# attention

## Syntax

## Description

The attention operation focuses on parts of the input using weighted multiplication operations.

## Examples

### Apply Attention Operation

Specify the sizes of the queries, keys, and values.

querySize = 100; valueSize = 120; numQueries = 64; numValues = 80; numObservations = 32;

Create random arrays containing the queries, keys, and values. For the queries, specify the `dlarray`

format `"CBT"`

(channel, batch, time).

```
queries = dlarray(rand(querySize,numObservations, numQueries),"CBT");
keys = dlarray(rand(querySize,numObservations, numValues));
values = dlarray(rand(valueSize,numObservations, numValues));
```

Specify the number of attention heads.

numHeads = 5;

Apply the attention operation.

[Y,weights] = attention(queries,keys,values,numHeads);

View the sizes and format of the output.

size(Y)

`ans = `*1×3*
120 32 64

dims(Y)

ans = 'CBT'

View the sizes and format of the weights.

size(weights)

`ans = `*1×4*
80 64 5 32

dims(weights)

ans = 0x0 empty char array

### Create Multihead Self Attention Function

You can use the `attention`

function to implement the multihead self attention operation [1] that focuses on parts of the input.

Create the `multiheadSelfAttention`

function, listed in the Multihead Self Attention Function section of the example. The `multiheadSelfAttention`

function takes as input the data `X`

, the number of heads, and the learnable weights for the queries, keys, values, and output data, and returns the multihead attention values.

The `X`

input must be an unformatted `dlarray`

object, where the first dimension corresponds to the input channels, the second dimension corresponds to the time or spatial dimension, and the third dimension corresponds to the batch dimension.

Create an array of sequence data.

numChannels = 10; numObservations = 128; numTimeSteps = 100; X = rand(numChannels,numObservations,numTimeSteps); X = dlarray(X); size(X)

`ans = `*1×3*
10 128 100

Specify the number of heads for multihead attention.

numHeads = 8;

Initialize the learnable parameters for multihead attention.

The learnable query, key, and value weights must be

`(numChannels*numHeads)`

-by-`numChannels`

arrays.The learnable output weights must be a

`(numChannels*numHeads)`

-by-`(numChannels*numHeads)`

array.

outputSize = numChannels*numHeads; WQ = rand(outputSize,numChannels); WK = rand(outputSize,numChannels); WV = rand(outputSize,numChannels); WO = rand(outputSize,outputSize);

Apply the multihead self attention operation.

Y = multiheadSelfAttention(X,numHeads,WQ,WK,WV,WO);

View the size of the output. The output has size `(numChannels*numHeads)`

-by-`numObservations`

-by-`(numTimeSteps)`

.

size(Y)

`ans = `*1×3*
80 128 100

**Multihead Self Attention Function**

The `multiheadSelfAttention`

function takes as input the data `X`

, the number of heads, and the learnable weights for the queries, keys, values, and output data, and returns the multihead attention values.

The

`X`

input must be an unformatted`dlarray`

object, where the first dimension corresponds to the input channels, the second dimension corresponds to the time or spatial dimension, and the third dimension corresponds to the batch dimension.The learnable query, key, and value weight matrices are

`(numChannels*numHeads)`

-by-`numChannels`

matrices.The learnable output weights matrix is a

`(numChannels*numHeads)`

-by-`(numChannels*numHeads)`

matrix.

function Y = multiheadSelfAttention(X,numHeads,WQ,WK,WV,WO) queries = pagemtimes(WQ,X); keys = pagemtimes(WK,X); values = pagemtimes(WV,X); A = attention(queries,keys,values,numHeads,DataFormat="CBT"); Y = pagemtimes(WO,A); end

### Create Luong Attention Function

You can use the `attention`

function to create a function that applies the Luong attention operation to its input. Create the `luongAttention`

function, listed at the end of the example, that applies the Luong attention operation.

Specify the array sizes.

numHiddenUnits = 100; latentSize = 16;

Create random arrays containing the input data.

hiddenState = dlarray(rand(numHiddenUnits,1)); Z = dlarray(rand(latentSize,1)); weights = dlarray(rand(numHiddenUnits,latentSize));

Apply the `luongAttention`

function.

