b1'], ['c1', 'd1']]]).numpy()
array([[[b'c0', b'd0']],
       [[b'a1', b'b1']]], dtype=object)

tf.gather_nd(
    batch_dims = 1,
    indices = [[[1, 0]], [[0, 1]]],
    params = [[['a0', 'b0'], ['c0', 'd0']],
              [['a1', 'b1'], ['c1', 'd1']]]).numpy()
array([[b'c0'],
       [b'b1']], dtype=object)

Args
`params`	A `Tensor`. The tensor from which to gather values.
`indices`	A `Tensor`. Must be one of the following types: `int32`, `int64`. Index tensor.
`name`	A name for the operation (optional).
`batch_dims`	An integer or a scalar 'Tensor'. The number of batch dimensions.