tf.keras.layers.EinsumDense

A layer that uses tf.einsum as the backing computation.

Inherits From: Layer, Module

tf.keras.layers.EinsumDense(
    equation,
    output_shape,
    activation=None,
    bias_axes=None,
    kernel_initializer='glorot_uniform',
    bias_initializer='zeros',
    kernel_regularizer=None,
    bias_regularizer=None,
    activity_regularizer=None,
    kernel_constraint=None,
    bias_constraint=None,
    **kwargs
)

This layer can perform einsum calculations of arbitrary dimensionality.

equation An equation describing the einsum to perform. This equation must be a valid einsum string of the form ab,bc->ac, ...ab,bc->...ac, or ab...,bc->ac... where 'ab', 'bc', and 'ac' can be any valid einsum axis expression sequence.
output_shape The expected shape of the output tensor (excluding the batch dimension and any dimensions represented by ellipses). You can specify None for any dimension that is unknown or can be inferred from the input shape.
activation Activation function to use. If you don't specify anything, no activation is applied (that is, a "linear" activation: a(x) = x).
bias_axes A string containing the output dimension(s) to apply a bias to. Each character in the bias_axes string should correspond to a character in the output portion of the equation string.
kernel_initializer Initializer for the kernel weights matrix.
bias_initializer Initializer for the bias vector.
kernel_regularizer Regularizer function applied to the kernel weights matrix.
bias_regularizer Regularizer function applied to the bias vector.
activity_regularizer Regularizer function applied to the output of the layer (its "activation").
kernel_constraint Constraint function applied to the kernel weights matrix.
bias_constraint Constraint function applied to the bias vector.

Examples:

Biased dense layer with einsums

This example shows how to instantiate a standard Keras dense layer using einsum operations. This example is equivalent to tf.keras.layers.Dense(64, use_bias=True).

layer = tf.keras.layers.EinsumDense("ab,bc->ac",
                                    output_shape=64,
                                    bias_axes="c")
input_tensor = tf.keras.Input(shape=[32])
output_tensor = layer(input_tensor)
output_tensor
<... shape=(None, 64) dtype=...>

Applying a dense layer to a sequence

This example shows how to instantiate a layer that applies the same dense operation to every element in a sequence. Here, the output_shape has two values (since there are two non-batch dimensions in the output); the first dimension in the output_shape is None, because the sequence dimension b has an unknown shape.

layer = tf.keras.layers.EinsumDense("abc,cd->abd",
                                    output_shape=(None, 64),
                                    bias_axes="d")
input_tensor = tf.keras.Input(shape=[32, 128])
output_tensor = layer(input_tensor)
output_tensor
<... shape=(None, 32, 64) dtype=...>

Applying a dense layer to a sequence using ellipses

This example shows how to instantiate a layer that applies the same dense operation to every element in a sequence, but uses the ellipsis notation instead of specifying the batch and sequence dimensions.

Because we are using ellipsis notation and have specified only one axis, the output_shape arg is a single value. When instantiated in this way, the layer can handle any number of sequence dimensions - including the case where no sequence dimension exists.

layer = tf.keras.layers.EinsumDense("...x,xy->...y",
                                    output_shape=64,
                                    bias_axes="y")
input_tensor = tf.keras.Input(shape=[32, 128])
output_tensor = layer(input_tensor)
output_tensor
<... shape=(None, 32, 64) dtype=...>