# patchEmbeddingLayer

## Description

A patch embedding layer maps patches of pixels to vectors. Use this layer in vision transformer neural networks to encode information about patches in images.

## Creation

### Syntax

### Description

creates a patch embedding layer and sets the `layer`

= patchEmbeddingLayer(`patchSize`

,`outputSize`

)`PatchSize`

and
`OutputSize`

properties.

This feature requires a Deep Learning Toolbox™ license.

sets additional properties using one or more name-value arguments.`layer`

= patchEmbeddingLayer(`patchSize`

,`outputSize`

,`Name=Value`

)

## Properties

### Patch Embedding

`PatchSize`

— Size of patches to split input images into

positive integer | row vector of positive integers

This property is read-only.

Size of patches to split input images into, specified as a positive integer or row vector of positive integers.

If `PatchSize`

is a vector, then each element of
`PatchSize`

is the size of the patch in the corresponding spatial
dimension of the input. If `PatchSize`

is a scalar, then the layer
uses the same value for all spatial dimensions of the input.

**Data Types: **`single`

| `double`

| `int8`

| `int16`

| `int32`

| `int64`

| `uint8`

| `uint16`

| `uint32`

| `uint64`

`SpatialFlattenMode`

— Mode for flattening output of convolution operation

`"column-major"`

(default) | `"row-major"`

Mode for flattening the output of the convolution operation, specified as
`"column-major"`

or `"row-major"`

.

If `SpatialFlattenMode`

is `"column-major"`

,
then the flatten operation outputs the data in its column-major representation. For
example, consider the input:

A = [ 1 2 3 4 5 6 7 8 9];

AFlat = [1 4 7 2 5 8 3 6 9];

If `SpatialFlattenMode`

is `"row-major"`

, then
the flatten operation outputs the data in its row-major representation. For example,
consider the input:

A = [ 1 2 3 4 5 6 7 8 9];

AFlat = [1 2 3 4 5 6 7 8 9];

Set this option when creating or importing models that require this representation.

`OutputSize`

— Size of output vectors

positive integer

This property is read-only.

Size of output vectors, specified as a positive integer.

**Data Types: **`single`

| `double`

| `int8`

| `int16`

| `int32`

| `int64`

| `uint8`

| `uint16`

| `uint32`

| `uint64`

`InputSize`

— Number of input channels

`"auto"`

(default) | positive integer

This property is read-only.

Number of input channels, specified as one of these values:

`"auto"`

— Automatically determine the number of input channels at training time.Positive integer — Configure the layer for the specified number of input channels.

`InputSize`

and the number of channels in the layer input data must match. For example, if the input is an RGB image, then`InputSize`

must be 3.

**Data Types: **`single`

| `double`

| `int8`

| `int16`

| `int32`

| `int64`

| `uint8`

| `uint16`

| `uint32`

| `uint64`

| `char`

| `string`

### Parameters and Initialization

`WeightsInitializer`

— Function to initialize weights

`"glorot"`

(default) | `"he"`

| `"narrow-normal"`

| `"zeros"`

| `"ones"`

| function handle

Function to initialize the weights, specified as one of these values:

`"glorot"`

— Initialize the weights with the Glorot initializer [1] [2] (also known as Xavier initializer). The Glorot initializer independently samples from a uniform distribution with zero mean and a variance of`2/(numIn + numOut)`

, where`numIn`

and`numOut`

are the values of the`InputSize`

and`OutputSize`

properties, respectively.`"he"`

– Initialize the weights with the He initializer [3]. The He initializer samples from a normal distribution with zero mean and a variance of`2/numIn`

, where`numIn`

is the value of the`InputSize`

property.`"narrow-normal"`

— Initialize the weights by independently sampling from a normal distribution with zero mean and a standard deviation of 0.01.`"zeros"`

— Initialize the weights with zeros.`"ones"`

— Initialize the weights with ones.Function handle — Initialize the weights with a custom function. If you specify a function handle, then the function must have the form

`weights = func(sz)`

, where`sz`

is the size of the weights.

The layer initializes the weights only when the `Weights`

property is empty.

**Data Types: **`char`

| `string`

| `function_handle`

`BiasInitializer`

— Function to initialize biases

`"zeros"`

(default) | `"narrow-normal"`

| `"ones"`

| function handle

Function to initialize the biases, specified as one of these values:

`"zeros"`

— Initialize the biases with zeros.`"ones"`

— Initialize the biases with ones.`"narrow-normal"`

— Initialize the biases by independently sampling from a normal distribution with a mean of zero and a standard deviation of 0.01.Function handle — Initialize the biases with a custom function. If you specify a function handle, then the function must have the form

`bias = func(sz)`

, where`sz`

is the size of the biases.

