ProjectedLayer

Compressed neural network layer using projection

Since R2023b

Description

A projected layer is a compressed neural network layer resulting from projection.

Creation

To compress a neural network using projection, use the compressNetworkUsingProjection function. This feature requires the Deep Learning Toolbox™ Model Quantization Library support package. This support package is a free add-on that you can download using the Add-On Explorer. Alternatively, see Deep Learning Toolbox Model Quantization Library.

Properties

Projected

OriginalClass — Class of original layer

character vector

This property is read-only.

Class of the original layer, returned as a character vector.

Example: 'nnet.cnn.layer.LSTMLayer'

Data Types: char

LearnablesReduction — Proportion of learnables removed in layer

scalar in the interval [0,1]

This property is read-only.

Proportion of learnables removed in the layer, returned as a scalar in the interval [0,1].

Data Types: double

Network — Neural network that represents projection

dlnetwork object

Neural network that represents projection, returned as a dlnetwork object.

The neural network that represents the projection depends on the type of layer:

Layer	Network
convolution2dLayer	Network containing three convolution2dLayer objects
fullyConnectedLayer	Network containing two fullyConnectedLayer objects
lstmLayer	Network containing a single lstmProjectedLayer object
gruLayer	Network containing a single gruProjectedLayer object

To replace the ProjectedLayer objects in a neural network with the equivalent network that represents the projection, use the unpackProjectedLayers function.

InputSize — Number of input channels

positive integer

This property is read-only.

Number of input channels, returned as a positive integer.

Data Types: double

OutputSize — Number of output channels

positive integer

This property is read-only.

Number of output channels, returned as a positive integer.

Data Types: double

InputProjectorSize — Number of columns of input projector

positive integer

This property is read-only.

Number of columns of the input projector, returned as a positive integer.

The input projector is the matrix Q used to project the layer input. For more information, see Projected Layer.

Data Types: double

OutputProjectorSize — Number of columns of output projector

positive integer

This property is read-only.

Number of columns of the output projector, returned as a positive integer.

The output projector is the matrix Q used to project the layer output. For more information, see Projected Layer.

Data Types: double

Layer

Name — Layer name

character vector | string scalar

Layer name, specified as a character vector or a string scalar. For Layer array input, the trainnet and dlnetwork functions automatically assign new unique names to layers that have the name "".

When you compress a neural network using the compressNetworkUsingProjection, the function replaces projectable layers with ProjectedLayer objects with the same name.

The ProjectedLayer object stores this property as a character vector.

Data Types: char | string

NumInputs — Number of inputs

positive integer

This property is read-only.

Number of inputs to the layer, returned as a positive integer.

Data Types: double

InputNames — Input names

cell array of character vectors

Input names, returned as a cell array of character vectors.

Data Types: cell

NumOutputs — Number of outputs

positive integer

This property is read-only.

Number of outputs from the layer, returned as a positive integer.

Data Types: double

OutputNames — Output names

cell array of character vectors

Output names, returned as a cell array of character vectors.

Data Types: cell

Examples

Compress Network Using Projection

Load the pretrained network in dlnetJapaneseVowels and the training data in JapaneseVowelsTrainData.

load dlnetJapaneseVowels
load JapaneseVowelsTrainData

Create a mini-batch queue containing the training data. To create a mini-batch queue from in-memory data, convert the sequences to an array datastore.

adsXTrain = arrayDatastore(XTrain,OutputType="same");

Create the minibatchqueue object.

• Specify a mini-batch size of 16.

• Preprocess the mini-batches using the preprocessMiniBatchPredictors function, listed in the Mini-Batch Predictors Preprocessing Function section of the example.

• Specify that the output data has format "CTB" (channel, time, batch).

mbq = minibatchqueue(adsXTrain, ...
    MiniBatchSize=16, ...
    MiniBatchFcn=@preprocessMiniBatchPredictors, ...
    MiniBatchFormat="CTB");

Compress the network.

[netProjected,info] = compressNetworkUsingProjection(net,mbq);

Compressed network has 83.4% fewer learnable parameters.
Projection compressed 2 layers: "lstm","fc"

View the network layers.

netProjected.Layers

ans = 
  4x1 Layer array with layers:

     1   'sequenceinput'   Sequence Input    Sequence input with 12 dimensions
     2   'lstm'            Projected Layer   Projected LSTM with 100 hidden units
     3   'fc'              Projected Layer   Projected fully connected layer with output size 9
     4   'softmax'         Softmax           softmax

View the projected LSTM layer. The LearnablesReduction property shows the proportion of learnables removed in the layer. The Network property contains the neural network that represents the projection.

netProjected.Layers(2)

ans = 
  ProjectedLayer with properties:

                   Name: 'lstm'
          OriginalClass: 'nnet.cnn.layer.LSTMLayer'
    LearnablesReduction: 0.8408
              InputSize: 12
             OutputSize: 100

   Hyperparameters
     InputProjectorSize: 8
    OutputProjectorSize: 7

   Learnable Parameters
                Network: [1x1 dlnetwork]

   Network Learnable Parameters
     Network/lstm/InputWeights      400x8 dlarray
     Network/lstm/RecurrentWeights  400x7 dlarray
     Network/lstm/Bias              400x1 dlarray
     Network/lstm/InputProjector    12x8  dlarray
     Network/lstm/OutputProjector   100x7 dlarray

   Network State Parameters
     Network/lstm/HiddenState  100x1 dlarray
     Network/lstm/CellState    100x1 dlarray

Use properties method to see a list of all properties.

