tf.keras.backend.batch_dot

tf.keras.backend.batch_dot(
    x,
    y,
    axes=None
)

Defined in tensorflow/python/keras/_impl/keras/backend.py.

Batchwise dot product.

batch_dot is used to compute dot product of x and y when x and y are data in batch, i.e. in a shape of (batch_size, :). batch_dot results in a tensor or variable with less dimensions than the input. If the number of dimensions is reduced to 1, we use expand_dims to make sure that ndim is at least 2.

Arguments:

  • x: Keras tensor or variable with ndim >= 2.
  • y: Keras tensor or variable with ndim >= 2.
  • axes: list of (or single) int with target dimensions. The lengths of axes[0] and axes[1] should be the same.

Returns:

A tensor with shape equal to the concatenation of `x`'s shape
(less the dimension that was summed over) and `y`'s shape
(less the batch dimension and the dimension that was summed over).
If the final rank is 1, we reshape it to `(batch_size, 1)`.

Examples: Assume x = [[1, 2], [3, 4]] and y = [[5, 6], [7, 8]] batch_dot(x, y, axes=1) = [[17, 53]] which is the main diagonal of x.dot(y.T), although we never have to calculate the off-diagonal elements.

Shape inference:
Let `x`'s shape be `(100, 20)` and `y`'s shape be `(100, 30, 20)`.
If `axes` is (1, 2), to find the output shape of resultant tensor,
    loop through each dimension in `x`'s shape and `y`'s shape:

* `x.shape[0]` : 100 : append to output shape
* `x.shape[1]` : 20 : do not append to output shape,
    dimension 1 of `x` has been summed over. (`dot_axes[0]` = 1)
* `y.shape[0]` : 100 : do not append to output shape,
    always ignore first dimension of `y`
* `y.shape[1]` : 30 : append to output shape
* `y.shape[2]` : 20 : do not append to output shape,
    dimension 2 of `y` has been summed over. (`dot_axes[1]` = 2)
`output_shape` = `(100, 30)`
    >>> x_batch = K.ones(shape=(32, 20, 1))
    >>> y_batch = K.ones(shape=(32, 30, 20))
    >>> xy_batch_dot = K.batch_dot(x_batch, y_batch, axes=[1, 2])
    >>> K.int_shape(xy_batch_dot)
    (32, 1, 30)