The layer initializes the biases only when the `Bias`

property is
empty.

**Data Types: **`char`

| `string`

| `function_handle`

`Weights`

— Learnable weights

`[]`

(default) | numeric array

Learnable weights.

If `PatchSize`

is a positive integer, then
`Weights`

is an `PatchSize`

-by-...-by-`PatchSize`

-by-`InputSize`

-by-`OutputSize`

numeric array
or `[]`

, where the number of dimensions of size
`PatchSize`

is the number of spatial dimensions of the
input.

If `PatchSize`

is a vector, then `Weights`

is an
`PatchSize(1)`

-by-...-by-`PatchSize(K)`

-by-`InputSize`

-by-`OutputSize`

numeric array
or `[]`

, where `K`

is the number of spatial
dimensions of the input.

The layer weights are learnable parameters. You can specify the initial value of the weights
directly using the `Weights`

property of the layer. When
you train a network, if the `Weights`

property of the layer
is nonempty, then the `trainnet`

(Deep Learning Toolbox) and
`trainNetwork`

(Deep Learning Toolbox) functions use the `Weights`

property as the initial value. If the `Weights`

property is
empty, then the software uses the initializer specified by the `WeightsInitializer`

property of the layer.

**Data Types: **`single`

| `double`

`Bias`

— Layer biases

`[]`

(default) | column vector

Layer biases, specified as a numeric column vector of length
`OutputSize`

or `[]`

.

The layer biases are learnable parameters. When you train a neural network, if `Bias`

is nonempty, then the `trainnet`

(Deep Learning Toolbox) and `trainNetwork`

(Deep Learning Toolbox) functions use the `Bias`

property as the initial value. If `Bias`

is empty, then software uses the initializer specified by `BiasInitializer`

.

**Data Types: **`single`

| `double`

### Learning Rate and Regularization

`WeightLearnRateFactor`

— Learning rate factor for weights

`1`

(default) | nonnegative scalar

Learning rate factor for the weights, specified as a nonnegative scalar.

The software multiplies this factor by the global learning rate to determine the learning rate for the weights in this layer. For example, if `WeightLearnRateFactor`

is `2`

, then the learning rate for the weights in this layer is twice the current global learning rate. The software determines the global learning rate based on the settings you specify using the `trainingOptions`

(Deep Learning Toolbox) function.

**Data Types: **`single`

| `double`

| `int8`

| `int16`

| `int32`

| `int64`

| `uint8`

| `uint16`

| `uint32`

| `uint64`

`BiasLearnRateFactor`

— Learning rate factor for biases

`1`

(default) | nonnegative scalar

Learning rate factor for the biases, specified as a nonnegative scalar.

The software multiplies this factor by the global learning rate to determine the learning rate for the biases in this layer. For example, if `BiasLearnRateFactor`

is `2`

, then the learning rate for the biases in the layer is twice the current global learning rate. The software determines the global learning rate based on the settings you specify using the `trainingOptions`

(Deep Learning Toolbox) function.

**Data Types: **`single`

| `double`

| `int8`

| `int16`

| `int32`

| `int64`

| `uint8`

| `uint16`

| `uint32`

| `uint64`

`WeightL2Factor`

— *L*_{2} regularization factor for
weights

1 (default) | nonnegative scalar

_{2}

*L _{2}* regularization factor for the weights,
specified as a nonnegative scalar.

The software multiplies this factor by the global *L _{2}* regularization factor to determine the

*L*regularization for the weights in this layer. For example, if

_{2}`WeightL2Factor`

is `2`

, then the *L*regularization for the weights in this layer is twice the global

_{2}*L*regularization factor. You can specify the global

_{2}*L*regularization factor using the

_{2}`trainingOptions`

(Deep Learning Toolbox) function.**Data Types: **`single`

| `double`

| `int8`

| `int16`

| `int32`

| `int64`

| `uint8`

| `uint16`

| `uint32`

| `uint64`

`BiasL2Factor`

— *L*_{2} regularization factor for biases

`0`

(default) | nonnegative scalar

_{2}

*L _{2}* regularization factor for the biases,
specified as a nonnegative scalar.

The software multiplies this factor by the global *L _{2}* regularization factor to determine the

*L*regularization for the biases in this layer. For example, if

_{2}`BiasL2Factor`

is `2`

, then the *L*regularization for the biases in this layer is twice the global

_{2}*L*regularization factor. The software determines the global

_{2}*L*regularization factor based on the settings you specify using the

_{2}`trainingOptions`

(Deep Learning Toolbox) function.**Data Types: **`single`

| `double`

| `int8`

| `int16`

| `int32`

| `int64`

| `uint8`

| `uint16`

| `uint32`

| `uint64`

### Layer

`Name`

— Layer name

`""`

(default) | character vector | string scalar

Layer name, specified as a character vector or a string scalar.
For `Layer`

array input, the `trainnet`

(Deep Learning Toolbox) and
`dlnetwork`

(Deep Learning Toolbox) functions automatically assign
names to layers with the name `""`

.