[context,scores] = luongAttention(hiddenState,Z,weights);

View the sizes of the outputs.

size(context)

`ans = `*1×2*
16 1

size(scores)

`ans = `*1×2*
1 1

**Luong Attention Function**

The `luongAttention`

function returns the context vector and attention scores according to the Luong "general" scoring [2]. This operation is equivalent to dot-product attention with queries, keys, and values specified as the hidden state, the weighted latent representation, and the latent representation, respectively.

function [context,scores] = luongAttention(hiddenState,Z,weights) numHeads = 1; queries = hiddenState; keys = pagemtimes(weights,Z); values = Z; [context,scores] = attention(queries,keys,values,numHeads, ... Scale=1, ... DataFormat="CBT"); end

## Input Arguments

`queries`

— Queries

`dlarray`

object

Queries, specified as a `dlarray`

object.

`queries`

can have at most one `"S"`

(spatial)
or `"T"`

(time) dimension. Any dimensions in
`queries`

labeled `"U"`

(unspecified) must be
singleton. If `queries`

is an unformatted `dlarray`

object, then specify the data format using the `DataFormat`

option.

The size of the `"C"`

(channel) dimension in `keys`

must
match the size of the corresponding dimension in `queries`

.

The size of the `"B"`

(batch) dimension in `queries`

, `keys`

, and `values`

must match.

`keys`

— Keys

`dlarray`

object | numeric array

Keys, specified as a `dlarray`

object or a numeric array.

If `keys`

is a formatted `dlarray`

object, then
its format must match the format of `queries`

. If
`keys`

is not a formatted `dlarray`

object, then the
function uses the same format as `queries`

.

The size of any `"S"`

(spatial) or `"T"`

(time) dimensions in `keys`

must match the size of the corresponding dimension in `values`

.

The size of the `"C"`

(channel) dimension in `keys`

must
match the size of the corresponding dimension in `queries`

.

The size of the `"B"`

(batch) dimension in `queries`

, `keys`

, and `values`

must match.

`values`

— Values

`dlarray`

object | numeric array

Values, specified as a `dlarray`

object or a numeric array.

If `values`

is a formatted `dlarray`

object, then
its format must match the format of `queries`

. Otherwise, the
function uses the same format as `queries`

.

The size of any `"S"`

(spatial) or `"T"`

(time) dimensions in `keys`

must match the size of the corresponding dimension in `values`

.

The size of the `"B"`

(batch) dimension in `queries`

, `keys`

, and `values`

must match.

`numHeads`

— Number of heads

positive integer

Number of heads, specified as a positive integer.

Each head performs a separate linear transformation of the input and computes attention weights independently. The layer uses these attention weights to compute a weighted sum of the input representations, generating a context vector. Increasing the number of heads lets the model capture different types of dependencies and attend to different parts of the input simultaneously. Reducing the number of heads can lower the computational cost of the layer.

The value of `numHeads`

must evenly divide the size of the
`"C"`

(channel) dimension of `queries`

,
`keys`

, and `values`

.

### Name-Value Arguments

Specify optional pairs of arguments as
`Name1=Value1,...,NameN=ValueN`

, where `Name`

is
the argument name and `Value`

is the corresponding value.
Name-value arguments must appear after other arguments, but the order of the
pairs does not matter.

*
Before R2021a, use commas to separate each name and value, and enclose*
`Name`

*in quotes.*

**Example: **`attention(queries,keys,values,numHeads,DataFormat="CBT")`

applies the attention operation for unformatted data and specifies the data format
`"CBT"`

(channel, batch, time).

`DataFormat`

— Description of data dimensions

character vector | string scalar

Description of the data dimensions, specified as a character vector or string scalar.

A data format is a string of characters, where each character describes the type of the corresponding data dimension.

The characters are:

`"S"`

— Spatial`"C"`

— Channel`"B"`

— Batch`"T"`

— Time`"U"`

— Unspecified

For example, consider an array containing a batch of sequences where the first, second,
and third dimensions correspond to channels, observations, and time steps, respectively. You
can specify that this array has the format `"CBT"`

(channel, batch,
time).

You can specify multiple dimensions labeled `"S"`

or `"U"`

.
You can use the labels `"C"`

, `"B"`

, and
`"T"`

at most once. The software ignores singleton trailing
`"U"`

dimensions after the second dimension.

