# tf.keras.backend.batch_dot

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Batchwise dot product.

### Aliases:

• `tf.compat.v1.keras.backend.batch_dot`
• `tf.compat.v2.keras.backend.batch_dot`
``````tf.keras.backend.batch_dot(
x,
y,
axes=None
)
``````

`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` and `axes` 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` : 100 : append to output shape
• `x.shape` : 20 : do not append to output shape, dimension 1 of `x` has been summed over. (`dot_axes` = 1)
• `y.shape` : 100 : do not append to output shape, always ignore first dimension of `y`
• `y.shape` : 30 : append to output shape
• `y.shape` : 20 : do not append to output shape, dimension 2 of `y` has been summed over. (`dot_axes` = 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)
``````