The `PatchEmbeddingLayer`

object stores this property as a character vector.

**Data Types: **`char`

| `string`

`NumInputs`

— Number of inputs

`1`

(default)

This property is read-only.

Number of inputs to the layer, returned as `1`

. This layer accepts a
single input only.

**Data Types: **`double`

`InputNames`

— Input names

`{'in'}`

(default)

This property is read-only.

Input names, returned as `{'in'}`

. This layer accepts a single input
only.

**Data Types: **`cell`

`NumOutputs`

— Number of outputs

`1`

(default)

This property is read-only.

Number of outputs from the layer, returned as `1`

. This layer has a
single output only.

**Data Types: **`double`

`OutputNames`

— Output names

`{'out'}`

(default)

This property is read-only.

Output names, returned as `{'out'}`

. This layer has a single output
only.

**Data Types: **`cell`

## Examples

### Create Patch Embedding Layer

Create a patch embedding layer that embeds patches of size 16 with an output size of 768.

patchSize = 16; embeddingOutputSize = 768; layer = patchEmbeddingLayer(patchSize,embeddingOutputSize)

layer = PatchEmbeddingLayer with properties: Name: '' PatchSize: 16 InputSize: 'auto' OutputSize: 768 SpatialFlattenMode: 'column-major' WeightsInitializer: 'glorot' BiasInitializer: 'zeros' WeightLearnRateFactor: 1 BiasLearnRateFactor: 1 WeightL2Factor: 1 BiasL2Factor: 1 Learnable Parameters Weights: [] Bias: [] State Parameters No properties. Use properties method to see a list of all properties.

Create a `dlnetwork`

object.

net = dlnetwork;

Specify layers of the network, including a patch embedding layer.

inputSize = [384 384 3]; maxPosition = (inputSize(1)/patchSize)^2 + 1; numHeads = 4; numKeyChannels = 4*embeddingOutputSize; numClasses = 1000; layers = [ imageInputLayer(inputSize) patchEmbeddingLayer(patchSize,embeddingOutputSize,Name="patch-emb") embeddingConcatenationLayer(Name="emb-cat") positionEmbeddingLayer(embeddingOutputSize,maxPosition,Name="pos-emb"); additionLayer(2,Name="add") selfAttentionLayer(numHeads,numKeyChannels,AttentionMask="causal") indexing1dLayer(Name="idx-first") fullyConnectedLayer(numClasses) softmaxLayer]; net = addLayers(net,layers);

Connect the embedding concatenation layer with the "in2" input of the addition layer.

net = connectLayers(net,"emb-cat","add/in2");

View the neural network architecture.

plot(net)

## Algorithms

### Patch Embedding Layer

A patch embedding layer maps patches of pixels to vectors. You can use this layer in vision transformer neural networks to encode information about patches in images.

The layer uses a convolution operation with the layer weights and biases to extract and project patches from the input. In particular, the layer:

Splits the input into non-overlapping patches.

Flattens the patches.

Projects the flattened patches to the output size.

Flattens the spatial dimensions of the projected output.

### Layer Input and Output Formats

Layers in a layer array or layer graph pass data to subsequent layers as formatted `dlarray`

(Deep Learning Toolbox) objects.
The format of a `dlarray`

object is a string of characters, in which each
character describes the corresponding dimension of the data. The formats consist of one or
more of these characters:

`"S"`

— Spatial`"C"`

— Channel`"B"`

— Batch`"T"`

— Time`"U"`

— Unspecified

For example, 2-D image data that is represented as a 4-D array, where the first two dimensions
correspond to the spatial dimensions of the images, the third dimension corresponds to the
channels of the images, and the fourth dimension corresponds to the batch dimension, can be
described as having the format `"SSCB"`

(spatial, spatial, channel,
batch).

You can interact with these `dlarray`

objects in automatic differentiation
workflows, such as those for developing a custom layer, using a `functionLayer`

(Deep Learning Toolbox)
object, or using the `forward`

(Deep Learning Toolbox) and `predict`

(Deep Learning Toolbox) functions with
`dlnetwork`

objects.

