`Dense`

implements the operation:
`output = activation(dot(input, kernel) + bias)`

where `activation`

is the element-wise activation function
passed as the `activation`

argument, `kernel`

is a weights matrix
created by the layer, and `bias`

is a bias vector created by the layer
(only applicable if `use_bias`

is `TRUE`

).

## Usage

```
layer_dense(
object,
units,
activation = NULL,
use_bias = TRUE,
kernel_initializer = "glorot_uniform",
bias_initializer = "zeros",
kernel_regularizer = NULL,
bias_regularizer = NULL,
activity_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.

- units
Positive integer, dimensionality of the output space.

- activation
Activation function to use. If you don't specify anything, no activation is applied (ie. "linear" activation:

`a(x) = x`

).- use_bias
Boolean, whether the layer uses a bias vector.

- 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.

- 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. This can be useful to reduce the computation cost of fine-tuning large dense layers. You can also enable LoRA on an existing

`Dense`

layer by calling`layer$enable_lora(rank)`

.- ...
For forward/backward compatability.

## 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.

## Note

If the input to the layer has a rank greater than 2, `Dense`

computes the dot product between the `inputs`

and the `kernel`

along the
last axis of the `inputs`

and axis 0 of the `kernel`

(using `tf.tensordot`

).
For example, if input has dimensions `(batch_size, d0, d1)`

, then we create
a `kernel`

with shape `(d1, units)`

, and the `kernel`

operates along axis 2
of the `input`

, on every sub-tensor of shape `(1, 1, d1)`

(there are
`batch_size * d0`

such sub-tensors). The output in this case will have
shape `(batch_size, d0, units)`

.

## Input Shape

N-D tensor with shape: `(batch_size, ..., input_dim)`

.
The most common situation would be
a 2D input with shape `(batch_size, input_dim)`

.

## Output Shape

N-D tensor with shape: `(batch_size, ..., units)`

.
For instance, for a 2D input with shape `(batch_size, input_dim)`

,
the output would have shape `(batch_size, units)`

.

## See also

Other core layers: `layer_einsum_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_depthwise_conv_1d()`

`layer_depthwise_conv_2d()`

`layer_discretization()`

`layer_dot()`

`layer_dropout()`

`layer_einsum_dense()`

`layer_embedding()`

`layer_feature_space()`

`layer_flatten()`

`layer_flax_module_wrapper()`

`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_jax_model_wrapper()`

`layer_lambda()`

`layer_layer_normalization()`

`layer_lstm()`

`layer_masking()`

`layer_max_pooling_1d()`

`layer_max_pooling_2d()`

`layer_max_pooling_3d()`

`layer_maximum()`

`layer_mel_spectrogram()`

`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()`