Mini-Batch Predictors Preprocessing Function

The preprocessMiniBatchPredictors function preprocesses a mini-batch of predictors by extracting the sequence data from the input cell array and truncating them along the second dimension so that they have the same length.

Note: Do not pad sequence data when doing the PCA step for projection as this can negatively impact the analysis. Instead, truncate mini-batches of data to have the same length or use mini-batches of size 1.

function X = preprocessMiniBatchPredictors(dataX)

X = padsequences(dataX,2,Length="shortest");

end

Unpack Projected Layers

Load the pretrained network in dlnetProjectedJapaneseVowels.

load dlnetProjectedJapaneseVowels

View the network properties.

net

net = 
  dlnetwork with properties:

         Layers: [4x1 nnet.cnn.layer.Layer]
    Connections: [3x2 table]
     Learnables: [9x3 table]
          State: [2x3 table]
     InputNames: {'sequenceinput'}
    OutputNames: {'softmax'}
    Initialized: 1

  View summary with summary.

View the network layers. The network has two projected layers.

net.Layers

ans = 
  4x1 Layer array with layers:

     1   'sequenceinput'   Sequence Input    Sequence input with 12 dimensions
     2   'lstm'            Projected Layer   Projected LSTM with 100 hidden units
     3   'fc'              Projected Layer   Projected fully connected layer with output size 9
     4   'softmax'         Softmax           softmax

Unpack the projected layers.

netUnpacked = unpackProjectedLayers(net)

netUnpacked = 
  dlnetwork with properties:

         Layers: [5x1 nnet.cnn.layer.Layer]
    Connections: [4x2 table]
     Learnables: [9x3 table]
          State: [2x3 table]
     InputNames: {'sequenceinput'}
    OutputNames: {'softmax'}
    Initialized: 1

  View summary with summary.

View the unpacked network layers. The unpacked network has a projected LSTM layer and two fully connected layers in place of the projected layers.

netUnpacked.Layers

ans = 
  5x1 Layer array with layers:

     1   'sequenceinput'   Sequence Input    Sequence input with 12 dimensions
     2   'lstm'            Projected LSTM    Projected LSTM layer with 100 hidden units, an output projector size of 7, and an input projector size of 8
     3   'fc_proj_in'      Fully Connected   4 fully connected layer
     4   'fc_proj_out'     Fully Connected   9 fully connected layer
     5   'softmax'         Softmax           softmax

Tips

• Code generation does not support ProjectedLayer objects. To replace ProjectedLayer objects in a neural network with the equivalent neural network that represents the projection, use the unpackProjectedLayers function or set the UnpackProjectedLayers option of the compressNetworkUsingProjection function to 1 (true).

Algorithms

Projected Layer

To compress a deep learning network, you can use projected layers. A projected layer is a type of deep learning layer that enables compression by reducing the number of stored learnable parameters. The layer introduces learnable projector matrices Q, replaces multiplications of the form $$Wx$$, where W is a learnable matrix, with the multiplication $$WQ{Q}^{\top }x$$, and stores Q and $$W\prime =WQ$$ instead of storing W. Projecting x into a lower dimensional space using Q typically requires less memory to store the learnable parameters and can have similarly strong prediction accuracy.

For some types of layers, you can represent a projected layer as a neural network containing two or more layers with fewer learnable parameters. For example, you can represent a projected convolution layer as three convolution layers that perform the input projection, convolution, and the output projection operations independently. When you compress a network using the compressNetworkUsingProjection function, the software replaces layers that support projection with ProjectedLayer objects that contain the equivalent neural network. To replace ProjectedLayer objects in a neural network with the equivalent neural network that represents the projection, use the unpackProjectedLayers function or set the UnpackProjectedLayers option of the compressNetworkUsingProjection function to 1 (true).

The compressNetworkUsingProjection function supports projecting these layers:

• convolution2dLayer

• fullyConnectedLayer

• lstmLayer

• gruLayer

The compressNetworkUsingProjection function replaces projectable layers with ProjectedLayer objects. A ProjectedLayer object contains information about the projection operation and contains the neural network that represents the projection.

The neural network that represents the projection depends on the type of layer:

Layer	Network
convolution2dLayer	Network containing three convolution2dLayer objects
fullyConnectedLayer	Network containing two fullyConnectedLayer objects
lstmLayer	Network containing a single lstmProjectedLayer object
gruLayer	Network containing a single gruProjectedLayer object

Layer Input and Output Formats

Layers in a layer array or layer graph pass data to subsequent layers as formatted dlarray 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 object, or using the forward and predict functions with dlnetwork objects.

To learn more about the supported input and output formats of a ProjectedLayer object, see the documentation for the layer given by the OriginalClass property.

References

[1] "Compressing Neural Networks Using Network Projection." Accessed July 20, 2023. https://www.mathworks.com/company/newsletters/articles/compressing-neural-networks-using-network-projection.html.

Version History

Introduced in R2023b