This table shows the supported input formats of `PatchEmbeddingLayer`

objects and the
corresponding output format. If the software passes the output of the layer to a custom
layer that does not inherit from the `nnet.layer.Formattable`

class, or a
`FunctionLayer`

object with the `Formattable`

property
set to `0`

(`false`

), then the layer receives an
unformatted `dlarray`

object with dimensions ordered according to the formats
in this table. The formats listed here are only a subset. The layer may support additional
formats such as formats with additional `"S"`

(spatial) or
`"U"`

(unspecified) dimensions.

Input Format | Output Format |
---|---|

`"SCB"` (spatial, channel, batch) | `"SCB"` (spatial, channel, batch) |

`"SSCB"` (spatial, spatial, channel, batch) | `"SCB"` (spatial, channel, batch) |

`"SSSCB"` (spatial, spatial, spatial, channel,
batch) | `"SCB"` (spatial, channel, batch) |

`"SCBT"` (spatial, channel, batch, time) | `"SCBT"` (spatial, channel, batch, time) |

`"SSCBT"` (spatial, spatial, channel, batch, time) | `"SCBT"` (spatial, channel, batch, time) |

`"SSSCBT"` (spatial, spatial, spatial, channel, batch,
time) | `"SCBT"` (spatial, channel, batch, time) |

`"SC"` (spatial, channel) | `"SC"` (spatial, channel) |

`"SSC"` (spatial, spatial, channel) | `"SC"` (spatial, channel) |

`"SSSC"` (spatial, spatial, spatial, channel) | `"SC"` (spatial, channel) |

In `dlnetwork`

objects, `PatchEmbeddingLayer`

objects also support
these input and output format combinations.

Input Format | Output Format |
---|---|

`"SCT"` (spatial, channel, time) | `"SCT"` (spatial, channel, time) |

`"SSCT"` (spatial, spatial, channel, time) | `"SCT"` (spatial, channel, time) |

`"SSSCT"` (spatial, spatial, spatial, channel, time) | `"SCT"` (spatial, channel, time) |

## References

[1] Dosovitskiy, Alexey, Lucas Beyer, Alexander Kolesnikov, Dirk Weissenborn, Xiaohua Zhai, Thomas Unterthiner, Mostafa Dehghani et al. "An Image is Worth 16x16 words: Transformers for Image Recognition at Scale." Preprint, submitted June 3, 2021. https://doi.org/10.48550/arXiv.2010.11929.

[2] Glorot,
Xavier, and Yoshua Bengio. "Understanding the Difficulty of Training Deep Feedforward Neural
Networks." In *Proceedings of the Thirteenth International Conference on Artificial
Intelligence and Statistics*, 249–356. Sardinia, Italy: AISTATS, 2010. https://proceedings.mlr.press/v9/glorot10a/glorot10a.pdf

[3] He, Kaiming,
Xiangyu Zhang, Shaoqing Ren, and Jian Sun. "Delving Deep into Rectifiers: Surpassing Human-Level
Performance on ImageNet Classification." In *2015 IEEE International Conference on
Computer Vision (ICCV)*, 1026–34. Santiago, Chile: IEEE, 2015. https://doi.org/10.1109/ICCV.2015.123

## Extended Capabilities

### C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

Code generation supports only 1-D and 2-D spatial data. 3-D spatial or more than 3-D spatial data format such as "SSS" or "SSSS" is not supported.

You can generate generic C/C++ code that does not depend on third-party libraries and deploy the generated code to hardware platforms.

### GPU Code Generation

Generate CUDA® code for NVIDIA® GPUs using GPU Coder™.

Usage notes and limitations:

Code generation supports only 1-D and 2-D spatial data. 3-D spatial or more than 3-D spatial data format such as "SSS" or "SSSS" is not supported.

You can generate CUDA code that is independent of deep learning libraries and deploy the generated code to platforms that use NVIDIA

^{®}or ARM^{®}GPU processors.

## Version History

**Introduced in R2023b**

### R2024a: Specify spatial flattening mode of patch embedding layers

Specify the mode for flattening output of the convolution operation using the `SpatialFlattenMode`

option. Set this option when creating or importing models
that require this representation.

## See Also

`visionTransformer`

| `selfAttentionLayer`

(Deep Learning Toolbox) | `embeddingConcatenationLayer`

(Deep Learning Toolbox) | `indexing1dLayer`

(Deep Learning Toolbox) | `trainnet`

(Deep Learning Toolbox) | `trainingOptions`

(Deep Learning Toolbox) | `dlnetwork`

(Deep Learning Toolbox)

### Topics

- Train Vision Transformer Network for Image Classification
- Deep Learning in MATLAB (Deep Learning Toolbox)
- List of Deep Learning Layers (Deep Learning Toolbox)
- Deep Learning Tips and Tricks (Deep Learning Toolbox)
- Data Sets for Deep Learning (Deep Learning Toolbox)

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