If the input data is not a formatted `dlarray`

object, then you must
specify the `DataFormat`

option.

For more information, see Deep Learning Data Formats.

**Data Types: **`char`

| `string`

`Scale`

— Multiplicative factor for scaled dot-product attention

`"auto"`

(default) | numeric scalar

Multiplicative factor for scaled dot-product attention [1], specified as one of these values:

`"auto"`

— Multiply the dot-product by $$\lambda =\frac{1}{\sqrt{{d}_{k}}}$$, where*d*denotes the number of channels in the keys divided by the number of heads._{k}Numeric scalar — Multiply the dot-product by the specified scale factor.

**Data Types: **`single`

| `double`

| `char`

| `string`

`PaddingMask`

— Mask indicating padding values

`dlarray`

object | logical array | binary-valued numeric array

Mask indicating which elements of the input correspond to padding values,
specified as a `dlarray`

object, a logical array, or a binary-valued
numeric array.

The function prevents and allows attention to elements of input data key-value
pairs when the corresponding element in `PaddingMask`

is
`0`

and `1`

, respectively.

If `PaddingMask`

is a formatted `dlarray`

object, then its format must match that of `keys`

. If
`PaddingMask`

is not a formatted `dlarray`

object,
then the function uses the same format as `keys`

. The size of the
`"S"`

(spatial), `"T"`

(time), and
`"B"`

(batch) dimensions in `PaddingMask`

must
match the size of the corresponding dimensions in `keys`

and
`values`

.

The padding mask can have any number of channels. The software uses the values in the first channel only to indicate padding values.

The default value is a logical array of ones with the same size as
`keys`

.

`AttentionMask`

— Attention mask

`"none"`

(default) | `"causal"`

| numeric array | logical array

Attention mask indicating which elements to include when applying the attention operation, specified as one of these values:

`"none"`

— Do not prevent attention to elements with respect to their positions. If`AttentionMask`

is`"none"`

, then the software prevents attention using only the padding mask.`"causal"`

— Prevent elements in position*m*in the`"S"`

(spatial) or`"T"`

(time) dimension of the input queries from providing attention to the elements in positions*n*, where*n*is greater than*m*in the corresponding dimension of the input keys and values. Use this option for auto-regressive models.Logical or numeric array — Prevent attention to elements of the input keys and values when the corresponding element in the specified array is

`0`

. The specified array must be an*N*-by-_{k}*N*matrix or a_{q}*N*-by-_{k}*N*-by-_{q}`numObservations`

array,*N*is the size of the_{k}`"S"`

(spatial) or`"T"`

(time) dimension of the input keys,*N*is the size of the corresponding dimension of the input queries, and_{q}`numObservations`

is the size of the`"B"`

dimension in the input queries.

**Data Types: **`single`

| `double`

| `int8`

| `int16`

| `int32`

| `int64`

| `uint8`

| `uint16`

| `uint32`

| `uint64`

| `logical`

| `char`

| `string`

`DropoutProbability`

— Dropout probability

`0`

(default) | scalar in the range [0, 1)

Dropout probability for the attention weights, specified as a scalar in the range [0, 1).

**Data Types: **`single`

| `double`

## Output Arguments

`Y`

— Result of attention operation

`dlarray`

object

Result of attention operation, returned as a `dlarray`

object.

If `queries`

is a formatted `dlarray`

object, then
`Y`

is a formatted `dlarray`

object with the same
dimension labels as `queries`

. The size of the
`"C"`

(channel) dimension of `Y`

is the same as
the size of the corresponding dimension in `values`

. The size of the
`"S"`

(spatial) or `"T"`

dimension of
`Y`

is the same size as the corresponding dimension in
`queries`

.

If `queries`

is not a formatted `dlarray`

object,
then `Y`

is an unformatted `dlarray`

object.

`weights`

— Attention weights

unformatted `dlarray`

object

Attention weights, returned as an unformatted `dlarray`

object.

