This layer can perform einsum calculations of arbitrary dimensionality.

## Usage

```
layer_einsum_dense(
object,
equation,
output_shape,
activation = NULL,
bias_axes = NULL,
kernel_initializer = "glorot_uniform",
bias_initializer = "zeros",
kernel_regularizer = NULL,
bias_regularizer = NULL,
kernel_constraint = NULL,
bias_constraint = NULL,
lora_rank = NULL,
...
)
```

## Arguments

- object
Object to compose the layer with. A tensor, array, or sequential model.

- 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

`NA`

or`NULL`

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.

- kernel_constraint
Constraint function applied to the

`kernel`

weights matrix.- bias_constraint
Constraint function applied to the bias vector.

- lora_rank
Optional integer. If set, the layer's forward pass will implement LoRA (Low-Rank Adaptation) with the provided rank. LoRA sets the layer's kernel to non-trainable and replaces it with a delta over the original kernel, obtained via multiplying two lower-rank trainable matrices (the factorization happens on the last dimension). This can be useful to reduce the computation cost of fine-tuning large dense layers. You can also enable LoRA on an existing

`EinsumDense`

layer by calling`layer$enable_lora(rank)`

.- ...
Base layer keyword arguments, such as

`name`

and`dtype`

.

## Value

The return value depends on the value provided for the first argument.
If `object`

is:

a

`keras_model_sequential()`

, then the layer is added to the sequential model (which is modified in place). To enable piping, the sequential model is also returned, invisibly.a

`keras_input()`

, then the output tensor from calling`layer(input)`

is returned.`NULL`

or missing, then a`Layer`

instance is returned.

## 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
`layer_Dense(64, use_bias=TRUE)`

.

```
input <- layer_input(shape = c(32))
output <- input |>
layer_einsum_dense("ab,bc->ac",
output_shape = 64,
bias_axes = "c")
output # shape(NA, 64)
```

**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 `NA`

, because the sequence dimension
`b`

has an unknown shape.

```
input <- layer_input(shape = c(32, 128))
output <- input |>
layer_einsum_dense("abc,cd->abd",
output_shape = c(NA, 64),
bias_axes = "d")
output # shape(NA, 32, 64)
```

**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.

```
input <- layer_input(shape = c(32, 128))
output <- input |>
layer_einsum_dense("...x,xy->...y",
output_shape = 64,
bias_axes = "y")
output # shape(NA, 32, 64)
```

## See also

Other core layers: `layer_dense()`

`layer_embedding()`

`layer_identity()`

`layer_lambda()`

`layer_masking()`

Other layers: `Layer()`

`layer_activation()`

`layer_activation_elu()`

`layer_activation_leaky_relu()`

`layer_activation_parametric_relu()`

`layer_activation_relu()`

`layer_activation_softmax()`

`layer_activity_regularization()`

`layer_add()`

`layer_additive_attention()`

`layer_alpha_dropout()`

`layer_attention()`

`layer_average()`

`layer_average_pooling_1d()`

`layer_average_pooling_2d()`

`layer_average_pooling_3d()`

`layer_batch_normalization()`

`layer_bidirectional()`

`layer_category_encoding()`

`layer_center_crop()`

`layer_concatenate()`

`layer_conv_1d()`

`layer_conv_1d_transpose()`

`layer_conv_2d()`

`layer_conv_2d_transpose()`

`layer_conv_3d()`

`layer_conv_3d_transpose()`

`layer_conv_lstm_1d()`

`layer_conv_lstm_2d()`

`layer_conv_lstm_3d()`

`layer_cropping_1d()`

`layer_cropping_2d()`

`layer_cropping_3d()`

`layer_dense()`

`layer_depthwise_conv_1d()`

`layer_depthwise_conv_2d()`

`layer_discretization()`

`layer_dot()`

`layer_dropout()`

`layer_embedding()`

`layer_feature_space()`

`layer_flatten()`

`layer_gaussian_dropout()`

`layer_gaussian_noise()`

`layer_global_average_pooling_1d()`

`layer_global_average_pooling_2d()`

`layer_global_average_pooling_3d()`

`layer_global_max_pooling_1d()`

`layer_global_max_pooling_2d()`

`layer_global_max_pooling_3d()`

`layer_group_normalization()`

`layer_group_query_attention()`

`layer_gru()`

`layer_hashed_crossing()`

`layer_hashing()`

`layer_identity()`

`layer_integer_lookup()`

`layer_lambda()`

`layer_layer_normalization()`

`layer_lstm()`

`layer_masking()`

`layer_max_pooling_1d()`

`layer_max_pooling_2d()`

`layer_max_pooling_3d()`

`layer_maximum()`

`layer_minimum()`

`layer_multi_head_attention()`

`layer_multiply()`

`layer_normalization()`

`layer_permute()`

`layer_random_brightness()`

`layer_random_contrast()`

`layer_random_crop()`

`layer_random_flip()`

`layer_random_rotation()`

`layer_random_translation()`

`layer_random_zoom()`

`layer_repeat_vector()`

`layer_rescaling()`

`layer_reshape()`

`layer_resizing()`

`layer_rnn()`

`layer_separable_conv_1d()`

`layer_separable_conv_2d()`

`layer_simple_rnn()`

`layer_spatial_dropout_1d()`

`layer_spatial_dropout_2d()`

`layer_spatial_dropout_3d()`

`layer_spectral_normalization()`

`layer_string_lookup()`

`layer_subtract()`

`layer_text_vectorization()`

`layer_tfsm()`

`layer_time_distributed()`

`layer_torch_module_wrapper()`

`layer_unit_normalization()`

`layer_upsampling_1d()`

`layer_upsampling_2d()`

`layer_upsampling_3d()`

`layer_zero_padding_1d()`

`layer_zero_padding_2d()`

`layer_zero_padding_3d()`

`rnn_cell_gru()`

`rnn_cell_lstm()`

`rnn_cell_simple()`

`rnn_cells_stack()`