`weights`

is a
*N _{k}*-by-

*N*-by-

_{q}`numHeads`

-by-`numObservations`

array, where *N*is the size of the

_{k}`"S"`

(spatial) or `"T"`

(time) dimension of
`keys`

, *N*is the size of the corresponding dimension in

_{q}`queries`

, and
`numObservations`

is the size of the `"B"`

(batch)
dimension in `queries`

.## Algorithms

### Dot-Product Attention

The attention operation focuses on parts of the input using weighted multiplication operations.

The single-head dot-product attention operation is given by

$$\text{attention}(Q,K,V)=\text{dropout}\left(\text{softmax}\left(\text{mask}\left(\lambda Q{K}^{\top},M\right)\right),p\right)V,$$

where:

*Q*denotes the queries.*K*denotes the keys.*V*denotes the values.$$\lambda $$ denotes the scaling factor.

*M*is a mask array of ones and zeros.*p*is the dropout probability.

The mask operation includes or excludes the values of the matrix multiplication setting values
of the input to $$-\infty $$ for zero-valued mask elements. The mask is the union of the padding and
attention masks. The softmax function normalizes the value of the input data across the
channel dimension such that it sums to one. The dropout operation sets elements to zero with
probability *p*.

### Multihead Self-Attention

The multihead self-attention operation for the input *X* is given by

$$\text{multiheadSelfAttention}(X,h,{W}^{Q},{W}^{K},{W}^{V},{W}^{O})=\text{concatenate}({\text{head}}_{1},\dots ,{\text{head}}_{h}){W}^{O},$$

where:

*h*is the number of heads.*W*is a learnable projection matrix for the queries.^{Q}*W*is a learnable projection matrix for the keys.^{K}*W*is a learnable projection matrix for the values.^{V}*W*is a learnable projection matrix for the output.^{O}

Each weight matrix is composed of concatenated weight matrices *W _{i}* for each head. Each $${\text{head}}_{i}$$ denotes the output of the head operation given by

$${\text{head}}_{i}=\text{selfAttention}\left(X{W}_{i}^{Q},X{W}_{i}^{K},X{W}_{i}^{V}\right).$$

### Deep Learning Array Formats

Most deep learning networks and functions operate on different dimensions of the input data in different ways.

For example, an LSTM operation iterates over the time dimension of the input data and a batch normalization operation normalizes over the batch dimension of the input data.

To provide input data with labeled dimensions or input data with additional layout information, you can use *data formats*.

A data format is a string of characters, where each character describes the type of the corresponding data dimension.

The characters are:

`"S"`

— Spatial`"C"`

— Channel`"B"`

— Batch`"T"`

— Time`"U"`

— Unspecified

For example, consider an array containing a batch of sequences where the first, second,
and third dimensions correspond to channels, observations, and time steps, respectively. You
can specify that this array has the format `"CBT"`

(channel, batch,
time).

To create formatted input data, create a `dlarray`

object and specify the format using the second argument.

To provide additional layout information with unformatted data, specify the format using the
`DataFormat`

argument.

For more information, see Deep Learning Data Formats.

## References

[1] Vaswani, Ashish, Noam Shazeer,
Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N. Gomez, Łukasz Kaiser, and Illia
Polosukhin. "Attention is all you need." *Advances in neural information processing
systems* 30 (December 2017): 6000-6010. https://papers.nips.cc/paper/7181-attention-is-all-you-need.

[2] Luong, Minh-Thang, Hieu Pham, and
Christopher D. Manning. "Effective approaches to attention-based neural machine translation."
*arXiv preprint arXiv:1508.04025* (2015).

## Extended Capabilities

### GPU Arrays

Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

Usage notes and limitations:

When at least one of these input arguments is a

`gpuArray`

object or a`dlarray`

object with underlying data of type`gpuArray`

, this function runs on the GPU.`queries`

`keys`

`values`

For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).

## Version History

**Introduced in R2022b**

## See Also

`padsequences`

| `dlarray`

| `dlgradient`

| `dlfeval`

| `lstm`

| `gru`

| `embed`

### Topics

- Define Custom Training Loops, Loss Functions, and Networks
- Train Network Using Model Function
- Sequence-to-Sequence Translation Using Attention
- Image Captioning Using Attention
- Multilabel Graph Classification Using Graph Attention Networks
- Language Translation Using Deep Learning
- List of Functions with dlarray Support

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